JP4923243B2 - Magnetic resonance imaging apparatus, magnetic resonance imaging method, arithmetic processing program, and information recording medium recording the same - Google Patents

Description

  The present invention relates to a technical field of an imaging apparatus using magnetic resonance imaging (MRI).

  2. Description of the Related Art In recent years, imaging apparatuses using magnetic resonance imaging (MRI) (hereinafter referred to as “MRI apparatuses”) have been known to capture images such as tomographic images of observation sites. This MRI apparatus detects a nuclear magnetic resonance signal generated from a subject by using, for example, a nuclear magnetic resonance (NMR) phenomenon of a proton, that is, a hydrogen nucleus, which is a main constituent material of the subject. In addition, position information is added to the detected nuclear magnetic resonance signal, and the intensity distribution of the signal is imaged.

  Specifically, in such an MRI apparatus, the subject is placed in an apparatus in which a static magnetic field is generated, and the strength of the static magnetic field is greater than the nuclear spins of the nuclei constituting the tissue in the subject. Precession is performed with the static magnetic field direction as the axis at a frequency (Larmor frequency) determined by. Further, this MRI apparatus is adapted to irradiate a subject with a high-frequency pulse having a frequency equal to the Larmor frequency to excite spins and make a transition to a high energy state. Then, after exciting the spin, this MRI apparatus stops the irradiation of the high frequency pulse, and electromagnetic waves emitted to the outside when each spin returns to a low energy state with a time constant corresponding to each state, This is detected by a high-frequency receiving coil tuned to this frequency, and when receiving by the receiving coil, position information in the space is used as frequency information by applying a gradient magnetic field in the triaxial direction to the static magnetic field space. To get.

  In particular, in such an MRI apparatus, in order to obtain position information, the level and timing of irradiation with various high-frequency pulses such as spin echo (SE) method or gradient echo (gradient echo (GRE)) method and application of a gradient magnetic field. In other words, pulse sequences are used, and linear gradient magnetic fields in which the magnetic field strength changes in proportion to the spatial coordinates along with these pulse sequences can be described by the Fourier transform formula of the spin density distribution function of the subject. An object is imaged by detecting a simple signal and performing an image reconstruction operation such as an inverse Fourier transform on the detected signal.

  On the other hand, there is also known an MRI apparatus that generates a characteristic magnetic field with a non-linear gradient in which the magnetic field strength changes nonlinearly in a static magnetic field space and performs image reconstruction calculation based on a nuclear magnetic resonance signal emitted from a subject. .

This MRI apparatus generates a characteristic magnetic field and spatially encodes the phase of local nuclear magnetization inside the subject in a nonlinear manner, and uses a magnetic field with a relatively weak magnetic field strength and a nonlinear gradient. Data for imaging the information on the entire region in the subject in a time-efficient manner can be acquired (see, for example, Patent Document 1).
Japanese Examined Patent Publication No. 2-63009

  However, in the various MRI apparatuses described above, various countermeasures are taken against artifacts (virtual images) caused by image processing, subject or RF (Radio Frequency) in a high-frequency pulse, while artifacts due to aliasing. That is, for the countermeasure against the folding artifact (Wrap-around Artifact) in which the part of the subject outside the imaging field of view (FOV: Field Of View) moves into the image of the subject imaged in the image processing, the imaging field of view is used. In addition to measures such as narrowing, there is no specific solution for solving the problem by post-processing.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a magnetic resonance imaging apparatus and the like that prevent artifacts due to aliasing in a post-processing operation.

  In order to solve the above-described problem, the invention according to claim 1 is configured such that a predetermined magnetic field is applied to the subject to generate magnetic resonance in atomic nuclei constituting the tissue of the subject, and the subject A magnetic resonance imaging apparatus for reconstructing an image inside a subject by spatially nonlinearly encoding a phase of an internal local nuclear magnetization and uniformly in the space where the subject is placed A magnetic field generating means for generating the predetermined magnetic field including at least a static magnetic field and a gradient magnetic field having a linear gradient, a high frequency pulse generating means for generating a high frequency pulse for generating magnetic resonance in the atomic nucleus of the atom, and the magnetic resonance. In order to modulate the phase in the spin of the nucleus into a quadratic function and encode the phase spatially nonlinearly, the magnetic field generating means and the high-frequency pulse generating means are A control means for controlling the operation in sequence, a receiving means for receiving a nuclear magnetic resonance signal emitted from the subject in accordance with the predetermined sequence and encoding it into predetermined data, and based on the encoded data Processing means for performing an image reconstruction operation for reconstructing an image inside the subject, and the processing means modulates the phase of the nucleus in a quadratic function form with respect to the encoded data. Fourier transform while performing phase modulation that modulates the phase in the spin of the nucleus based on a parameter composed of a value relating to the magnetic field strength to be adjusted, a constant specific to the nucleus and a value for determining the reconstructed image size In addition, the image reconstruction calculation is performed by performing inverse Fourier transform.

  With this configuration, in the invention described in claim 1, the phase of the spin of the nucleus is modulated in the form of a quadratic function in the received nuclear magnetic resonance signal, and together with the value related to the magnetic field strength used for the modulation, Based on a parameter composed of values for determining the configured image size, image reconstruction operation is performed by performing Fourier transform and inverse Fourier transform while performing phase modulation that modulates the phase of the spin of the nucleus. Therefore, the inside of the subject can be imaged with the size value set as the parameter.

  Therefore, the invention according to claim 1 is a case where the size of the subject is larger than the field of view (image size) of the reconstructed image due to the movement of the subject during imaging or the lack of imaging conditions. Since the scale of the reconstructed image can be adjusted to an arbitrary size according to the parameter, if the parameter is adjusted to make the subject size smaller than the reconstructed image size, the post-processing operation Can provide a reconstructed image free from aliasing artifacts.

  According to a second aspect of the present invention, in the magnetic resonance imaging apparatus of the first aspect, the magnetic field generating means generates a static magnetic field in a space where the subject is placed. A gradient magnetic field generation circuit for generating a gradient magnetic field in the space, and a non-linear gradient in which the magnetic field intensity changes nonlinearly in the space, and is used for diffusing the spin phases of the nuclei in the subject A characteristic magnetic field generation circuit that generates a characteristic magnetic field whose intensity changes in the form of a quadratic function, and a time when the processing means applies the characteristic magnetic field as a value related to the magnetic field intensity constituting the parameter Is used to perform the image reconstruction calculation on the encoded data.

  With this configuration, the invention according to claim 2 can receive a nuclear magnetic resonance signal in which the phase in the spin of the nucleus is modulated into a quadratic function by applying a characteristic magnetic field, and apply a characteristic magnetic field. Since the image reconstruction operation is performed by performing Fourier transform and inverse Fourier transform while performing phase modulation that modulates the phase in the spin of the nucleus using the time to do so, the size value set as the parameter The imaging of the inside of the subject can be performed.

  Therefore, the invention described in claim 2 is a case where the size of the subject is larger than the field of view (image size) of the reconstructed image due to movement during imaging of the subject or inadequate imaging conditions. The scale of the image reconstructed according to the parameters in the post-processing can be adjusted to an arbitrary size.

  According to a third aspect of the present invention, in the magnetic resonance imaging apparatus of the second aspect, the processing means performs a Fourier transform on the encoded data based on the phase modulation and the parameters. In addition, the inverse Fourier transform is performed on the Fourier-transformed data while giving a predetermined phase modulation and coefficient, and the inverse Fresnel transform is performed.

  With this configuration, in the invention described in claim 3, since the data encoded based on the received nuclear magnetic resonance signal has the same type as the Fresnel diffraction formula, the time for applying the characteristic magnetic field is unique to the nucleus. Based on a parameter composed of a constant and the reciprocal of the size value of the reconstructed image, if the inverse Fresnel transform is performed while performing phase modulation to modulate the phase in the spin of the nucleus, the parameter is set. The inside of the subject can be imaged by the size value.

  According to a fourth aspect of the present invention, there is provided the magnetic resonance imaging apparatus according to the second aspect, wherein the processing means determines the phase modulation and the image size for the encoded data. The image reconstruction operation is performed by performing Fourier transform based on the parameter using the inverse number and repeating the inverse Fourier transform while giving predetermined phase modulation and a coefficient to the Fourier transformed data. Have.

  With this configuration, when the Fourier transform is performed based on the parameter using the value for determining the image size as the reciprocal, the parameter according to the fourth aspect is obtained by repeating the Fourier transform and the inverse Fourier transform. The inside of the subject can be imaged with the size value set as.

  According to a fifth aspect of the present invention, in the magnetic resonance imaging apparatus according to the first aspect, the magnetic field generating means includes a static magnetic field generating circuit that generates a static magnetic field in a space where the subject is placed. A gradient magnetic field generating circuit for generating a gradient magnetic field in the space, and the high-frequency pulse generating means generates the high-frequency pulse for applying a second-order phase modulation to the gradient magnetic field, and the processing Means has a configuration in which the image reconstruction calculation is performed on the encoded data using the intensity of the gradient magnetic field as a value relating to the magnetic field intensity constituting the parameter.

  With this configuration, the invention according to claim 5 is capable of receiving a nuclear magnetic resonance signal in which the phase in the spin of the nucleus is modulated by a quadratic function by a high-frequency pulse and applying a characteristic magnetic field. The image reconstruction operation is performed by performing Fourier transform and inverse Fourier transform while performing phase modulation that modulates the phase in the spin of the nucleus using the time of the time, so the size value set as the parameter Imaging of the inside of the subject can be performed.

  Therefore, the invention according to claim 5 is the case where the size of the subject is larger than the field of view (image size) of the image reconstructed due to the movement during imaging of the subject or the lack of imaging conditions. The scale of the reconstructed image can be adjusted to an arbitrary size according to the parameters in the post-processing operation

  According to a sixth aspect of the present invention, in the magnetic resonance imaging apparatus according to the fifth aspect, the processing means is a value for determining the phase modulation and the image size for the encoded data. The image reconstruction operation is performed by performing Fourier transform based on the parameter using the inverse number and repeating the inverse Fourier transform while giving predetermined phase modulation and a coefficient to the Fourier transformed data. Have.

  With this configuration, in the invention described in claim 6, since the data encoded based on the received nuclear magnetic resonance signal has the same type as the Fresnel diffraction formula, the time for applying the characteristic magnetic field is unique to the nucleus. Based on a parameter composed of a constant and the reciprocal of the size value of the reconstructed image, if the inverse Fresnel transform is performed while performing phase modulation to modulate the phase in the spin of the nucleus, the parameter is set. The inside of the subject can be imaged by the size value.

  According to a seventh aspect of the present invention, in the magnetic resonance imaging apparatus according to the fifth aspect, the processing means sets values for determining the phase modulation and the image size for the encoded data. The image reconstruction operation is performed by performing Fourier transform based on the parameter used as the reciprocal and repeating the inverse Fourier transform while giving predetermined phase modulation and a coefficient to the Fourier transformed data. is doing.

  With this configuration, when the Fourier transform is performed based on the parameter using the value for determining the image size as the reciprocal, the invention according to claim 7 repeats the Fourier transform and the inverse Fourier transform, thereby performing the parameter conversion. The inside of the subject can be imaged with the size value set as.

  In the invention according to claim 8, a predetermined magnetic field is applied to the subject to cause magnetic resonance in atomic nuclei constituting the tissue of the subject, and local nuclear magnetization inside the subject. A magnetic resonance imaging method for reconstructing an image inside the subject by spatially nonlinearly encoding the phase of the subject, wherein a uniform static magnetic field and a linear gradient are generated in the space in which the subject is placed. A magnetic field generating step for generating the predetermined magnetic field including at least a gradient magnetic field, a high frequency pulse generating step for generating a high frequency pulse for generating magnetic resonance in the atomic nucleus of the atom, and a spin of the atomic nucleus by generating the magnetic resonance Control the operation of the static magnetic field, the gradient magnetic field, and the high-frequency pulse in a predetermined sequence in order to modulate the phase at a quadratic function and encode the phase spatially nonlinearly. A receiving step for receiving a nuclear magnetic resonance signal emitted from the subject in accordance with the predetermined sequence and encoding the signal into predetermined data, and the inside of the subject based on the encoded data And a processing step for performing an image reconstruction operation for reconstructing the image of the object. When reconstructing the image inside the subject, the phase of the nucleus is expressed as a quadratic function with respect to the encoded data. A phase modulation that modulates the phase in the spin of the nucleus based on a parameter composed of a value relating to the magnetic field intensity for modulation in a uniform manner, a constant specific to the nucleus and a value for determining a reconstructed image size The image reconstruction calculation is performed by executing Fourier transform and inverse Fourier transform.

  With this configuration, the invention according to claim 8 is such that the phase of the spin of the nucleus is modulated into a quadratic function in the received nuclear magnetic resonance signal, together with the value related to the magnetic field strength used for the modulation, Based on a parameter composed of values for determining the configured image size, image reconstruction operation is performed by performing Fourier transform and inverse Fourier transform while performing phase modulation that modulates the phase of the spin of the nucleus. Therefore, the inside of the subject can be imaged with the size value set as the parameter.

  Therefore, the invention according to claim 8 is the case where the size of the subject is larger than the field of view (image size) of the image reconstructed due to movement during imaging of the subject or lack of imaging conditions. Since the scale of the reconstructed image can be adjusted to an arbitrary size according to the parameter, if the parameter is adjusted to make the subject size smaller than the reconstructed image size, the post-processing operation Can provide a reconstructed image free from aliasing artifacts.

  In the invention according to claim 9 or 10, a predetermined magnetic field is applied to the subject to cause magnetic resonance in atomic nuclei constituting the tissue of the subject, A magnetic resonance imaging apparatus that reconstructs an image inside a subject by spatially nonlinearly encoding the phase of nuclear magnetization, and having a uniform static magnetic field and linearity in the space where the subject is placed A magnetic field generating means for generating the predetermined magnetic field including at least a gradient magnetic field having a gradient; a high-frequency pulse generating means for generating a high-frequency pulse for generating magnetic resonance in the atomic nucleus; and the atomic nucleus for generating the magnetic resonance. In order to modulate the phase of the spin in a quadratic function and encode the phase spatially nonlinearly, the magnetic field generating means and the high-frequency pulse generating means are arranged in a predetermined sequence. Control means for controlling the operation, and a computer receives a nuclear magnetic resonance signal emitted from the subject according to the predetermined sequence, encodes it into predetermined data, and reconstructs an image inside the subject In the magnetic resonance imaging apparatus that performs an image reconstruction operation, the computer receives the nuclear magnetic resonance signal emitted from the subject in accordance with the predetermined sequence, encodes it into predetermined data, and acquires it Calculating means for reconstructing an image inside the subject based on the encoded data, and output means for generating and outputting image data by performing the image reconstruction calculation; And the calculation means uses the encoded data when reconstructing the image inside the subject. Then, based on a parameter composed of a value related to the magnetic field intensity for modulating the phase of the nucleus into a quadratic function, a constant specific to the nucleus, and a value for determining a reconstructed image size, The image reconstruction calculation is performed by performing Fourier transform and inverse Fourier transform while performing phase modulation for modulating the phase in the spin.

  With this configuration, the invention according to claim 9 or 10 is such that the phase of the spin of the nucleus is modulated into a quadratic function in the received nuclear magnetic resonance signal, and a value specific to the nucleus along with a value related to the magnetic field strength used for the modulation. And image reconstruction by executing Fourier transform and inverse Fourier transform while performing phase modulation to modulate the phase of the spin of the nucleus based on a parameter composed of values for determining the image size to be reconstructed Since the calculation is performed, the inside of the subject can be imaged with the size value set as the parameter.

  Therefore, the invention according to claim 9 or 10 is a case where the size of the subject is larger than the field of view (image size) of the image reconstructed due to movement during imaging of the subject or inadequate imaging conditions. However, since the scale of the reconstructed image can be adjusted to an arbitrary size according to the parameter, if the parameter is adjusted to make the subject size smaller than the reconstructed image size, the ex post facto A reconstructed image free from artifacts due to aliasing can be provided by arithmetic processing.

  The present invention performs reconstruction according to the parameters even when the size of the subject is larger than the field of view (image size) of the image to be reconstructed due to movement during imaging of the subject or lack of imaging conditions. Since the scale of the generated image can be adjusted to an arbitrary size, if the parameter is adjusted to make the subject size smaller than the reconstructed image size, there will be no artifacts due to aliasing in the post-processing. A reconstructed image can be provided.

  Next, preferred embodiments of the present invention will be described with reference to the drawings. In addition, this invention includes the range which has the technical feature, and is not limited to drawing shown below.

  The embodiment described below is an embodiment when the present invention is applied to an MRI apparatus and a method used for the MRI apparatus.

[First Embodiment]
First, a first embodiment of the MRI apparatus according to the present application will be described with reference to FIGS.

  First, the schematic operation of the MRI apparatus of this embodiment will be described with reference to FIG. 1 and FIG. FIG. 1 is a block diagram showing the configuration of the MRI apparatus of this embodiment, and FIG. 2 is a diagram for explaining the effects of the MRI apparatus of this embodiment.

  As shown in FIG. 1, the MRI apparatus 100 according to the present embodiment generates a uniform static magnetic field in a predetermined space, and applies X to a subject placed in the predetermined space at a predetermined timing. A gradient magnetic field in the triaxial directions of the Y and Z axes and a magnetic field whose applied magnetic field intensity changes in a quadratic function (hereinafter referred to as “characteristic magnetic field”) are generated and superimposed on the static magnetic field. It has become.

  Further, the MRI apparatus 100 irradiates the subject 10 with a high-frequency magnetic pulse for causing magnetic resonance in the nucleus constituting the tissue of the subject 10 at a predetermined timing, and irradiates the subject 10 with the high-frequency magnetic pulse, Each echo signal emitted by the magnetic resonance of the nuclei constituting the tissue of the subject 10 is detected, a predetermined calculation process is performed on the detected echo signal, and a tomogram of a desired examination site in the subject 10 is detected. Image data representing an image is generated.

  The MRI apparatus 100 according to the present embodiment applies a high-frequency magnetic field to the subject 10 in a superimposed magnetic field in which a gradient magnetic field with a linear gradient in which the magnetic field strength changes linearly and a characteristic magnetic field are superimposed on a static magnetic field, and the high-frequency magnetic field An induced voltage is detected by capturing a nuclear magnetic resonance alternating magnetic field generated by energy absorption resonance with the nucleus in the subject 10 when applied.

  Further, the MRI apparatus 100 uses a detected value of the induced voltage to obtain a composite value of the phase of each magnetization of each part that is nonlinear with respect to the spatial coordinates, specifically, a square function. An echo signal having a proportional amplitude is acquired. In particular, the MRI apparatus 100 according to the present embodiment generates a characteristic magnetic field in synchronization with a linear gradient magnetic field in the phase encoding direction, and sequentially acquires echo signals each time a gradient magnetic field in the phase encoding direction is applied. It is like that.

  The MRI apparatus 100 according to the present embodiment applies time τ during which a characteristic magnetic field is applied to data (hereinafter referred to as “measurement data”) configured by each acquired echo signal, a constant specific to the nucleus (nucleus). Based on a parameter (hereinafter referred to as “imaging parameter”) consisting of a coefficient (magnet rotation ratio) γ and a coefficient for determining a reconstructed image size (hereinafter simply referred to as “image size coefficient”) α In order to generate image data indicating a tomographic image (two-dimensional image) of a desired examination site in the subject 10 by performing inverse Fresnel transformation while performing phase modulation for modulating the phase in the spin of each atomic nucleus The image reconstruction calculation is performed.

  That is, the MRI apparatus 100 according to the present embodiment sets the parameters as measurement parameters by performing inverse Fresnel transformation based on the imaging parameters on the measurement data composed of the echo signals acquired in the superimposed magnetic field as described above. Imaging of a desired examination site in the subject 10 can be performed with the image size coefficient α.

  For example, in a method for reconstructing an image by performing inverse Fourier transform on measurement data acquired by a conventional method without applying a characteristic magnetic field (hereinafter referred to as “Fourier transform imaging method”), As shown in FIG. 2A, when an alias occurs in the reconstructed image, the alias cannot be removed afterwards by arithmetic processing.

  In addition, a method for reconstructing an image by performing inverse Fourier transform while performing phase modulation on the measurement data acquired as described above (hereinafter referred to as “inverse Fourier transform reconstruction method by phase diffusion Fourier transform imaging method”). ), The size of the subject 10 is larger than the field of view (image size) of the image reconstructed due to movement during imaging of the subject 10 or inadequate imaging conditions. In such a case, an alias occurs as shown in FIG.

  However, as shown in FIG. 2C, the MRI apparatus 100 according to the present embodiment is measurement data that is reconfigured due to movement of the subject 10 during imaging or imperfect imaging conditions, but aliases occur in the image. Even in such a case, since the scale of the reconstructed image can be adjusted to an arbitrary size, the imaging parameter, specifically, the image size coefficient is set so that the subject 10 size is smaller than the reconstructed image size. If α is adjusted, a reconstructed image free from artifacts due to aliasing can be provided by a post-processing operation.

  Each of the reconstructed images shown in FIGS. 2B and 2C is calculated based on the same measurement data by the inverse Fourier transform reconstruction method based on the phase diffusion Fourier transform image method and the method according to this embodiment. It is the processed image.

  Next, the configuration and operation of each part in the MRI apparatus 100 of this embodiment will be described with reference to FIG. 1 and FIG. FIG. 3 is a sequence diagram showing a pulse sequence of the present embodiment.

  The MRI apparatus 100 of this embodiment irradiates a subject 10 with a static magnetic field coil 20 that generates a uniform static magnetic field, a gradient magnetic field / characteristic magnetic field coil 30 that applies a gradient magnetic field and a characteristic magnetic field, and a high-frequency pulse. And a receiving coil 50 for detecting an echo signal, a highly stable DC power source 105 for driving the static magnetic field coil 20, and a gradient magnetic field / A gradient magnetic field power supply unit 110 that drives the characteristic magnetic field coil and a characteristic magnetic field generation circuit 115 that generates the characteristic magnetic field and drives the gradient magnetic field / characteristic magnetic field coil 30 are provided.

  The MRI apparatus 100 also includes a high-frequency oscillator 120 that generates a high-frequency signal, a pulse generator 125 that generates a high-frequency pulse based on the high-frequency signal from the high-frequency oscillator 120, and a high-frequency amplifier that amplifies the generated high-frequency pulse. 130, a receiving circuit 135 that receives an echo signal from the receiving coil 50, a phase detector 140 that detects the phase of the echo signal, and an analog / digital converter (hereinafter referred to as “digital / analog converter”) that digitizes the signal from the phase detector 140. , "A / D converter") 145.

  Further, the MRI apparatus 100 performs predetermined arithmetic processing on the detected echo signal, generates image data indicating a tomographic image of a desired examination site in the subject 10, and a signal processing control unit 150 that controls the entire apparatus. A sequencer 155 for giving various instructions necessary for obtaining a tomographic image of the subject 10 to each unit, and a display 160 for displaying the generated image data are provided.

  For example, the static magnetic field coil 20 and the highly stable DC power supply unit 105 of the present embodiment constitute the magnetic field generation means and the static magnetic field generation circuit of the present invention, and the gradient magnetic field / characteristic magnetic field coil 30 of the present embodiment The magnetic field generating means, the gradient magnetic field generating circuit, and the characteristic magnetic field generating circuit of the invention are configured. Further, for example, the gradient magnetic field power supply unit 110 of the present embodiment constitutes the magnetic field generation means and the gradient magnetic field generation circuit of the present invention, and the characteristic magnetic field generation circuit 115 includes the magnetic field generation means and the characteristic magnetic field generation circuit of the present invention. The pulse generator 125 and the irradiation coil 40 of the present embodiment constitute a high-frequency pulse generator. Further, for example, the sequencer 155 of the present embodiment constitutes the control means of the present invention, the reception coil 50 and the phase detector 140 constitute the reception means of the present invention, and the signal processing control unit 150 includes the present invention. The processing means is configured.

  The static magnetic field coil 20 is constituted by, for example, an electromagnet, an air-core coil magnet, a superconducting magnet, or a permanent magnet, and forms a uniform static magnetic field in a predetermined space where the subject 10 is placed. ing.

  The gradient magnetic field / characteristic magnetic field coil 30 is composed of, for example, a parallel wire, a rectangular coil, or a circular coil, and the magnetic field strength in the three-axis directions of X, Y, and Z generated by the gradient magnetic field power supply unit 110 is linear. For each gradient magnetic field Gx, Gy, Gz having a varying linear gradient and a characteristic magnetic field whose magnetic field strength varies spatially in a quadratic function, for example, phase encoding direction (y direction) and reading direction (x direction) Thus, a characteristic magnetic field having the following (Equation 3) is applied in a predetermined space.

  The irradiation coil 40 is disposed in the vicinity of the subject 10. The irradiation coil 40 receives a high-frequency pulse amplified to a predetermined signal level. The irradiation coil 40 receives one or a plurality of generated high-frequency pulses from the input high-frequency pulse. To the subject 10. For example, the irradiation coil 40 applies a 90-degree pulse, a 180-degree pulse, or a pulse at an arbitrary angle to the subject 10 as a high-frequency pulse.

  In the high-frequency pulse irradiated to the subject 10, if the frequency of the high-frequency magnetic field matches the nuclear magnetic resonance frequency of the nucleus in the subject 10, resonance absorption of the applied high-frequency magnetic field energy occurs. A nuclear magnetic resonance alternating magnetic field (magnetic resonance signal) is captured by the receiving coil 50 to detect a dielectric voltage.

  The receiving coil 50 is disposed in the vicinity of the subject 10. The receiving coil 50 is adapted to detect an electromagnetic wave emitted from the irradiation coil 40 and emitted by magnetic resonance of atomic nuclei constituting the tissue of the subject 10, that is, an echo signal (magnetic resonance signal). . In particular, the receiving coil 50 of the present embodiment has a Larmor frequency determined by the gradient magnetic field on which the subject 10 is mounted after the disappearance of the pulsed high-frequency magnetic field when a high-frequency pulse is applied. An echo signal generated by the nuclear spin excited by the specimen 10 and attenuated in time is detected, and the detected echo signal is output to the receiving circuit 135.

  The highly stable DC power supply unit 105 is connected to the sequencer 155 and drives the static magnetic field coil 20 in accordance with an instruction from the sequencer 155 to form a uniform static magnetic field in a predetermined space as described above. Yes.

  The gradient magnetic field power supply unit 110 is connected to the sequencer 155, and drives the gradient magnetic field / characteristic magnetic field coil 30 based on an instruction from the sequencer 155. In particular, the gradient magnetic field power supply unit 110 of the present embodiment generates gradient magnetic fields Gx, Gy, and Gz in three axial directions, and controls the gradient magnetic field / characteristic magnetic field coil 30 so that the gradient magnetic fields Gx, Gy, and Gz are predetermined. It is designed to be applied in the space.

  The characteristic magnetic field generation circuit 115 is connected to the sequencer 155 and generates a characteristic magnetic field for a predetermined time τ in accordance with an instruction from the sequencer 155. Further, the characteristic magnetic field generation circuit 115 drives the gradient magnetic field / characteristic magnetic field coil 30 and applies the generated characteristic magnetic field to the subject 10 via the gradient magnetic field / characteristic magnetic field coil 30.

  The high frequency oscillator 120 oscillates a high frequency signal at a frequency equal to the Larmor frequency corresponding to the magnetic field strength of the gradient magnetic field on which the subject 10 is placed, and outputs the oscillated high frequency signal to the pulse generation unit 125. Yes.

  A high-frequency signal oscillated by the high-frequency oscillator 120 is input to the pulse generation unit 125. The pulse generation unit 125 is based on the input high-frequency signal under an instruction from the sequencer 155. A high-frequency pulse having a high-frequency magnetic field having a high-frequency magnetic field equal to the Larmor frequency corresponding to the magnetic field strength of the gradient magnetic field placed inside the subject 10 and having a predetermined frequency spectrum is generated. , And output to the high-frequency amplifier 130.

  A high-frequency pulse is input to the high-frequency amplifier 130, and this high-frequency amplifier circuit amplifies the signal level of the input high-frequency pulse to a predetermined signal level, and applies it to the irradiation coil 40. It is designed to output.

  An echo signal detected by the reception coil 50 is input to the reception circuit 135, and the reception circuit 135 amplifies the input echo signal to a predetermined signal level, and the phase detector 140. To output.

  The echo signal output from the receiving circuit 135 is input to the phase detector 140. The phase detector 140 is connected to the sequencer 155, detects the phase of the echo signal in accordance with an instruction from the sequencer 155, and outputs the detected echo signal to the A / D converter 145. .

  The detected echo signal is input to the A / D converter 145, and the A / D converter 145 converts the input echo signal into a digital quantity and converts it into a signal processing control unit 150. To output.

  The signal processing control unit 150 performs a variety of arithmetic processing such as inverse Fresnel transformation using the detected and digitized echo signal as measurement data, and generates a reconstructed image indicating a tomographic image of the examination site of the subject 10. An arithmetic processing unit 151 that generates image data to be displayed and a system control unit 153 that controls the entire MRI apparatus 100 are connected to each unit via a bus B.

  Every time a characteristic magnetic field is applied to the arithmetic processing unit 151, a digitized phase signal is input. The arithmetic processing unit 151 sequentially acquires each input phase signal to generate measurement data, and performs arithmetic processing such as inverse Fresnel transformation on the measurement data to output an image to be output to the display 160. Data is generated, and the generated image data is output to the display 160. Details of the arithmetic processing in the arithmetic processing unit 151 of the present embodiment will be described later.

  The display 160 is configured by, for example, a liquid crystal element, an EL (Electro Luminescence) element, or a CRT (Cathode Ray Tube), and displays a predetermined image based on input image data.

  The system control unit 153 is connected to each unit and includes, for example, a CPU, a ROM, a RAM, and a hard disk, and controls each unit of the MRI apparatus 100. Specifically, various control information for controlling each part of the MRI apparatus 100 is recorded in the ROM, and various programs such as a control program and an OS (Operating System) are recorded in the hard disk. The CPU executes various processes by executing a program recorded on the hard disk, and the RAM is used as a work area.

  The system control unit 153 is further provided with input means such as a keyboard or a switch (not shown) as means for instructing to temporarily stop or release the stop of the apparatus.

  The sequencer 155 is connected to the high stability DC power supply unit 105, the gradient magnetic field power supply unit 110, the characteristic magnetic field generation circuit 115, the high frequency oscillator 120, and the phase detector 140, and generates a magnetic field in each unit by a predetermined pulse sequence, or The echo signal is detected.

  Specifically, as shown in FIG. 3, the sequencer 155 of the present embodiment images a desired part of the subject 10 as a two-dimensional image (slice image) in a predetermined space where a uniform static magnetic field is generated. A sequence control is performed in which a 90-degree pulse, which is a high-frequency pulse, is simultaneously applied together with a gradient magnetic field Gz for reconstruction, and then a characteristic magnetic field is applied for a time τ.

  The sequencer 155 applies the gradient magnetic field Gy in the phase encoding direction (y direction) and the gradient magnetic field Gx in the reading direction (x direction) at the respective timings, and sends an echo signal for a predetermined time (after the echo time tx). For example, sequence control for detecting only 2tx) is performed. At this time, the sequencer 155 detects the phase of the detected echo signal.

  The sequencer 155 changes the number of phase encodes by generating a characteristic magnetic field and repeating this pulse sequence at a predetermined repetition time TR, that is, the magnitude of the encode gradient magnetic field Gy applied at the time ty. The sequence control to change is performed, and the arithmetic processing unit 151 is made to acquire the phase signal. Note that the arithmetic processing unit 151 of the present embodiment is configured to construct the above-described measurement data from the phase signal acquired in this way.

  As described above, the MRI apparatus 100 of the present embodiment applies a high-frequency pulse while applying a gradient magnetic field having a linear gradient in which the magnetic field strength changes linearly in a predetermined space where a uniform static magnetic field is generated. In this magnetic field, when a characteristic magnetic field whose magnetic field intensity changes on a quadratic function is applied to the subject 10 only for a certain time τ, the nuclear spin in the subject 10 in the absence of a high-frequency magnetic field is converted into a static magnetic field. By performing free differential motion at a Larmor frequency that is uniquely determined by the environment, the phase of the spin of each nucleus excited in the subject 10 according to the strength of the characteristic magnetic field for each location in the subject 10 Can be changed.

  That is, when each magnetic field as described above is generated in a uniform static magnetic field, information indicating the location in the subject 10 is in the form of phase information. An echo signal in the form of integrating the contribution can be acquired.

  In addition, when the MRI apparatus 100 sequentially detects the phase signal in the echo signal while generating the characteristic magnetic field, the magnetic field intensity of the characteristic magnetic field changes nonlinearly, so that the nuclear spin of each place in the subject 10 is changed. Since the contribution to the phase signal varies from place to place, the necessary number of phase signals are acquired, the above-described measurement data is configured, and a predetermined calculation is performed on the measurement data to form an image along with the relaxation time. At that time, information on the spin density as a reference can be separated and extracted for each place (part).

  Next, details of the arithmetic processing unit 151 in the MRI apparatus 100 of the present embodiment will be described with reference to FIG. FIG. 4 is a diagram for explaining the principle of the arithmetic processing of the present embodiment in the arithmetic processing of the arithmetic processing unit 151 in the MRI apparatus 100 of the present embodiment as compared with the conventional method.

The MRI apparatus 100 according to the present embodiment applies the gradient magnetic field Gz, the high-frequency pulse, the gradient magnetic field Gy in the phase encoding direction, and the gradient magnetic field Gx in the reading direction as described above when performing image reconstruction of a two-dimensional image. In addition, a characteristic magnetic field whose magnetic field intensity changes nonlinearly is applied to the subject 10 only for a predetermined time τ, and echo signals are sequentially detected while generating a characteristic magnetic field. When the MRI apparatus 100 ignores the attenuation of the signal due to relaxation, the measurement data v (shown in (Expression 4) from (Expression 1) to (Expression 3) by the detected signal in each echo signal detected sequentially. k _x , k _y ) can be acquired.

(Equation 1) shows measurement data acquired in the case where no characteristic magnetic field is applied, that is, in the Fourier transform imaging method. In (Equation 1), (k _x = γG _x t _x ) and (ky = ΓG _y t _y ), (Equation 2) is obtained. In this embodiment, for example, a quadratic function-like magnetic field satisfying (Equation 3) is applied as the characteristic magnetic field, and the gradient magnetic field Gy in the phase encoding direction (y direction) is as shown in FIG. The gradient magnetic field Gx in the reading direction (x direction) is applied for the time 3tx. However, (rho) shows a to-be-photographed function and (gamma) shows the intrinsic | native constant (nuclear magnetorotation ratio) of a nucleus.

  In addition, this (Formula 4) can be derived from the same form as the Fresnel diffraction formula by changing the formula and changing the variables as shown in (Formula 5) to (Formula 7). However, x ′ and y ′ in (Expression 7) are in a form in which variable conversion is performed according to (Expression 8) below.

However, the above (Formula 7) has a form in which the measurement data v (x ′, y ′) variable-converted by x ′ and y ′ is multiplied by a secondary phase modulation term. . Further, v _fr indicates the measurement data converted into the Fresnel conversion format.

As described above, in the present embodiment, the measurement data as described above can be acquired. For this reason, the arithmetic processing unit 151 of the present embodiment performs the above-described measurement data on the acquired measurement data based on the image size coefficient α that is set in advance or set by the operator's operation indicating the reconstructed image size. As described above, it is possible to perform inverse Fresnel transformation while adjusting the phase transformation in the spin of the nucleus and the variable transformation, and the reconstructed image ρ _α (x, y) showing the tomographic image of the examination site of the subject 10 is obtained. Image data to be displayed can be generated.

  Specifically, the arithmetic processing unit 151 of the present embodiment includes an image size coefficient α, a time τ for applying a characteristic magnetic field, a constant γ specific to a nucleus, and a coefficient b for applying a characteristic magnetic field. Parameters are configured, and based on the imaging parameters, the following inverse Fresnel transform is performed.

(1) First, the arithmetic processing unit 151 according to the present embodiment performs imaging while converting the measurement data v (k _x , k _y ) acquired as described above into measurement data v (x ′, y ′). Based on the parameter αγbτ, the phase modulation process and Fourier transform shown in (Equation 9) are executed. Note that F [...] Indicates a Fourier transform (the same applies to the following equations).

(2) Next, the arithmetic processing unit 151 applies phase modulation to the Fourier-transformed measurement data. In other words, the arithmetic processing unit 151 has a phase modulation term exp {−j (ω _x ² + ω _y ² / (4αγbτ))} in (Equation 11), that is, T which is an inverse phase term of S _{1 in} (Equation 10). Multiply by ₁ to perform phase modulation.

  More specifically, since the Fresnel transform equation shown in (Equation 7) is integral in convolution, the Fourier transform becomes (Equation 11), and the arithmetic processing unit 151 of this embodiment is ( The antiphase term corresponding to the secondary modulation term appearing in Equation 11) is multiplied by the Fourier transformed measurement data.

Note that the Fourier transform of exp {−jαγbτ (x ′ ² + y ′ ² )} is a value shown in (Expression 12). Further, in (Equation 11), coefficients and antiphase terms other than the second-order modulation term are multiplied after inverse Fourier transform, as will be described later. However, since it is a coefficient other than the secondary modulation term, an antiphase term, and a constant, it may be multiplied before the inverse Fourier transform.

(3) Next, the arithmetic processing unit 151 performs inverse Fourier transform on the measurement data v obtained by multiplying the phase of the measurement data v by the antiphase term in the secondary phase modulation term, and performs the above-described (expression) The remaining coefficient indicated by 11) and the antiphase term are multiplied as a predetermined coefficient to generate image data for displaying the reconstructed image ρ _α (x, y).

  That is, as shown in (Equation 13), the arithmetic processing unit 151 of the present embodiment performs Fourier transform on a function obtained by performing phase modulation on the measurement data v (x ′, y ′), and Since phase modulation is performed after Fourier transform and inverse Fourier transform is performed, a reconstructed image can be generated in the same space as the original measurement data v.

  In (Equation 13), since x and y are each multiplied by α, it can be seen that the reproduced image is scaled, that is, enlarged or reduced by α times. The derivation of (Equation 13) will be described later.

However, F < ^-1 > [...] shows an inverse Fourier transform (same in the following formula | equation), N shows the data number of the measurement data v. In this case, the resolution and field of view of the reconstructed image are expressed by (Equation 14) and (Equation 15).

  (4) Finally, the arithmetic processing unit 151 finally corrects the reconstructed image ρ (x, y) by multiplying the value of exp shown in (Equation 13) by an antiphase term or taking an absolute value. ) Value is calculated.

  As described above, the arithmetic processing unit 151 according to the present embodiment calculates the reconstructed image ρ (x, y) indicating the tomographic image of the examination region of the subject 10 by performing the arithmetic processing. Based on this, image data is generated. The arithmetic processing unit 151 can perform processing for scaling by the image size coefficient α, in other words, processing for reducing or enlarging the image size.

  That is, the arithmetic processing unit 151 according to the present embodiment performs reconstruction by performing inverse Fourier transform on the measurement data illustrated in FIG. 4A when performing arithmetic processing for generating a reconstructed image based on the measurement data. Compared to the case of the inverse Fourier transform reconstruction method in the phase diffusion Fourier transform imaging method for generating an image, as shown in FIG. 4B, the size of the reconstructed image ρ is freely changed by the image size coefficient α. By changing the size, the imaging field of view is expanded by (Equation 15), and the reconstructed image is within the range of the field of view. It is possible to provide a reconstructed image having no image.

FIG. 4 (a) shows an operation based on the measurement data v (k _x , k _y ) by the inverse Fourier transform reconstruction method in the phase diffusion Fourier transform imaging method (without variable conversion with respect to (Expression 4)). FIG. 4B shows an image reconstructed when the processing is performed, and FIG. 4B is based on the measurement data v (x ′, y ′) by the arithmetic processing unit 151 of the present embodiment (for Expression 7). An image reconstructed when an arithmetic process is performed (an image in which the image size is changed by the value of α) is shown.

  In addition, the arithmetic processing unit 151 of the present embodiment uses the value of the imaging parameter (for example, αγbτ) in the arithmetic processing as described above, but it is clear even if the imaging parameter is not a true value (1.0). Since an image can be reconstructed, a clear image can be reconstructed by always using the same α value in the course of calculation processing even if an imaging parameter is configured using an image size coefficient α. It has become.

That is, the measurement data v a _conventional method of reconstructing an image by simply performing an inverse Fourier transform shown in (Expression 16) (Fourier transform imaging method) or a signal of the phase diffusion Fourier transform method shown in (Expression 17) In the method of reconstructing an image by performing transformation (inverse Fourier transform reconstruction method using phase diffusion Fourier transform imaging method), aliasing artifacts occur when the size of the reconstructed image becomes larger than the field of view. However, it is extremely difficult to reproduce an image without alias afterwards, but the arithmetic processing unit 151 of the present embodiment sets the image size coefficient α to an appropriate value by performing the above arithmetic processing. By doing so, it is possible to generate an image of any size, and to generate an image that eliminates aliasing artifacts. Going on.

  The resolution and field of view in the inverse Fourier transform reconstruction method based on the Fourier transform imaging method and the phase diffusion Fourier transform imaging method are shown in (Equation 18) and (Equation 19).

Next, a description will be given derive (equation 13) when calculating the reconstructed image [rho _alpha generated by the arithmetic processing unit 151 by using the above equation (4).

A function obtained by multiplying (Equation 4) by αγbτ obtained by multiplying true γbτ by α as an imaging parameter and multiplying by an exponent term ext {−jαγbτ (x ′ ² + y ′ ² )} is an expression of (Equation 20).

When the shoulder C in the exponent term ext {−jαγbτ (x ′ ² + y ′ ² ) −jαγbτ (x ² + y ² ) in (Expression 20) is deformed, (Expression 21) is obtained, and (Expression 4) becomes (Expression 22). ).

  Here, when (Equation 22) is transformed into (Equation 23), and u and w are rewritten as x and y as shown in (Equation 24), (Equation 24) becomes the above-mentioned (Equation 13). Since the Fresnel transformation is shown, the (Equation 13) can be derived by performing the inverse Fresnel transformation. However, (Expression 25) is satisfied in (Expression 23).

  Also, unlike the above, (Equation 13) can be derived as follows.

  First, as shown in (Expression 26), the measurement data v (x ′, y ′) subjected to variable conversion is Fourier-transformed, and (Expression 26) is arranged as shown in (Expression 27).

Here, R (ω _x , ω _y )) means the Fourier transform of the reconstructed image ρ (x, y). Therefore, when the above (formula 5) is arranged, the form of the convolution integral shown in (formula 28) become.

  Further, since the phase term before the integral term of (Expression 28) is canceled by the imaging parameter αγbτ, (Expression 28) becomes a descriptive expression of convolution integral as shown in (Expression 29). Therefore, (Equation 13) can be derived from the convolution theorem and the scaling law of Fourier transform, as shown in (Equation 30).

  Next, the operation of the measurement data calculation process including the measurement data acquisition process in the MRI apparatus 100 of the present embodiment will be described with reference to FIG. FIG. 5 is a flowchart showing the operation of the measurement data calculation process including the measurement data acquisition process in the MRI apparatus 100 of the present embodiment.

  First, when the system control unit 153 detects an instruction to display a tomographic image (two-dimensional image) at a predetermined examination site in the subject 10 as a reconstructed image via an operation unit (not shown) (step S101). The system control unit 153 controls the sequencer 155 and other units to generate a static magnetic field, and after generating a characteristic magnetic field for a predetermined time according to a predetermined sequence, each gradient magnetic field and high-frequency pulse are detected by the subject. 10 and every time a phase encoding direction gradient magnetic field is applied, an echo signal is detected and its phase is detected, and the arithmetic processing unit 151 acquires measurement data (step S102).

  Next, the system control unit 153 causes the following arithmetic processing to be executed based on the preset image size coefficient α based on the measurement data acquired by the arithmetic processing unit 151.

First, the system control unit 153 causes the arithmetic processing unit 151 to phase-modulate the measurement data v (k _x , k _y ) based on the imaging parameter αγbτ, execute the Fourier transform (step S103), and the Fourier transform is performed. The measured data is multiplied by the secondary phase modulation term to perform phase modulation (step S104).

Next, the system control unit 153 performs an inverse Fourier transform on the signal generated in Step 104 (Step S105), and multiplies the signal generated in Step 104 by a predetermined coefficient and a predetermined inverse phase term to reconstruct the signal. An image ρ _α (x, y) is generated (step S106).

Finally, the system control unit 153 causes the arithmetic processing unit 151 to correct the reconstructed image ρ _α (x, y) and calculate the final value of the reconstructed image ρ (x, y) (step S107). ), The calculated final reconstructed image ρ (x, y) is output to the display 160 to display a two-dimensional image, that is, a tomographic image of the examination site in the subject 10 (step S108). End.

  As described above, when the MRI apparatus 100 according to the present embodiment performs the second-order phase modulation process on the data encoded based on the received nuclear magnetic resonance signal, it becomes the same type as the Fresnel diffraction type, and thus applies the characteristic magnetic field. For example, if the inverse Fresnel transformation is performed while performing phase modulation for modulating the phase in the spin of the nucleus based on the parameter composed of the time constant for the nucleus, the size constant of the reconstructed image, and the size factor of the reconstructed image The inside of the subject 10 can be imaged with the size value set as a parameter.

  Therefore, the MRI apparatus 100 of the present embodiment is a case where the size of the subject 10 is larger than the field of view (image size) of the reconstructed image due to movement during imaging of the subject 10 or inadequate imaging conditions. However, since the scale of the reconstructed image can be adjusted to an arbitrary size according to the image size coefficient α, if the parameters are adjusted so that the size of the subject 10 is smaller than the reconstructed image size. Further, it is possible to provide a reconstructed image free from artifacts due to aliasing by post-processing.

  Note that the MRI apparatus 100 according to the present embodiment may repeatedly perform image reconstruction while changing the image size with respect to a set of acquired measurement data to provide various images with high resolution. This makes it possible to provide an abnormality in the subject 10 as an image even when it cannot be found by only one image having no aliasing artifacts by the above-described processing.

  That is, as described above, the MRI apparatus 100 according to the present embodiment performs image reconstruction that removes aliasing artifacts based on measurement data. However, aliasing artifacts are generated by a conventional method such as an inverse Fourier transform method. This means that the image is reproduced with high resolution because the physical spacing of the pixels is small. By reconstructing, various images with high resolution may be provided.

  For example, the MRI apparatus 100 of the present embodiment uses measurement data obtained under imaging conditions in which aliasing artifacts occur when image reconstruction processing is performed by an inverse Fourier transform reconstruction method as shown in FIG. On the other hand, when the above calculation processing is performed by changing the image size to 0.9 times, 0.8 times, 0.7 times, 0.6 times, and 0.5 times, and the tomographic image is reconstructed, As shown in FIGS. 6B to 6E, the image size shown in FIG. 6B is 0 for a part of the image, that is, an image of a region where no aliasing artifact is generated in FIG. Compared to a tomographic image having a resolution of 5 times, a tomographic image having a high resolution can be provided. Thereby, the MRI apparatus 100 of this embodiment can raise the precision of the image diagnosis in medical treatment as what can discover the abnormality in the subject 10 which cannot be discovered by normal imaging.

  However, FIG. 6 is an example of an image when the image reconstruction is repeatedly performed while changing the image size with respect to the obtained set of measurement data, and FIG. 6A is an inverse Fourier transform reconstruction. FIG. 6B shows a tomographic image that has been arithmetically processed by the method, FIG. 6B shows a tomographic image that has been reconstructed by the arithmetic processing in this embodiment with an image size of 0.9 times, and FIG. It is a tomographic image reconstructed by the arithmetic processing in the present embodiment at a magnification of 0.8. FIG. 6D shows a tomographic image reconstructed by the arithmetic processing in the present embodiment with an image size of 0.7 times, and FIG. 6E shows the present embodiment with an image size of 0.6 times. FIG. 6C is a tomographic image reconstructed by the arithmetic processing in the present embodiment having an image size of 0.5 times. Further, in FIGS. 6B to 6E, when the image size is adjusted so as to reduce the area where the artifact is turned back, as shown in each figure, the resolution is reduced accordingly.

  On the other hand, the characteristic magnetic field generation unit of the present embodiment is merely configured to generate a quadratic function-like magnetic field. However, the magnetic field strength contours are cylindrical, bar-shaped characteristic magnetic fields, and star-shaped stars. Any change in magnetic field strength, such as a characteristic magnetic field, a spherical or elliptical characteristic magnetic field, and the like should only have a magnetic field strength component proportional to the square of the distance from the center position.

  Further, in the present embodiment, calculation processing for generating a reconstructed image is performed while acquiring measurement data. However, in order to generate a reconstructed image based on measurement data acquired in advance. You may make it perform the arithmetic processing of.

  Further, the MRI apparatus 100 of the present embodiment includes a computer and a recording medium, and stores a control program for executing the image reconstruction calculation process when the image reconstruction calculation process is executed. Each process similar to the above may be performed by reading.

[Second Embodiment]
Next, a second embodiment of the MRI apparatus according to the present application will be described with reference to FIG.

  In this embodiment, the resolution of the reconstructed image is enlarged or reduced by the image size coefficient α and the image size is adjusted (multiplied by α) (see (Equation 14)) instead of the resolution in the first embodiment. Is characterized by the fact that the image size is adjusted (multiplied by 1 / α) by enlarging or reducing the image by the reciprocal of the image size coefficient. Specifically, image reconstruction calculation is performed by repeating Fourier transform and inverse Fourier transform while performing phase modulation using the imaging parameter α = (cγbτ / (c−1)).

  In the MRI apparatus 100 of the present embodiment, since the configuration other than the arithmetic processing in the arithmetic processing unit 151 and the processing of each unit are the same as those in the first embodiment, the same members are denoted by the same reference numerals and the description thereof will be given. Is omitted.

  First, details of the arithmetic processing unit 151 of the present embodiment will be described.

  The arithmetic processing unit 151 of the present embodiment applies an image size coefficient α, a time τ for applying a characteristic magnetic field, a constant γ specific to a nucleus, and a characteristic magnetic field, which are set in advance or set by an operator's operation. An imaging parameter composed of the coefficient b is configured, and the imaging parameter is converted into a predetermined value, and the following Fourier transform and inverse Fourier transform are performed based on the variable-converted imaging parameter. It has become.

(1) First, similarly to the first embodiment, the arithmetic processing unit 151 of the present embodiment converts the acquired measurement data v (k _x , k _y ) into measurement data v (x ′, y ′). However, the Fourier transform shown in (Expression 31) is executed.

  (2) Next, in order to convert the imaging parameter γbτ into a predetermined value based on the image size coefficient, the arithmetic processing unit 151 multiplies the phase modulation term on the measurement data (Equation 31) subjected to Fourier transform, The inverse Fourier transform is performed by changing the coefficient of the shoulder of the exponent term. That is, as shown in (Expression 32), the arithmetic processing unit 151 multiplies the right side of (Expression 31) by a predetermined value U, and then performs inverse Fourier transform. Here, c is a coefficient for phase modulation (hereinafter referred to as “phase modulation coefficient”), and as will be described later, this phase modulation coefficient c includes image scale coefficient α and α = (c−1) / There is a relationship of c.

  That is, the arithmetic processing unit 151 according to the present embodiment converts the imaging parameter from (γbτ) to (cγbτ / (c-1)), and obtains measurement data of the Fresnel conversion formula obtained by converting the imaging parameter. ing.

(3) Next, the arithmetic processing unit 151 applies phase modulation to the measurement data in which the imaging parameters are converted, as in the first embodiment. In other words, the arithmetic processing unit 151 performs phase modulation by multiplying the antiphase term T ₂ in the secondary phase modulation term S ₂ shown in (Equation 34).

More specifically, since the Fresnel transformation equation shown in (Equation 32) can be modified as shown in (Equation 35), the arithmetic processing unit 151 of the present embodiment performs the second order appearing in (Equation 35). The antiphase term for the modulation term is multiplied by the Fourier transformed measurement data. Note that k ′ _x and k ′ _y in (Expression 35) satisfy (Expression 36).

(4) Next, the arithmetic processing unit 151 performs inverse Fourier transform on the measurement data v that has been phase-adjusted by multiplying the anti-phase term in the secondary phase modulation term by the above-described (formula 34) is multiplied as a predetermined coefficient to generate image data for displaying the reconstructed image ρ _c (x, y).

That is, as shown in (Expression 34), since the square brackets are in the form of inverse Fourier transform, the arithmetic processing unit 151 of the present embodiment multiplies T ₂ in (Expression 33), and then performs inverse Fourier transform. In order to perform conversion and further perform phase modulation, the antiphase term T ₂ of the coefficient shown in (Equation 37) is multiplied, so that the original measurement data v and A reconstructed image can be generated in the same space.

  In this (Equation 38), x and y are each multiplied by α = (c−1) / c, so that the reproduced image is scaled to α times, that is, enlarged or reduced as in the first embodiment. You can see that

However, in this case, the pixel width Δx _{f of the} image reconstructed by (Expression 38) by (Expression 14) and (Expression 35) can be expressed by (Expression 39).

  In the first embodiment, as described above, since the resolution of the image is multiplied by the image size coefficient (α) as shown in (Equation 14), the reconstructed reconstructed image is reduced (or enlarged). In this embodiment, since the resolution is (1 / (image size coefficient (?)) Times as shown in (Equation 39) in this embodiment, the reconstructed image is the first embodiment. On the contrary, it is designed to enlarge (or reduce).

  Next, the operation of the measurement data calculation process including the measurement data acquisition process in the MRI apparatus 100 of this embodiment will be described with reference to FIG. FIG. 7 is a flowchart showing the operation of the measurement data calculation process including the measurement data acquisition process in the MRI apparatus 100 of the present embodiment.

  First, when the system control unit 153 detects an instruction for displaying a tomographic image (two-dimensional image) at a predetermined examination site in the subject 10 as a reconstructed image via the operation unit (step S201), the system The control unit 153 controls the sequencer 155 and other units to generate a static magnetic field, apply each gradient magnetic field and high-frequency pulse to the subject 10 according to a predetermined sequence, and gradient magnetic field in the phase encoding direction. Each time the signal is applied, the echo signal is detected to acquire the phase signal, and the arithmetic processing unit 151 acquires the measurement data (step S202).

  Next, the system control unit 153 causes the following arithmetic processing to be executed based on the preset image size coefficient α = (c−1) / c based on the measurement data acquired by the arithmetic processing unit 151.

First, the system control unit 153 converts the imaging parameter from γbτ to (cγbτ / (c−1)), and the measurement processing unit 151 sends the measurement data v (k _x , k _y ) to the measurement data v (x ', Y') while performing variable transformation on the basis of the transformed imaging parameter (cγbτ / (c-1)) (step S203), the Fourier-transformed measurement data is subjected to second order. The phase modulation term is multiplied to perform phase modulation (step S204).

  Next, the system control unit 153 performs an inverse Fourier transform on the operation processing unit 151 that has been subjected to phase adjustment by multiplying the measurement data v by a secondary phase modulation term (step S205).

  Next, the system control unit 153 causes the arithmetic processing unit 151 to perform phase modulation by multiplying the measurement data v subjected to inverse Fourier transform by a secondary phase modulation term (step S206).

Next, the system control unit 153 performs inverse Fourier transform on the arithmetic processing unit 151 obtained by multiplying the measurement data v by the second-order phase modulation term (step S207) and a predetermined coefficient. And a predetermined antiphase term are multiplied to generate a reconstructed image ρ _c (x, y) (step S208).

Finally, the system control unit 153 causes the arithmetic processing unit 151 to correct the reconstructed image ρ _c (x, y) and calculate the final value of the reconstructed image ρ (x, y) (step S209). ), The calculated final reconstructed image ρ (x, y) is output to the display 160 to display a two-dimensional image, that is, a tomographic image at a predetermined examination site of the subject 10 (step S210). This operation is terminated.

  As described above, the MRI apparatus 100 of the present embodiment is similar to the first embodiment in that the size of the subject 10 is based on the field of view (image size) reconstructed due to the movement of the subject 10 during imaging or the lack of imaging conditions. Since the scale of the reconstructed image can be adjusted to an arbitrary size according to the parameter even when the image becomes larger, the parameter is set so that the size of the subject 10 is smaller than the reconstructed image size. Is adjusted, it is possible to provide a reconstructed image free from artifacts due to aliasing by post-processing.

  As in the first embodiment, the MRI apparatus 100 according to the present embodiment repeatedly performs image reconstruction while changing the image size with respect to a set of acquired measurement data, and generates various high-resolution images. You may make it provide. This makes it possible to provide an abnormality in the subject 10 as an image even when it cannot be found by only one image having no aliasing artifacts by the above-described processing.

  In addition, the characteristic magnetic field generation unit of the present embodiment is merely configured to generate a quadratic function-like magnetic field. However, the magnetic field strength contours are cylindrical, rod-shaped characteristic magnetic fields, and star-shaped stars. Any change in magnetic field strength, such as a characteristic magnetic field, a spherical or elliptical characteristic magnetic field, and the like should only have a magnetic field strength component proportional to the square of the distance from the center position.

  Further, in the present embodiment, calculation processing for generating a reconstructed image is performed while acquiring measurement data. However, in order to generate a reconstructed image based on measurement data acquired in advance. You may make it perform the arithmetic processing of.

  Further, the MRI apparatus 100 of the present embodiment includes a computer and a recording medium, and stores a control program for executing the image reconstruction calculation process when the image reconstruction calculation process is executed. Each process similar to the above may be performed by reading.

[Third Embodiment]
Next, a third embodiment of the MRI apparatus according to the present application will be described with reference to FIGS.

  In the present embodiment, in the first embodiment, a characteristic magnetic field whose magnetic field intensity changes in a quadratic function is superimposed on the static magnetic field, and the phase in the spin of the nucleus in the subject is modulated in a quadratic function. Instead, it is characterized in that the phase in the spin of the nuclei in the subject is modulated into a quadratic function by generating a high-frequency pulse that applies second-order phase modulation to the gradient magnetic field.

  The MRI apparatus according to the present embodiment has other configurations, operations, and reconstructed image calculation processes except that a characteristic magnetic field is not applied and a high-frequency pulse that applies second-order phase modulation to a gradient magnetic field is generated. Since the calculation processing of the measurement data is the same as that of the first embodiment, the same number is assigned to the same member, and the description thereof is omitted.

  First, the schematic operation of the MRI apparatus of this embodiment will be described with reference to FIGS. 8 and 9. FIG. 8 is a block diagram showing a configuration of the MRI apparatus of the present embodiment, and FIG. 9 is an example of a high frequency pulse applied to the subject in the present embodiment.

  As shown in FIG. 8, the MRI apparatus 200 according to the present embodiment generates a uniform static magnetic field in a predetermined space, and applies X to a subject placed in the predetermined space at a predetermined timing. A gradient magnetic field in the three-axis directions of the Y and Z axes is generated.

  The MRI apparatus 200 irradiates the subject 10 with a high-frequency pulse that applies second-order phase modulation to the applied gradient magnetic field in accordance with a predetermined sequence, and the high-frequency magnetism irradiated from the irradiation coil 50. Each echo signal emitted by the magnetic resonance of the nuclei constituting the tissue of the subject 10 by the pulse is detected, a predetermined calculation process is performed on the detected echo signal, and a desired examination site in the subject 10 is detected. Image data indicating a tomographic image of the image is generated.

  In particular, the MRI apparatus 200 of the present embodiment applies a high-frequency pulse that satisfies (Equation 40) in the phase encoding direction (y direction) and the reading direction (x direction).

  Specifically, in the MRI apparatus 200 of the present embodiment, for example, when a high frequency pulse satisfying (Equation 40) called a chirp wave shown in FIG. The second-order phase modulation of (Equation 40) is given to the spin in the reading direction (x direction) at.

Here, t is the elapsed time, ω ₀ is the resonance frequency, u is a constant, and the vibration of the waveform is determined by ω ₀ t + ut ² . Further, a (t) is a function (function for forming a pulse envelope) for giving an outline to the chirp wave waveform, and A (x) is a Fourier transform function of a (t). It is. Moreover, (*) indicates a convolution integral.

Similarly, when a similar high-frequency pulse is applied under application of the gradient magnetic field Gy, second-order phase modulation can also be applied in the phase encoding direction (y direction).
Further, if the time for applying the high-frequency pulse is made longer, A (x) in (Equation 41) becomes a delta function, and the term of A (x) can be almost ignored. At this time, the MRI apparatus of the present embodiment can acquire the measurement data v shown in (Expression 42). However, (Formula 42) satisfies (Formula 43).

Here, if the gradient magnetic fields Gx and Gy are equal in intensity, and this is G (Gx = Gy), (Equation 44) is obtained, and the MRI apparatus 200 of the present embodiment has the same format as that of the first embodiment (Equation 14). Measurement data v, that is, measurement data v obtained by modulating the spin phase of the nuclei in the subject 10 into a quadratic function can be acquired. However, in (Equation 44), (Dγ ² G ² ) / u corresponds to γbτ in the imaging parameters of the first embodiment.

Therefore, as in the first embodiment, the MRI apparatus 200 according to the present embodiment is acquired based on an image size coefficient α that is set in advance or set by an operator's operation indicating the reconstructed image size. As described above, it is possible to perform inverse Fresnel transformation while adjusting variable transformation and phase modulation in the spin of the nucleus as described above, and a reconstructed image ρ showing a tomographic image of the examination site of the subject 10 Image data for displaying _α (x, y) can be generated.

  Next, the configuration and operation of each unit in the MRI apparatus 200 of the present embodiment will be described with reference to FIG.

  The MRI apparatus 200 of the present embodiment includes a static magnetic field coil 20, a gradient magnetic field coil 60 that applies a gradient magnetic field and a characteristic magnetic field, an irradiation coil 40, and a reception coil 50. In addition, a high-stable DC power supply unit 105 that drives the static magnetic field coil 20 and a gradient magnetic field power supply unit 110 that generates a gradient magnetic field and drives the gradient magnetic field coil 60 are provided.

  The MRI apparatus 200 includes a high-frequency oscillator 120 that generates a high-frequency signal, a pulse generation unit 225 that generates a high-frequency pulse based on the high-frequency signal from the high-frequency oscillator 120, and a high-frequency amplifier that amplifies the generated high-frequency pulse. 130, a receiving circuit 135, a phase detector 140, and an A / D converter 145.

  The MRI apparatus 200 further includes a signal processing control unit 150, a sequencer 155, and a display 160.

  For example, the static magnetic field coil 20 and the highly stable DC power supply unit 105 of the present embodiment constitute the magnetic field generation means and the static magnetic field generation circuit of the present invention, and the gradient magnetic field coil 60 and the gradient magnetic field power supply unit 110 of the present embodiment. Constitutes a magnetic field generating means and a gradient magnetic field generating circuit of the present invention. Further, for example, the pulse generation unit 225 and the irradiation coil 40 of the present embodiment constitute high frequency pulse generation means, and the sequencer 155 constitutes control means of the present invention. Further, for example, the receiving coil 50 and the phase detector 140 of the present embodiment constitute a receiving means of the present invention, and the signal processing control unit 150 constitutes a processing means of the present invention.

  The gradient magnetic field 60 is composed of, for example, parallel wires, rectangular coils, or circular coils, and a linear gradient in which the magnetic field strengths in the three-axis directions of X, Y, and Z generated by the gradient magnetic field power supply unit 110 change linearly. Each of the gradient magnetic fields Gx, Gy, Gz having the following is applied in a predetermined space.

  A high frequency signal oscillated by the high frequency oscillator 120 is input to the pulse generation unit 225, and the pulse generation unit 125 is based on the input high frequency signal under an instruction from the sequencer 155. A high-frequency pulse called a chapter wave described above, which has a high-frequency magnetic field equal to the Larmor frequency corresponding to the magnetic field strength of the gradient magnetic field placed in the subject 10 and a predetermined frequency spectrum, is generated. , And output to the high-frequency amplifier 130.

  As described above, the MRI apparatus 200 according to the present embodiment is similar to the Fresnel diffraction type when the second-order phase modulation processing is performed on the data encoded based on the received nuclear magnetic resonance signal, as in the first embodiment. Therefore, while applying phase modulation to modulate the phase in the spin of the nucleus based on the parameter configured from the time for applying the characteristic magnetic field, the nuclear specific constant and the size factor of the reconstructed image, If inverse Fresnel transformation is performed, the inside of the subject 10 can be imaged with the size value set as the parameter.

  Therefore, the MRI apparatus 200 of the present embodiment is a case where the size of the subject 10 is larger than the field of view (image size) of the image reconstructed due to movement during imaging of the subject 10 or inadequate imaging conditions. However, since the scale of the reconstructed image can be adjusted to an arbitrary size according to the image size coefficient α, if the parameters are adjusted so that the size of the subject 10 is smaller than the reconstructed image size. Further, it is possible to provide a reconstructed image free from artifacts due to aliasing by post-processing.

  In the present embodiment, the reconstructed image calculation process can be performed by the method of the second embodiment. That is, as described above, since the calculation can be performed on the basis of the measurement data v in the second embodiment, it can be performed by the method of the second embodiment.

In this embodiment, by applying a high-frequency pulse called a chapter wave to the gradient magnetic field, measurement data v obtained by modulating the spin phase of the nucleus in the subject 10 into a quadratic function is obtained. However, if various magnetic fields can be applied so that the measurement data v including (Equation 45) can be acquired as data for performing the reconstruction image calculation process, the first embodiment and the first embodiment can be performed using the image size coefficient α. The reconstructed image calculation process in the second embodiment can be applied. However, Q is a predetermined constant, including constants specific nuclear (nuclear gyromagnetic ratio), _{k x} and ky are the same manner as described above, .GAMMA.g _x t _x and .GAMMA.g _y t phase encoding direction, such as _y (y ) Is a function of the application time ty in the gradient magnetic field Gy in the direction), the application time tx in the gradient magnetic field Gx in the reading direction (x direction), and ρ.

  Further, the MRI apparatus 100 of the present embodiment includes a computer and a recording medium, and stores a control program for executing the image reconstruction calculation process when the image reconstruction calculation process is executed. Each process similar to the above may be performed by reading.

It is a block diagram which shows the structure of 1st Embodiment of the MRI apparatus which concerns on this application. It is a figure for demonstrating the effect in the MRI apparatus of 1st Embodiment. It is a sequence diagram which shows the pulse sequence of 1st Embodiment. It is a figure for demonstrating the principle of the arithmetic processing of 1st Embodiment in the arithmetic processing of the arithmetic processing part in the MRI apparatus of 1st Embodiment compared with the conventional method. It is a flowchart which shows the operation | movement of the calculation process of the said measurement data including the measurement data acquisition process in the MRI apparatus of 1st Embodiment. It is an example of an image when image reconstruction is repeatedly performed while changing the image size with respect to a set of acquired measurement data. It is a flowchart which shows the operation | movement of the calculation process of the said measurement data including the measurement data acquisition process in the MRI apparatus of 2nd Embodiment. It is a block diagram which shows the structure of 2nd Embodiment of the MRI apparatus which concerns on this application. It is a figure for demonstrating the effect in the MRI apparatus of 2nd Embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 ... Subject 20 ... Static magnetic field coil 30 ... Gradient magnetic field / characteristic magnetic field coil 40 ... Irradiation coil 50 ... Receiving coil 60 ... Gradient magnetic field coil 100 ... MRI apparatus 105 ... High stable DC power supply part 110 ... Gradient magnetic field power supply part 115 ... Feature Magnetic field generation circuit 120... High-frequency transmission circuit 125, 225... Pulse generation unit 130... High-frequency amplifier 135 ... Reception circuit 140 ... Phase detector 145 ... A / D converter 150 ... Signal processing control unit 151. Part 155 ... Sequencer 160 ... Display

Claims (7)

A predetermined magnetic field is applied to the subject to cause magnetic resonance in atomic nuclei constituting the subject's tissue, and the local nuclear magnetization phase inside the subject is spatially nonlinearly encoded to A magnetic resonance imaging apparatus for reconstructing an image inside a subject,
A magnetic field generating means for generating the predetermined magnetic field including at least a uniform static magnetic field and a gradient magnetic field having a linear gradient in a space in which the subject is placed;
High-frequency pulse generating means for generating a high-frequency pulse for causing magnetic resonance in the atomic nucleus;
In order to cause the magnetic resonance to modulate the phase of the spin of the nucleus into a quadratic function and to encode the phase spatially nonlinearly, the magnetic field generating means and the high-frequency pulse generating means are arranged in a predetermined sequence. Control means for controlling the operation,
Receiving means for receiving a nuclear magnetic resonance signal emitted from the subject according to the predetermined sequence, and encoding the signal into predetermined data;
Processing means for performing an image reconstruction operation for reconstructing an image inside the subject based on the encoded data;
With
Said processing means (1) relative to the previous SL encoded data, values for the magnetic field strength for modulating the phase of the nuclei in the quadratic function-shaped, the nuclei-specific constants and reconstructed image size Based on a parameter composed of values for determining the value , Fourier transform is performed while performing predetermined phase modulation, and (2) reverse while giving predetermined phase modulation and a coefficient to the Fourier-transformed data. A magnetic resonance imaging apparatus that performs the image reconstruction calculation by performing Fourier transformation and performing inverse Fresnel transformation . The magnetic resonance imaging apparatus of claim 1.
The magnetic field generating means is
A static magnetic field generation circuit for generating a static magnetic field in a space in which the subject is placed;
A gradient magnetic field generating circuit for generating a gradient magnetic field in the space;
A characteristic magnetic field that generates a characteristic magnetic field that is a non-linear gradient in which the magnetic field intensity changes non-linearly in the space and that changes in intensity in a quadratic function used to diffuse the spin phase of the nuclei in the subject. Generating circuit;
Have
The magnetism is characterized in that the processing means performs the image reconstruction operation on the encoded data using a time when the characteristic magnetic field is applied as a value related to the magnetic field intensity constituting the parameter. Resonance imaging device. The magnetic resonance imaging apparatus of claim 1.
The magnetic field generating means is
A static magnetic field generation circuit for generating a static magnetic field in a space where the subject is placed;
A gradient magnetic field generating circuit for generating a gradient magnetic field in the space;
Have
The high-frequency pulse generating means generates the high-frequency pulse that gives secondary phase modulation to the gradient magnetic field;
The magnetic resonance imaging apparatus characterized in that the processing means performs the image reconstruction calculation on the encoded data using the intensity of the gradient magnetic field as a value relating to the magnetic field intensity constituting the parameter. . The magnetic resonance imaging apparatus according to any one of claims 1 to 3 ,
The processing means performs the Fourier transform on the encoded data based on the parameter using the phase modulation and the value for determining the image size as an inverse, and the Fourier-transformed data A magnetic resonance imaging apparatus for performing the image reconstruction calculation by repeating the inverse Fourier transform.   A predetermined magnetic field is applied to the subject to cause magnetic resonance in atomic nuclei constituting the subject's tissue, and the local nuclear magnetization phase inside the subject is spatially nonlinearly encoded to A magnetic resonance imaging method for reconstructing an image inside a subject,
  A magnetic field generating step for generating the predetermined magnetic field including at least a uniform static magnetic field and a gradient magnetic field having a linear gradient in a space in which the subject is placed;
  A high-frequency pulse generating step for generating a high-frequency pulse for generating magnetic resonance in the atomic nucleus;
  In order to cause the magnetic resonance to modulate the phase of the spin of the nucleus into a quadratic function and to encode the phase spatially nonlinearly, the static magnetic field, the gradient magnetic field, and the high-frequency pulse are in a predetermined sequence. A control process for controlling the operation at
  Receiving a nuclear magnetic resonance signal emitted from the subject according to the predetermined sequence, and encoding it into predetermined data;
  A processing step of performing an image reconstruction operation for reconstructing an image inside the subject based on the encoded data;
  Including
  When reconstructing an image inside the object, (1) a value relating to a magnetic field intensity for modulating the phase of the nucleus into a quadratic function with respect to the encoded data, a constant specific to the nucleus And a Fourier transform is performed while performing a predetermined phase modulation based on a parameter composed of values for determining a reconstructed image size, and (2) a predetermined phase is applied to the Fourier-transformed data. A magnetic resonance imaging method comprising performing an inverse Fourier transform while giving a modulation and a coefficient, and performing an inverse Fresnel transform to perform the image reconstruction calculation.   A predetermined magnetic field is applied to the subject to cause magnetic resonance in atomic nuclei constituting the subject's tissue, and the local nuclear magnetization phase inside the subject is spatially nonlinearly encoded to A magnetic resonance imaging apparatus for reconstructing an image inside a subject, wherein the predetermined magnetic field including at least a uniform static magnetic field and a gradient magnetic field having a linear gradient is generated in a space in which the subject is placed A magnetic field generating means for generating, a high frequency pulse generating means for generating a high frequency pulse for generating a magnetic resonance in the atomic nucleus of the atom, a phase of the spin of the atomic nucleus is modulated in a quadratic function form by generating the magnetic resonance, and Control means for controlling the operation of the magnetic field generation means and the high-frequency pulse generation means in a predetermined sequence in order to encode the phase spatially nonlinearly. The magnetic resonance image which receives the nuclear magnetic resonance signal emitted from the subject according to the predetermined sequence by the data and encodes the data into predetermined data to reconstruct the image inside the subject. In the conversion device,
  The computer,
  Receiving means for receiving a nuclear magnetic resonance signal emitted from the subject according to the predetermined sequence, and encoding and acquiring the predetermined data;
  A calculation means for performing an image reconstruction calculation for reconstructing an image inside the subject based on the encoded data;
  Output means for generating and outputting image data by performing the image reconstruction calculation;
  And function as
  As the calculation means, when reconstructing an image inside the subject, (1) while performing phase modulation to modulate the phase of the spin of the nucleus with respect to the encoded data, Performing a Fourier transform based on a parameter composed of a value relating to a magnetic field intensity for modulating the phase into a quadratic function, a constant specific to the nucleus and a value for determining a reconstructed image size, and (2) An arithmetic processing program that performs inverse Fourier transform while giving predetermined phase modulation and a coefficient to Fourier transformed data, and performs the image reconstruction calculation by performing inverse Fresnel transform. An information storage medium readable by a computer, wherein the arithmetic processing program according to claim 6 is stored.