JP2016224837A - Information processing device and filter generation device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To implement high resolution processing of information obtained from objects.SOLUTION: An information processing device 1 comprises: first computation means 10 that subjects a frequency conversion of an imaging picture which is information that can be represented by a convolution integration of a blur function f(x) set based on a measurement and an original picture of a subject and is obtained from the subject on a memory, and obtains a spectrum F(ω) of the imaging picture; second computation means 20 that implements processing of inverting a code of the spectrum F(ω) of the imaging picture in a preliminarily selected frequency section in comparison of the blur function f(x) with an ideal function I(x); and third computation means 30 that calculates information in a real space restored by subjecting a spectrum F(ω) of the imaging picture having the processing implemented to an inverse frequency conversion as the original picture.SELECTED DRAWING: Figure 1

Description

  The present invention relates to an information processing apparatus and a filter generation apparatus, and more particularly to an information processing apparatus and a filter generation apparatus that perform processing for restoring an original image from a captured image.

  For example, the resolution of an image obtained by a medical X-ray imaging system is obtained from a cutoff frequency of a modulation transfer function (MTF) of the imaging system. As a measure for improving the MTF, for example, the pixel size of an X image detector, which is a recording medium for detecting and recording X-rays transmitted through a subject, can be reduced as much as possible. However, an image detector with a small pixel size is expensive. Further, if the pixel size of the image detector is reduced, the light receiving sensitivity is lowered. Therefore, there is a limit to reducing the pixel size for use in medical X-ray imaging due to the problem of exposure dose.

  Another method for improving the MTF is to make the focal spot size of the X-ray tube as small as possible. However, in a medical X-ray apparatus, for example, a focal size of 0.2 mm × 0.2 mm is regarded as a technical limit of today for a fixed anode X-ray tube. In addition, if the focal spot size of the X-ray tube is reduced, a large current cannot flow through the X-ray tube and the irradiation dose is reduced.

  Furthermore, as another method for improving the MTF, the enlargement ratio of the subject can be as close to 1.0 as possible. The enlargement ratio of the subject is obtained from the ratio of the distance from the focus to the image detector and the distance from the focus to the subject. When the subject and the image detector are separated from each other, a blur component corresponding to a penumbra of the focal point is generated corresponding to the distance. This blur component depends on the enlargement ratio of the subject. In particular, in an imaging system in which the subject and the recording medium cannot be brought into close contact with each other, for example, X-ray CT (Computed Tomography), the penumbra size (hereinafter referred to as blur size) of the focus is increased even if the focus size is reduced. As a result, the resolution drops.

  Conventionally, there has been known a method of restoring an image by removing blur in the frequency domain using Fourier transform or the like on a blurred image (degraded image) obtained by photographing a subject (for example, Patent Documents). 1 and Patent Document 2).

JP 2013-162369 A Japanese Patent No. 4799428

  For example, in a medical X-ray imaging system, the resolution of an output image that is projected in a visible form is determined depending on the pixel size of the recording medium and the blur size on the recording medium on which the focus is projected. Then, in the two-dimensional information (image) of the subject recorded on the recording medium by photographing the subject, when the blur size due to the focus of the X-ray tube is larger than the pixel size of the recording medium, the output image is caused by the focus. It becomes a deteriorated image. In the prior art, it is impossible to restore a high-resolution image from a degraded image to a resolution determined by the Nyquist frequency of a recording medium that records two-dimensional information of a subject.

  The present invention has been made in view of the above problems, and an object thereof is to provide an information processing apparatus and a filter generation apparatus that perform high resolution processing on information obtained from a target.

  In order to solve the above-described problem, the information processing apparatus according to the present invention is information that can be expressed by a convolution integral of a one-dimensional or two-dimensional impulse response set based on measurement and target original information. In a frequency section selected in advance by comparing the impulse response and the ideal function, the first calculation means for obtaining the spectrum of the target recording information by converting the frequency of the target recording information obtained from the target on the memory, Second calculation means for performing a process of inverting the sign of the spectrum of the target record information, and information in the real space restored by performing inverse frequency conversion on the spectrum of the target record information subjected to the process. 3rd calculating means to calculate as, It is characterized by the above-mentioned.

  In the information processing apparatus according to the present invention, the impulse response may be a blur function that represents one of a focus blur of an X-ray imaging system, a blur caused by lens aberration, or a waveform rounding of a communication system. preferable.

According to such a configuration, the information processing apparatus converts the information in the real space into the information in the frequency space by the first calculation means, performs the predetermined process on the information in the frequency space by the second calculation means, Information in the frequency space is converted into information in the real space by the third computing means. Here, the second calculation means performs a process of inverting the sign of the spectrum of the target recording information in a frequency section selected in advance in the spectrum of the target recording information. The frequency interval in which the sign of the spectrum of the target recording information is inverted by the second calculation means is selected in advance by comparing the impulse response with the ideal function. For example, when it is determined to cancel out of focus blur projected on a recording medium in an X-ray imaging system, a function obtained by frequency conversion (for example, Fourier transform) of the blur function (impulse response) and the ideal function is compared. In this case, in the cos component and the sin component of the blur function after the Fourier transform, an arithmetic process is performed to invert the sign of the frequency sections having phases different from those of the cos component and the sin component of the ideal function after the Fourier transform. Then, the position that is the zero point of the waveform representing the blur function in the frequency space is obtained. A frequency section in which the sign of the spectrum of the target recording information is inverted can be selected from the position that becomes the zero point.
Since the second calculation means performs the inversion process, the waveform representing the spectrum of the target recording information has a shape as if the position of the zero point is extended and the cutoff frequency is shifted to the high frequency side. And a 3rd calculating means calculates the information obtained by carrying out reverse frequency conversion of the spectrum of the object recording information to which this inversion process was performed as original information. The calculated original information is higher in resolution than the target recording information by the increase in the cutoff frequency.
With this configuration, the information processing apparatus can restore the high-resolution original information with high resolution determined by the Nyquist frequency of the recording medium that records the target information from the target recording information.

  In the information processing apparatus according to the present invention, the first calculation means may include a first function calculation means for calculating the first function by frequency-converting the blur function on a memory, a delta function or a delta function. Second function calculating means for calculating a second function by frequency-converting the ideal function preset in advance on a memory, wherein the second computing means is configured to include the second function in the first function. A frequency section different from the sign of the function is selected, and in the selected frequency section, a process of making the phase of the first function coincide with the phase of the second function by inverting the sign of the first function A phase inversion unit; a second phase inversion unit that performs a process of inverting the sign of the spectrum of the target recording information in a frequency section selected by the first phase inversion unit; and a plurality of predetermined frequencies. A gain correction coefficient calculating means for calculating a gain correction coefficient as a result of dividing the function by the first function with the sign inverted; and the gain correction coefficient in the spectrum of the target recording information with the sign inverted. Multiplying means for multiplying, and the third computing means performs inverse frequency transform on the spectrum of the target recording information multiplied by the gain correction coefficient, thereby using the restored information in the real space as the original information. It is preferable to calculate.

  According to such a configuration, in the information processing apparatus, the first function and the second function are calculated by frequency-converting the blur function and the ideal function by the first calculation unit. Then, the second computing means of the information processing apparatus selects a frequency section different from the sign of the second function in the first function by the first phase inverting means, and inverts the sign of the first function in the selected frequency section. To do. Then, the second phase inverting means inverts the sign of the spectrum of the target recording information in the selected frequency section. As a result, the waveform representing the spectrum of the target recording information is shifted from the position where the zero is located to the position where the waveform representing the ideal function is zero in the frequency space. Then, the second calculating means divides the second function by the first function for each predetermined frequency while the phases of the first function and the second function are matched with each other by the gain correction coefficient calculating means. Is calculated. This gain correction coefficient is a coefficient for correcting the gain of the waveform representing the blur function to approach the ideal function waveform. Therefore, the information processing apparatus multiplies the spectrum of the target recording information by the gain correction coefficient by the multiplying unit, thereby bringing the waveform shape representing the target recording information spectrum closer to the waveform shape representing the ideal function in the frequency space. be able to. The information processing apparatus calculates original information by converting information in the frequency space into information in the real space. This calculated original information has a higher resolution than the original target recording information because the target recording information whose sign has been inverted in the frequency space is gain-corrected by an ideal function to reduce blur and then returned to the real space. Imaged.

  In the information processing apparatus according to the present invention, the first calculation means may include a first function calculation means for calculating the first function by frequency-converting the blur function on a memory, a delta function or a delta function. Second function calculating means for calculating a second function by frequency-converting the ideal function preset in advance on a memory, wherein the second computing means is configured to include the second function in the first function. A frequency section different from the sign of the function is selected, and in the selected frequency section, a process of making the phase of the first function coincide with the phase of the second function by inverting the sign of the first function A phase inversion unit; a second phase inversion unit that performs a process of inverting the sign of the spectrum of the target recording information in a frequency section selected by the first phase inversion unit; and a plurality of predetermined frequencies. Gain correction coefficient calculation means for calculating a gain correction coefficient as a result of dividing the function by the first function with the sign inverted, and the third calculation means has the object with the sign inverted. Information generating means for generating a real space information by performing reverse frequency conversion of a spectrum of recorded information, reverse frequency converting means for performing reverse frequency conversion of the gain correction coefficient, and the gain correction coefficient subjected to the reverse frequency conversion in the real space Numerical conversion means for converting into a numerical filter of a predetermined size, and convolution operation means for calculating information obtained by convolving the information in the generated real space and the numerical filter as the original information; Are preferably provided.

  According to such a configuration, in the information processing apparatus, the first function and the second function are calculated by frequency-converting the blur function and the ideal function by the first calculation unit. Then, the second computing means of the information processing apparatus selects a frequency section different from the sign of the second function in the first function by the first phase inverting means, and inverts the sign of the first function in the selected frequency section. To do. Then, the second phase inverting means inverts the sign of the spectrum of the target recording information in the selected frequency section. As a result, the waveform representing the spectrum of the target recording information is shifted from the position where the zero is located to the position where the waveform representing the ideal function is zero in the frequency space. Then, the second calculating means divides the second function by the first function for each predetermined frequency while the phases of the first function and the second function are matched with each other by the gain correction coefficient calculating means. Is calculated. And the 3rd calculating means converts the information in these frequency spaces into the information in real space. At this time, the third computing means performs inverse frequency conversion on the spectrum of the target recording information, performs inverse frequency conversion on the gain correction coefficient, and converts the gain correction coefficient subjected to the inverse frequency conversion into a numerical filter in the real space. And a 3rd calculating means calculates original information by convolving the information in the real space and the numerical filter which were produced | generated by carrying out reverse frequency conversion of the spectrum of object recording information. Therefore, the information processing apparatus has equivalently processed the waveform shape representing the spectrum of the target recording information in the frequency domain by the above processing in the real space to be close to the waveform shape representing the ideal function in the frequency space. Become. Therefore, the calculated original information is obtained by multiplying the target recording information whose sign is inverted in the frequency space and the gain correction coefficient for reducing the blur of the target recording information by the ideal function after returning to the real space. Therefore, the resolution is higher than the original target recording information.

  In the information processing apparatus according to the present invention, the target recording information is a photographed image of a predetermined subject, the memory includes a first memory that stores an image having a predetermined number of pixels, and four times the predetermined number of pixels. A second memory for storing an image having the number of pixels described above, wherein the first computing means transfers the captured image and the blur function from the first memory to the second memory, and the captured image and the Images obtained by enlarging one pixel of the blur function to 2 × 2 pixels on the second memory are generated, and the enlarged image is frequency-converted and set as the ideal function on the second memory 2 The frequency of the pixel × 2 pixel image is converted, and the second calculation unit and the third calculation unit perform calculation using a function obtained by frequency conversion of the image enlarged on the second memory, The third operator Preferably, the stage calculates, as an original image of the subject, an image obtained by compressing 2 × 2 pixels into one pixel in an image restored by inverse frequency conversion on the second memory.

  In order to configure a second memory that stores an image having a pixel number four times that of the first memory, each pixel of the first memory may be divided into, for example, four. Setting an image of 2 pixels × 2 pixels on the second memory is equivalent to setting an image of only one pixel, that is, a delta function in the first memory. If a delta function of only one pixel is set as an ideal function in a normal memory and Fourier transformed, the result is 1 regardless of the frequency. Therefore, when a delta function of only one pixel is used as an ideal function in a normal memory, if a gain correction coefficient for reducing blur of target recording information is calculated, the calculated gain correction coefficient is extremely large at a high frequency. Value. As a result, the finally calculated original image may be an image with enhanced noise. Therefore, in order to avoid noise enhancement, it is desirable to set the ideal function to a size of 2 pixels. However, for the purpose of high resolution processing, the ideal function should be set to a size equivalent to 1 pixel or less. In view of this, the information processing apparatus includes a second memory that is divided into four by dividing each pixel of the memory into 2 × 2 pixels compared to the original memory. Accordingly, the information processing apparatus can set the ideal function as a delta function. If the ideal function is set to the delta function, the image calculated as the original image by the information processing apparatus is obtained by multiplying the original image of the subject that is not affected by the shooting with the delta function as a blur function. The generated image, that is, an image that is not affected at all by the blur function, is the highest resolution as an image restored from the captured image.

  In order to solve the above problem, the filter generation apparatus according to the present invention performs first frequency conversion on a memory for a blur function representing a one-dimensional or two-dimensional impulse response set based on measurement. A first function calculating means for calculating a function, a second function calculating means for calculating a second function by frequency-converting a delta function or an ideal function approximated to the delta function in advance on a memory, and A frequency interval different from the sign of the second function is selected in the first function, and the phase of the first function is changed to the phase of the second function by inverting the sign of the first function in the selected frequency interval. A phase inversion means for performing a matching process, and a gain correction coefficient as a result of dividing the second function by the first function with the sign inverted at a plurality of predetermined frequencies, respectively; A gain correction coefficient calculating means for outputting, a reverse frequency converting means for performing reverse frequency conversion on the gain correction coefficient, and a numerical value for converting the gain correction coefficient subjected to the reverse frequency conversion into a numerical filter having a predetermined element size in real space. Conversion means.

  According to this configuration, in the filter generation device, the first function calculation unit calculates the first function obtained by frequency-converting the blur function, and the second function calculation unit calculates the second function obtained by frequency-converting the ideal function. . And a filter production | generation apparatus selects the frequency area different from the code | symbol of a 2nd function in a 1st function by a phase inversion means, and inverts the code | symbol of a 1st function in the selected frequency area. Then, the filter generation device calculates the gain correction coefficient by dividing the second function by the first function for each predetermined frequency in a state where the phases of the first function and the second function are matched by the gain correction coefficient calculation means. calculate. Then, the filter generation device performs inverse frequency conversion on the gain correction coefficient, and converts the gain correction coefficient subjected to the inverse frequency conversion into a numerical filter in real space. Therefore, it is possible to generate a numerical filter by measuring a blur function in advance and setting a desired ideal function and performing the above-described processing by the filter generation device. Thereby, when the filter generation device is incorporated in the information processing device, for example, if the numerical filter is generated in advance and stored in the storage means, the information generated in the separate process and the numerical filter read from the storage means Since the original information can be easily calculated only by convolution, the final output information can be quickly output as the original information.

  The information processing apparatus according to the present invention can perform high resolution processing on information obtained from a target. In addition, the filter generation device according to the present invention can be used for high resolution processing of information obtained from a target.

1 is a block diagram schematically showing an information processing apparatus according to a first embodiment of the present invention. FIGS. 2A and 2B are schematic diagrams for explaining a first function calculating unit in FIG. 1, in which FIG. 1A shows a blurring function of an imaging system, and FIG. FIGS. 2A and 2B are schematic diagrams for explaining a second function calculating unit in FIG. 1, where FIG. 1A shows an ideal function, and FIG. 1B shows its MTF. It is a schematic diagram explaining the 1st phase inversion means of FIG. 1, Comprising: The phase inversion process which makes the phase of a blurring function the same phase as an ideal function is shown. It is a schematic diagram explaining the frequency conversion means of FIG. 1, Comprising: (a) is a picked-up image, (b) has shown the Fourier transform. It is a schematic diagram explaining the 2nd phase inversion means of FIG. 1, Comprising: The phase inversion process which makes the phase of a picked-up image the same phase as an ideal function is shown. (A) is an original image, (b) is an image of a comparative example that does not use phase inversion processing, and (c) is an image of an embodiment that uses phase inversion processing. FIGS. 7B and 7C are schematic views showing enlarged images of FIGS. 7B and 7C, where FIG. 7A shows a comparative example and FIG. 7B shows an example. It is a block diagram which shows typically the information processing apparatus which concerns on 2nd Embodiment of this invention. It is a schematic diagram explaining the gain correction coefficient calculation means of FIG. It is a schematic diagram explaining the multiplication means of FIG. It is explanatory drawing of the image produced | generated with the information processing apparatus of FIG. 9, Comprising: (a) is an original image, (b) is a comparative example, (c) is an Example. It is a conceptual diagram which shows typically the memory of the information processing apparatus which concerns on the modification of 2nd Embodiment of this invention. It is a block diagram which shows typically the information processing apparatus which concerns on 3rd Embodiment of this invention.

DESCRIPTION OF EMBODIMENTS Embodiments for implementing an information processing apparatus and a filter generation apparatus according to the present invention will be described in detail with reference to the drawings.
[First Embodiment]
As shown in FIG. 1, the information processing apparatus 1 mainly includes a first calculation unit 10, a second calculation unit 20, a third calculation unit 30, and a memory 40. The information processing apparatus 1 is configured by a general computer, for example, and includes a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), a HDD (Hard Disk Drive), an input / output interface, and the like. ing. The memory 40 is composed of an HDD or a general image memory.

  The first calculation means 10 obtains the spectrum of the target recording information by subjecting the target recording information obtained from the target to frequency conversion on the memory 40. Here, the target recording information is information that can be expressed by a convolution integral of the impulse response set based on the measurement and the target original information. In the following description, the frequency transform is assumed to be Fourier transform.

  In the present embodiment, as an example, it is assumed that the target recording information is a medical X-ray image (hereinafter simply referred to as a captured image) obtained by imaging a human body. At this time, the impulse response is obtained by measuring a penumbra of the focal point of the X-ray imaging system, and is represented by a blur function. When the target recording information is a photographed image, the blur function (impulse response) is two-dimensional, but for the sake of simplicity, it is one-dimensional below, and the relationship between the original image to be obtained by restoration, the photographed image, and the blur function Will be described using mathematical expressions.

  It is assumed that an output image with blur, that is, a captured image that is captured by capturing a subject, is represented by o (x). Note that x represents a position in the real space. The blur function (impulse response) at this time is represented by f (x). Also, let r (x) be an image with no out-of-focus when the subject is photographed, that is, an original image to be obtained by restoration. At this time, it is known that the following formula (1) holds. Here, the symbol “*” indicates a convolution integral.

In addition, after Fourier transforming each of the captured image o (x), the blur function f (x), and the original image r (x), the following equation (2) is obtained as a convolution theorem between the converted functions. It is known to hold. Here, F ^−j [•] indicates an operator that performs Fourier transform on the function in parentheses.

  As is clear from the above equation (1), the shot image o (x) having blur is the blur function f (x) set based on the measurement and the original image r (x ) And convolution integral.

  In the present embodiment, it is assumed that digital data of a photographed image is input from the outside during processing of the information processing apparatus 1. The captured image may be stored in the memory 40 inside the information processing apparatus 1 before the image restoration process.

  In the present embodiment, it is assumed that the blur of the focal point of the X-ray imaging system is measured and the blur function f (x) is set before the restoration process. An example of the blur function f (x) is shown in FIG. In the blur function f (x) represented by the rectangular function, the width of the rectangular function (blur size D) corresponds to a penumbra on the image plane on the X-ray imaging system recording medium. Note that the height (amplitude) of the rectangular function is normalized to a predetermined value. Here, the blur size D of the blur function f (x) on the recording medium can be obtained from the focal spot size of the X-ray tube and the enlargement factor. Specifically, assuming that the focal shape of the X-ray tube is a rectangular function having a width of, for example, 800 μm and the enlargement ratio is, for example, 2.0, the blur size D is 800 μm.

  As shown in FIG. 1, the first calculation means 10 includes a frequency conversion means 12. Here, the first calculation means 10 is also provided with the preprocessing means 11 in order to preprocess the information input to the frequency conversion means 12.

  Moreover, the 1st calculating means 10 may be provided with the 1st function calculation means 13 and the 2nd function calculation means 14 as needed. When the first calculation unit 10 includes the first function calculation unit 13 and the second function calculation unit 14, the second calculation unit 20 includes the first phase inversion unit 21.

  The preprocessing unit 11 performs preprocessing so that no artifacts appear in an image obtained by restoring a captured image (blurred image). The preprocessing is processing performed in advance in order to reduce unnecessary periodic image components when image processing is performed by inverse Fourier transform after finishing predetermined image processing in the frequency domain. The preprocessing unit 11 can suppress artifacts by a general method. For example, preprocessing can be performed with a window function typified by a Hanning window (or hann window). In addition, for example, a Hamming filter, a ButterWorth filter, a Gauss filter, a smoothing filter, or the like may be used. The preprocessing unit 11 is not an essential component of the present invention, but is preferably provided as an artifact countermeasure.

  The preprocessing unit 11 takes in digital data of a photographed image from a connected recording medium (not shown), develops it in the memory 40, and performs preprocessing. Note that when the photographed image is a photograph, the preprocessing unit 11 scans the photograph. The preprocessing unit 11 outputs the preprocessed captured image to the frequency conversion unit 12. Hereinafter, this preprocessed photographed image with blur will be referred to as o (x).

The frequency conversion means 12 performs Fourier transform on the preprocessed captured image o (x) on the memory 40 to obtain a spectrum F _o (ω) of the captured image defined by the following equation (3). . In the following, it is shown that the function F with the subscript is a function calculated by Fourier transforming the function represented by the subscript. Note that ω is a spatial frequency. The frequency conversion unit 12 outputs the spectrum F _o (ω) of the captured image to the second phase inversion unit 22 of the second calculation unit 20.

The first function calculating means 13 performs a Fourier transform on the blur function f (x) on the memory 40, thereby obtaining the first function F _f (ω) defined by the following equation (4) as a blur transfer function. Is to be calculated. Hereinafter, the first function F _f (ω) is referred to as a blur function MTF. The first function calculation unit 13 outputs the calculated MTF (that is, F _f (ω)) of the blur function to the first phase inversion unit 21.

  When the blur function f (x) in the real space is represented by the rectangular function shown in FIG. 2A, the MTF of the blur function calculated by Fourier transforming the rectangular function by the first function calculating unit 13 is shown in FIG. Shown in (b). The horizontal axis of the graph of FIG. 2B is the spatial frequency ω [cycles / mm], and the vertical axis is MTF. Note that the waveform of the function obtained by Fourier transforming the rectangular function is represented by the same waveform as the sinc function, but in the graph of FIG. 2 (b), the waveform is exaggerated and schematically shown for easy understanding. .

  In the graph of FIG. 2B, frequency sections in which the MTF is positive (for example, sections 103 and 104) and frequency sections in which the MTF is negative (for example, sections 101 and 102) appear alternately, and the space When the frequency ω is an integral multiple of 1 / D, the MTF value is zero.

The second function calculating unit 14 shown in FIG. 1 performs the Fourier transform on the ideal function I (x) on the memory 40, thereby obtaining the first function defined by the following equation (5) as the transfer function of the ideal photographing system. Two functions F _I (ω) are calculated. Hereinafter, the second function F _i (ω) is referred to as an ideal function MTF. Here, the ideal function I (x) is a delta function or a function set in advance approximating the delta function. The second function calculating means 14 outputs the calculated ideal function MTF (F _i (ω)) to the first phase inverting means 21.

  An example of the ideal function I (x) is shown in FIG. In the ideal function I (x) represented by the rectangular function, the rectangular function width (width 2d) is set to a smaller value than the width (blur size D) of the blur function f (x), and a desired value is set. Can do. However, the minimum value of the width of the rectangular function is a width corresponding to two pixels of the pixel size of the recording medium. Specifically, if the width of one pixel of the recording medium is 100 μm and the blur size D is 800 μm, the width (width 2d) of the rectangular function is set to 200 μm ≦ 2d <800 μm. Note that the height (amplitude) of the rectangular function is normalized to a predetermined value.

  Note that the width (width 2d) of the ideal function I (x) can be arbitrarily set, but 1/2, 1 of the blur size D so that the blur size D is divisible for the phase inversion processing described later. / 3, 1/4,...

  When the ideal function I (x) in the real space is represented by the rectangular function shown in FIG. 3A, the MTF of the ideal function calculated by Fourier transforming the rectangular function by the second function calculating unit 14 is shown in FIG. Shown in (b). The horizontal axis of the graph in FIG. 3B is the spatial frequency ω, and the vertical axis is MTF. In the graph of FIG. 3B, frequency intervals in which the MTF is positive and frequency intervals in which the MTF is negative appear alternately, and the spatial frequency ω is an integral multiple of 1 / (2d). The value of MTF is 0. In addition, in the graph of FIG.3 (b), a waveform is exaggerated and it has shown typically.

The second calculation means 20 shown in FIG. 1 inverts the sign of the spectrum F _o (ω) of the captured image in a frequency section selected in advance by comparing the blur function f (x) with the ideal function I (x). The process which performs is performed. The second computing means 20 includes second phase inverting means 22. In addition, the 2nd calculating means 20 may be provided with the 1st phase inversion means 21 as needed.

The first phase inversion means 21 receives the MTF (F _f (ω)) of the blur function from the first function calculation means 13 and the ideal function MTF (F _i (ω) from the second function calculation means 14. ) Is entered. The first phase inversion means 21 selects a frequency section different from the sign of the MTF of the ideal function in the MTF of the blur function, and inverts the sign of the MTF of the blur function in the selected frequency section to thereby change the phase of the MTF of the blur function. Is matched with the MTF phase of the ideal function. The first phase inversion means 21 inverts the sign in the frequency section selected based on the ideal function as described later for the cos component and the sin component of the MTF of the blur function. This process is a process of correcting the blur function reflecting the measured defocusing to be a desired ideal function with a reduced degree of blur. Hereinafter, this process is referred to as a phase inversion process.

A specific example of this phase inversion process will be described with reference to FIGS. Here, as an example, the width (bokeh size D) of the rectangular function shown in FIG. 2A is 800 μm, and the width (2d) of the rectangular function shown in FIG. 3A is set to 200 μm. I will do it. That is, D = 8d. Under this assumption, the value of the MTF (F _i (ω)) of the ideal function shown in FIG. 3B is a range where the spatial frequency ω [cycles / mm] is from 0 to 1 / (2d), that is, A positive value is obtained when 0 ≦ ω <5, and a zero point is obtained when ω = 5.

Therefore, the first phase inverting means 21 uses the MTF (F _f (ω) of the blur function based on a certain frequency section (0 ≦ ω <5) in which the sign of the MTF of the ideal function is positive. ), The sign of the frequency having a negative sign is inverted. Note that the first phase inversion means 21 does nothing in this range (0 ≦ ω <5) for the frequency section in which the sign of the blur function MTF (F _f (ω)) is positive.

Specifically, the value of the MTF (F _f (ω)) of the blur function shown in FIG. 2B is such that the spatial frequency ω [cycles / mm] is, for example, 0 ≦ ω <5, that is, ω is 0 to 4 In the range up to / D, the frequency sections in which the MTF value is negative are 1 / D <ω <2 / D (section 101) and 3 / D <ω <4 / D (section 102).
Therefore, the first phase inverting means 21, the sign of the MTF (F _f (ω)) of the section 101, the sign of the MTF (F _f (ω)) of the section 102, to positive inversion from negative. The function after the phase is inverted in this way is expressed as F _fp (ω) to distinguish it from the function before the inversion. The graph of FIG. 4 shows this inverted function F _fp (ω) superimposed on the ideal function MTF (F _i (ω)).

Further, in the present embodiment, the first phase inversion means 21 makes the MTF of the blur function out of the frequency section in which the sign of the ideal function MTF (F _i (ω)) is negative when the two phases are matched. The sign of the frequency section in which the sign of (F _f (ω)) is positive is inverted.
The value of the ideal function MTF (F _i (ω)) shown in FIG. 3B is a negative value when the spatial frequency ω is, for example, 5 <ω <10. the sign of the MTF (F _f (ω)) of the / D <ω <5 / D ( section 103), the sign of MTF (F _f (ω)) of the 6 / D <ω <7 / D ( section 104) , Is inverted from positive to negative. Note that the first phase inversion means 21 does nothing in this range (5 <ω <10) for the frequency section in which the sign of the blur function MTF (F _f (ω)) is negative.

In the case where the second computing means 20 includes, for example, the first phase inverting means 21, the first phase inverting means 21 provides information such as the frequency interval in which the MTF value of the ideal function is positive and the frequency interval in which the ideal function is negative. It outputs to the 2nd phase inversion means 22 as phase inversion information.
On the other hand, when the second calculation means 20 does not include the first phase inversion means 21, the phase inversion information is recorded in the memory 40 in advance, or the operator of the information processing apparatus 1 can input a desired value. By doing so, the second phase inversion means 22 acquires the phase inversion information.

The second phase inverting means 22 has the same configuration as that of the first phase inverting means 21, but the target for performing the phase inversion process is different. The second phase inverting means 22 performs processing for inverting the sign of the spectrum F _o (ω) of the captured image (preprocessed captured image o (x)) in the frequency section selected by the first phase inverting means 21. It is something to apply.

In other words, the second phase inversion means 22 selects a frequency section different from the sign of the MTF of the ideal function in the spectrum F _o (ω) of the captured image (preprocessed captured image o (x)), and selects the selected frequency. Processing for matching the phase of the spectrum F _o (ω) of the captured image o (x) with the phase of the MTF of the ideal function by inverting the sign of the spectrum F _o (ω) of the captured image o (x) in the section. Apply.

  A specific example of this phase inversion processing will be described with reference to FIGS. 5 to 6 (refer to FIGS. 1 to 4 as appropriate). FIG. 5A is a schematic diagram illustrating an example of a preprocessed captured image o (x). In this example, the photographed image o (x) is an X-ray image photographed using an image detector having a tooth size of, for example, 100 μm with a tooth as a subject.

FIG. 5B shows a spectrum F _o (ω) of the photographed image calculated by Fourier transforming the preprocessed photographed image o (x) by the frequency conversion means 12. Since the blur function of the X-ray imaging system is directly applied to the captured image, the spectrum F _o (ω) of the captured image is periodically positive and negative as with the MTF of the blur function (see FIG. 2B). I will take.
FIG. 5 (b) is a conceptual diagram schematically showing waveforms exaggerated to help understanding. In the case of complex image data, the waveform fluctuates positive / negative at every frequency after Fourier transform. It may become.

Here, similarly to the specific example of the phase inversion processing by the first phase inversion means 21, as an example, the width (bokeh size D) of the rectangular function shown in FIG. 2A is 800 μm, and FIG. It is assumed that the width (2d) of the rectangular function shown in a) is set to 200 μm. In this case, since the value of the ideal function MTF (F _i (ω)) shown in FIG. 3B is a positive value when 0 ≦ ω <5, in the spectrum F _o (ω) of the photographed image, FIG. In the position of the end point of the frequency section 102 shown in (b), ω = 5. Further, as described above, the blur function of the X-ray imaging system is applied directly to the captured image, and therefore, corresponding to the MTF (F _f (ω)) of the blur function shown in FIG. In the spectrum F _o (ω), as shown in FIG. 5B, ω at the position of the start point (zero point) of the frequency section 101 corresponds to a cutoff frequency when no special processing is performed.

Under this assumption, the second phase inverting means 22 inverts the sign of the spectrum F _o (ω) of the photographed image o (x) in the frequency sections 101 and 102 as shown in FIG.
The spectrum after the phase is inverted in this way is denoted as F _op (ω) in order to distinguish it from the spectrum before the inversion. The graph of FIG. 6 shows the inverted spectrum F _op (ω) superimposed on the ideal function MTF (F _i (ω): see FIG. 3B).
Here, an example in which the sign is inverted in one direction in the frequency sections 101 and 102 will be described. However, in the case of image data having a waveform that swings positive / negative in the frequency sections 101 and 102, In the area where the sign is negative, the sign is inverted to positive, and in the area where the sign is positive, the sign is inverted to negative.

As shown in FIG. 6, the spectrum F _o the (omega) and the phase inversion of the captured image o (x), MTF ideal function phase spectrum F _o (omega) of the captured image _{o (x) (F i (} ω In the waveform representing the spectrum F _op (ω) after matching the phase of)), the position of ω as the zero point is extended to 1 / (2d), and the cutoff frequency is shifted to the high frequency side. Shape. In this example, there is an effect that the cut-off frequency becomes four times that before the processing before and after the phase inversion.

In the present embodiment, the second phase inversion means 22 performs the smoothing process on the spectrum F _op (ω) after the phase inversion. In this smoothing process, the value of the spectrum F _op (ω) does not become 0 by performing image processing by applying a smoothing filter to a frequency section in which the value of the spectrum F _op (ω) becomes 0 if it remains as it is. It is to make. The operator of the information processing device 1 can set and input a desired value for interpolation to the smoothing filter, so that the second phase inversion unit 22 can acquire this interpolation information.

The second phase inverting means 22 is interpolated using data before and after the frequency interval the value of the spectrum F _op (omega) becomes zero is intact (the value of the spectrum F _op (ω)). At this time, instead of using only the nearest neighbor (pre- and post-data), for example, three data including the nearest data and the corresponding data are removed, or five data including data adjacent to the front and rear are further removed. In addition, it is preferable to interpolate with the previous and subsequent values in the remaining data. The interpolation method at this time is not particularly limited, but for example, linear interpolation may be used. The spectrum after the smoothing process is also expressed as F _op (ω).

  The third calculation means 30 converts information in the frequency space that has been subjected to the predetermined processing by the second calculation means 20 into information in the real space. In the present embodiment, as shown in FIG. 1, the third calculation unit 30 includes an information generation unit (inverse frequency conversion unit) 31 and a post-processing unit 32.

The information generation means 31 calculates information in the real space restored by performing an inverse Fourier transform on the spectrum F _op (ω) after the phase inversion process is performed on the spectrum of the captured image as an original image. Note that this original image is an image having no out-of-focus when the subject is photographed, that is, an image to be obtained by restoration, and corresponds to r (x) in the above equation (1).

In this embodiment, the information generation means 31 performs an inverse Fourier transform on the spectrum F _op (ω) that has been subjected to the phase inversion process and the smoothing process. Image information in real space generated by performing inverse Fourier transform on F _op (ω) is denoted as O _p (x). This image information O _p (x) is an image obtained corresponding to the preprocessed captured image o (x).

The post-processing unit 32 is not an essential component of the present invention, but when the information processing apparatus 1 includes the pre-processing unit 11, the post-processing unit 32 includes the post-processing unit 32 correspondingly. The post-processing means 32 performs post-processing on the image information O _p (x) so that no artifacts appear in the image to be obtained by restoration. The post-processing unit 32 performs processing opposite to that of the pre-processing unit 11. For example, when the preprocessing unit 11 performs preprocessing with a Hanning window, the postprocessing unit 32 applies reverse hanning to restore the original state. The final output image after this post-processing is the restored image calculated by the information processing apparatus 1. This restored image is output to an output device such as a liquid crystal display.

In order to confirm the performance of the information processing apparatus 1 according to the present embodiment, the following experiment 1 was performed.
In Experiment 1, a well-known Siemens star chart (hereinafter simply referred to as a star chart) shown in FIG. 7A was used as a subject (original image). The star chart is made of lead and formed in a disk shape, and a plurality of wedges that radiate from the center to the periphery form a black and white striped pattern. Thereby, it can be seen that the more the radial black and white striped pattern is seen near the center of the star chart, the higher the resolving power of the photographing apparatus is.

  In this experiment 1, a star chart was photographed, and an image generated without phase inversion processing (comparative example) and an image generated with phase inversion processing (implementation) in order to confirm the improvement in resolution by phase inversion processing Example).

  FIG. 7B is an image (an image of a comparative example) showing a part of the star chart generated without using the phase inversion process. FIG. 8A is a schematic diagram showing an enlargement of the vicinity of the center of the star chart in the image of the comparative example. Note that the surface of the star chart is darker than the background. That is, the black wedge part is the surface of the star chart.

  FIG. 7C is an image (an example image) showing a part of a star chart generated by using the phase inversion process. FIG. 8B is a schematic diagram showing an enlargement of the vicinity of the center of the star chart in the image of the embodiment.

In the comparative example shown in FIG. 8A, the wedge image is divided into three regions 81a, 82a, 83a from the center of the star chart toward the edge. In terms of the spectrum of the image of this comparative example, a region 83a indicates a region where the spectrum is a positive value, a region 82a indicates a region where the spectrum is a negative value, and a region 81a indicates a region where the spectrum is a positive value. Indicates.
In the area 83a shown in FIG. 8A, it can be seen that the monochrome binary is correctly resolved. On the other hand, the area 82a is an image (pseudo-resolution) obtained by reversing black and white, and it can be seen that the area 81a is resolved as the original black and white image.

Here, the boundary portion between the region 83a and the region 82a indicated by an elliptical broken line in FIG. 8A is the spatial frequency position (zero point) when the spectrum value is 0 in terms of the spectrum of the image of the comparative example. ) Image information.
Similarly, the boundary portion between the region 82a and the region 81a indicated by an elliptical broken line in FIG. 8A is the position of the spatial frequency when the spectrum value becomes 0 again in terms of the spectrum of the image of the comparative example ( This corresponds to zero point image information. For these zeros, even if the spectrum is returned by inverse Fourier transform, there is no original information, so image information is lost and resolution is not performed. As a result, the wedge image becomes discontinuous, resulting in an unnatural image.

  When the captured image is a general-purpose image, even if there is a slight error, it may be tolerated. However, especially in the case of a medical X-ray image used for diagnosis, the true image is faithfully preserved in the diagnostic image. Need to be reproduced. Therefore, in the case of the image of the comparative example, the region 83a shown in FIG. 8A of the star chart is treated as being correctly resolved, and the region 82a to the region 81a are ignored as being not resolved. ing.

On the other hand, in the embodiment, as described above, the second phase inverting means 22 performs the phase inverting process. Therefore, as shown in FIG. 6, the waveform representing the spectrum F _op (ω) after the phase inversion is obtained by _checking that the zero point position is extended to 1 / (2d) and the cutoff frequency is shifted to the high frequency side. The effect is produced. Accordingly, as shown in FIGS. 7C and 8B, when the wedge image is divided into three regions 81b, 82b, and 83b from the center of the star chart toward the edge, the regions 81b to 83b are obtained. It can be seen that everything is resolved with. Therefore, it was confirmed that the resolution was improved when the phase inversion process was used.

Furthermore, in the embodiment, as described above, the second phase inversion means 22 performs the smoothing process on the spectrum F _op (ω) after the phase inversion, so that the image spectrum of the embodiment can be said. For example, a non-zero interpolation value is assigned to the zero point before processing. Therefore, the image is also resolved at the boundary between the region 83b and the region 82b indicated by the elliptical broken line and the boundary between the region 82b and the region 81b indicated by the elliptical broken line in FIG. Become a natural image.

  As described above, according to the information processing apparatus 1 of the present embodiment, by performing the phase inversion process, it is possible to perform correction to bring the blur function closer to a desired ideal function, and cancel the pseudo-resolution component. The frequency domain information where the image spectrum is negative can be extracted. As a result, it is possible to restore a high-resolution original image in which the blur is reduced as compared with the shot image having the blur. Therefore, the information processing apparatus 1 can restore an original image with a high resolution determined by the Nyquist frequency of the recording medium.

In addition, since the information processing apparatus 1 performs correction to bring the blur function closer to a desired ideal function, when the information processing apparatus 1 is incorporated in, for example, an X-ray imaging apparatus, the information processing apparatus 1 is more than an X-ray tube disposed in the apparatus. An image equivalent to an image taken with a minute X-ray tube can be obtained.
Furthermore, since this X-ray imaging apparatus can remove the influence of a penumbra image resulting from the focal point size of the X-ray tube, that is, blur, it is possible to realize an X-ray imaging apparatus having high output and high resolution. It becomes possible.

[Second Embodiment]
An information processing apparatus according to the second embodiment will be described with reference to FIG. This information processing apparatus 1B is mainly different in that a function of gain correction processing described later is added to the function of the information processing apparatus 1 of FIG. In the information processing apparatus 1B, the same components as those shown in FIG. The information processing apparatus 1B includes a first calculation unit 10B, a second calculation unit 20B, a third calculation unit 30B, and a memory 40.

In addition to the pre-processing means 11 and the frequency conversion means 12, the 1st calculating means 10B is provided with the 1st function calculation means 13 and the 2nd function calculation means 14.
Among these, the second function calculation means 14 outputs the calculated ideal function MTF (F _i (ω)) to the first phase inversion means 21 and the gain correction coefficient calculation means 23 of the second calculation means 20B. Since other configurations are as described above, description thereof is omitted here.

The second computing means 20B includes a first phase inverting means 21, a second phase inverting means 22, a gain correction coefficient calculating means 23, a multiplying means 24, and a second preprocessing means 25. In addition, the same code | symbol as FIG. 1 is attached | subjected to the same structure as the structure shown in FIG. 1, and description is abbreviate | omitted.
The first phase inverting means 21 outputs the function F _fp (ω) (see FIG. 4) after inverting the phase for the blur function MTF (F _f (ω)) to the gain correction coefficient calculating means 23.

The function F _fp (ω) related to the blur function is input from the first phase inversion unit 21 to the gain correction coefficient calculation unit 23, and the ideal function MTF (F _i (ω)) from the second function calculation unit 14. Is entered. As shown in the following equation (6), the gain correction coefficient calculation unit 23 divides the ideal function MTF (F _i (ω)) by the function F _fp (ω) related to the blur function, thereby obtaining a gain. The correction coefficient Q (ω) is calculated.

Q (ω) = F _i (ω) / F _fp (ω) (6)

Specifically, as shown in FIG. 10 and the following equation (7), the gain correction coefficient calculation unit 23 calculates the amplitude mb (n) of the ideal function MTF (F _i (ω)) at a plurality of predetermined frequencies n. ) _Is respectively divided by the amplitude ma (n) of the function F _fp (ω) related to the blur function, thereby calculating the gain correction coefficient Q (n) for each frequency n. Here, the amplitude of the waveform is represented by a height with respect to the ω axis. This Q (n) is called the Q value. The frequency interval for calculating the Q value is appropriately set according to the purpose, for example.

  Q (n) = mb (n) / ma (n) (7)

The gain correction coefficient calculating unit 23 temporarily sets the Q value at the zero point to 0 so that the Q value does not diverge at the frequency (zero point) at which the value of the function F _fp (ω) related to the blur function is 0. Keep it. Note that the Q value at the zero point is interpolated in a subsequent process. The gain correction coefficient calculation unit 23 outputs the gain correction coefficient Q (ω) to the multiplication unit 24.

The multiplication unit 24 receives from the second phase inversion unit 22 the spectrum F _op (ω) that has _undergone phase inversion processing relating to the captured image o (x), and from the gain correction coefficient calculation unit 23 to the gain correction coefficient Q. (Ω) is input. The multiplier 24 multiplies the spectrum F _op (ω) by a gain correction coefficient Q (ω). Hereinafter, the spectrum of the calculation result is expressed as a corrected spectrum F _F (ω) as shown in the following equation (8). This multiplication processing is called gain correction processing.

F _F (ω) = F _op (ω) × Q (ω) (8)

More specifically, the zero point of F _op (ω) shown in FIG. 6 has already been eliminated from the spectrum F _op (ω) input to the multiplication unit 24. That is, by the smoothing process described above, a non-zero interpolation value has been given to the zero point before the process.

In the present embodiment, the multiplication unit 24 performs the Q value interpolation process at the zero point of the function F _fp (ω) related to the blur function. In the gain correction coefficient Q (ω) input to the multiplication means 24, the Q value at these zero points is temporarily set to zero. However, since Q value data is set for the peripheral frequencies before and after the zero point, the Q value at the zero point can be interpolated from the frequency data before and after the zero point. The interpolation method at this time is not particularly limited, and may be the same as the interpolation method in the smoothing process, for example.

By performing the smoothing process and the interpolation process, the multiplication unit 24 can perform a meaningful multiplication so that the product does not become zero in the gain correction process. As a result, the shape of the spectrum F _op (ω) related to the photographed image o (x) as shown in FIG. 6 is brought close to the shape of the ideal function MTF (F _i (ω)), and correction as shown in FIG. 11 is performed. The resulting spectrum F _F (ω) can be obtained. Note that the smoothing process may be performed in addition to the interpolation process in the multiplication unit 24, and only the phase inversion process may be performed in the second phase inversion unit 22 instead.

The second preprocessing means 25 performs preprocessing on the spectrum F _F (ω) shown in FIG. 11 so that artifacts in the image obtained by restoring the captured image do not appear. The second preprocessing unit 25 is different from the preprocessing unit 11 in that image processing is performed in a frequency space. The second preprocessing means 25 can perform preprocessing with a window function typified by a Hanning window, for example.

As shown in FIG. 9, the third calculation means 30B includes information generation means (inverse frequency conversion means) 31B and post-processing means 32B.
The information generating unit 31B calculates information in the real space restored by performing inverse frequency conversion on the spectrum subjected to the gain correction processing as an original image. In the present embodiment, the information generating unit 31B performs inverse Fourier transform on the spectrum that has been subjected to gain correction processing and preprocessed by the second preprocessing unit 25. The image information in the real space generated by the information generation unit 31B is denoted as O _a (x). This image information O _a (x) is an image obtained corresponding to the preprocessed captured image o (x).
The post-processing unit 32B is the same as the post-processing unit 32 except that post-processing is performed on the image information O _a (x). The first memory 41 and the second memory 42 will be described later.

In order to confirm the performance of the information processing apparatus 1B according to the present embodiment, the following experiment 2 was performed.
In Experiment 2, X-ray imaging was performed using the star chart shown in FIG. As shown in FIG. 12B, the captured image has a blur caused by the focal point of the X-ray tube. The digital data of the photographed image was taken into the information processing apparatus 1B, and image processing including phase inversion processing and gain correction processing was performed. The final output image at that time is shown in FIG. According to the information processing apparatus 1B, a final output image having a resolution higher than that of the photographed image can be obtained, and it has been confirmed that the blur has been eliminated to such an extent that it does not cause an obstacle even when used for medical treatment.

  According to the information processing apparatus 1B of the present embodiment, by performing gain correction processing in addition to phase inversion processing, it is possible to perform correction that brings the blur function closer to the ideal function. As a result, it is possible to restore a high-resolution original image in which blurring is further reduced as compared with a blurred captured image.

[Modification of Second Embodiment]
As illustrated in FIG. 9, the information processing apparatus 1 </ b> B according to the modification of the second embodiment includes a first memory 41 and a second memory 42 in the memory 40.
The first memory 41 stores an image having a predetermined number of pixels, and stores a captured image and a blur function f (x) input to the information processing apparatus 1B according to this modification. Here, the predetermined number of pixels may include, for example, horizontal 512 pixels × vertical 512 pixels, horizontal 1024 pixels × vertical 768 pixels, and the like.

  The second memory 42 stores an image having a number of pixels that is four times or more the predetermined number of pixels. Here, as schematically shown in FIG. 13, it is assumed that the second memory 42 has twice as many pixels as twice as many pixels as the first memory 41. In this sense, the second memory 42 is also referred to as a quadruple memory.

  In the present modification, the first computing means 10B shown in FIG. 9 transfers the captured image and the blur function f (x) from the first memory 41 to the second memory 42. The first computing unit 10B generates an image in which one pixel of the captured image and the blur function f (x) is enlarged on the second memory 42 to 2 × 2 pixels.

The frequency conversion means 12 performs a Fourier transform on the captured image enlarged on the second memory 42. The spectrum of the obtained photographed image is based on the photographed image magnified twice in the horizontal and vertical directions, so that it is expressed as F _2o (ω) in distinction from F _o (ω) shown in the above equation (3). To do. Note that the pre-process means 11 pre-processes the enlarged photographed image before Fourier transform. The preprocessed captured image is denoted as o ₂ (x).

The first function calculation unit 13 performs a Fourier transform on the blur function f (x) expanded on the second memory 42. Since the MTF of the obtained blur function is based on the blur function that is doubled horizontally and vertically, it is expressed as F _2f (ω) in distinction from F _f (ω) shown in the equation (4). To do.

  In this modification, an image of 2 pixels × 2 pixels is set on the second memory 42 as the ideal function I (x). If one pixel of the captured image is calculated without being enlarged on the memory 40, the narrowest width (2d) of the rectangular function representing the ideal function I (x) in the real space is used to obtain the MTF in the frequency space. As a minimum, two pixels are required. On the other hand, the width of the rectangular function of the delta function corresponds to one pixel. Therefore, when the captured image is not enlarged, the delta function cannot be made the ideal function I (x). However, setting an image of four pixels (two pixels on one side) on the quadruple memory (second memory 42) as in this modification sets an image of one pixel on the first memory 41, that is, a delta function. Is equivalent to that.

Then, the second function calculating unit 14 performs a Fourier transform on the ideal function I (x), which is an image of four pixels, on the second memory 42. The obtained MTF of the ideal function is equivalent to the fact that a one-pixel image representing the delta function is based on an ideal function that is expanded two times in the horizontal and vertical directions, so that F _i (ω And F _2i (ω).

Similarly, the use of the quadruple memory in the processing of the second calculation means 20B is represented as follows by adding a subscript “2”.
The first phase inversion means 21 _{obtains a} function F _2fp (ω) by _performing phase inversion processing on the MTF (F _2f (ω)) of the blur function.
The second phase inversion means 22 _{obtains the} inverted spectrum F _2op (ω) by _performing phase inversion processing on the spectrum (F _2o (ω)) of the captured image.
The gain correction coefficient calculation means 23 performs the calculation of the following equation (6a).
The multiplying unit 24 performs the calculation of the following equation (8a) as the gain correction processing.

Q (ω) = F _2i (ω) / F _2fp (ω) Expression (6a)
F _2F (ω) = F _2op (ω) × Q (ω) (8a)

Similarly, the use of the quadruple memory in the processing of the third computing means 30B is represented as follows by adding a subscript “2”. The information generating unit 31B performs inverse Fourier transform on the spectrum that has been subjected to the gain correction process and preprocessed by the second preprocessing unit 25. The image information in the real space generated by the information generating unit 31B is expressed as O _2a (x). This image information O _2a (x) is an image obtained corresponding to the preprocessed captured image o ₂ (x). However, one pixel of the preprocessed captured image o ₂ (x) is enlarged to 2 × 2 pixels on the second memory 42. Therefore, the information generating unit 31B compresses 2 × 2 pixels into one pixel in the image information O _2a (x) in the real space. The compressed image information is again defined as O _a (x). Then, the post-processing means 32B performs post-processing on the image information O _a (x). As a result, the information processing apparatus 1B according to the modification outputs the calculated original image.

  According to the information processing apparatus according to the modification of the second embodiment, by setting the ideal function as a delta function, it is possible to perform correction to bring the blur function closer to the delta function. As a result, the restored image is an image that is not affected by the blur function at all, and the highest resolution is achieved as an image restored from the captured image. This restored image is an image having a resolution limit of the Nyquist frequency determined by the pixel size of the recording medium in any photographing system.

[Third Embodiment]
An information processing apparatus according to the third embodiment will be described with reference to FIG. 14 (see FIGS. 1 and 9 as appropriate). FIG. 14 schematically shows a filter generation device according to an embodiment of the present invention as will be described later. In the information processing apparatus 1C, the same components as those shown in FIG. The information processing apparatus 1C includes a first calculation unit 10B, a second calculation unit 20C, and a third calculation unit 30C. Since the first calculation means 10B has the same configuration as that described in the second embodiment, description thereof is omitted.

The second computing means 20C includes a first phase inverting means 21, a second phase inverting means 22, and a gain correction coefficient calculating means 23. Since these are part of the configuration of the second calculation means 20B shown in FIG. 9, detailed description thereof is omitted. However, in the present embodiment, the second phase inversion unit 22 outputs the phase-inverted spectrum F _op (ω) to the information generation unit 31 of the third calculation unit 30C.

  Further, in the present embodiment, the gain correction coefficient calculation means 23 performs the Q value interpolation processing at the zero point without temporarily setting the Q value at the zero point to 0 when calculating the gain correction coefficient Q (ω). It was decided. Since this interpolation process is the same as the interpolation process performed by the multiplication unit 24 of the second embodiment, a description thereof will be omitted. The gain correction coefficient calculation means 23 outputs the calculated gain correction coefficient Q (ω) to the inverse frequency conversion means 33 of the third calculation means 30C.

The third calculation means 30C includes information generation means (inverse frequency conversion means) 31, post-processing means 32C, reverse frequency conversion means 33, numerical value conversion means 34, and convolution calculation means 35. As in the first embodiment, the information generation unit 31 performs inverse Fourier transform on the spectrum F _op (ω) that has been subjected to phase inversion processing and smoothing processing by the second phase inversion unit 22. However, the information generating unit 31 outputs the image information O _p (x) in the real space generated by performing the inverse Fourier transform on the spectrum F _op (ω) to the convolution calculating unit 35. This image information O _p (x) is an image obtained corresponding to the preprocessed captured image o (x), and corresponds to the original image r (x) of the above-described equation (1).
The post-processing means 32C is the same as the post-processing means 32 of the first embodiment except that post-processing is performed on the image information O _b (x) generated and output by the convolution operation means 35.

  The gain correction coefficient Q (ω) is input from the gain correction coefficient calculation means 23 to the inverse frequency conversion means 33. The inverse frequency converting means 33 performs inverse frequency conversion of the gain correction coefficient Q (ω). Hereinafter, the gain correction coefficient subjected to inverse frequency conversion is denoted as Q (x). The gain correction coefficient Q (x) appears as a density distribution in real space. The inverse frequency conversion means 33 outputs this gain correction coefficient Q (x) to the numerical value conversion means 34.

  The numerical conversion means 34 converts the gain correction coefficient Q (x) into a numerical filter having a predetermined size in the real space. Since the gain correction coefficient Q (x) appears as a density distribution in the real space, the numerical conversion means 34 creates a numerical filter (hereinafter referred to as filter F (x)) in which this is converted into a numerical value. The size of the filter F (x) is not particularly limited. For example, it may be 3 × 1, 5 × 1, 7 × 1, or more. As long as it is two-dimensional, for example, a matrix of 3 × 3, 5 × 5 or more may be used. The numerical value conversion means 34 outputs the filter F (x) to the convolution calculation means 35.

The convolution calculator 35 calculates information obtained by convolving the image information O _p (x) generated by the information generator 31 and the filter F (x) as an original image. Here, the image information obtained by the convolution is expressed as O _b (x). Note that the image information O _b (x) corresponds to the original image r (x) of the above-described equation (1). In this case, this convolution operation processing can be expressed by the following relational expression (9).

O _b (x) = O _p (x) * F (x) (9)

Here, a supplementary explanation will be given regarding the origin of the formula (9). The relational expression obtained by performing inverse Fourier transform on the sides of the relational expression (formula (8)) showing the gain correction processing performed by the information processing apparatus 1B of FIG. 9 is expressed by the following formula (10). In Expression (10), F ^{+ j} [•] indicates an operator that performs inverse Fourier transform on the function in parentheses.

  Furthermore, the expression (10) can be replaced with image information and filter expressions generated by the information processing apparatus 1C as in the following expressions (11), (12), and (13).

That is, when the formula (10) is rearranged, the above-described formula (9) is obtained.
In short, the information processing apparatus 1C is configured to perform image processing corresponding to the gain correction processing performed in the information processing apparatus 1B of FIG. 9 in the real space region.

  The information processing apparatus 1 </ b> C according to the third embodiment performs the gain correction process in the frequency domain equivalently by performing the filtering process in the real space domain on the blurred captured image. Similar to the embodiment, it is possible to perform correction to make the blur function closer to the ideal function. In addition, since the information processing apparatus 1C performs filtering processing in the real space region on the blurred captured image, an effect of reducing artifacts in the restored image compared to the case of performing image correction on the captured image in the frequency domain. Play.

[Filter generator]
As shown in FIG. 14, the filter generation device 50 constitutes a part of the information processing device 1C. Specifically, the filter generation device 50 includes a first function calculation unit 13, a second function calculation unit 14, a first phase inversion unit 21, a gain correction coefficient calculation unit 23, an inverse frequency conversion unit 33, Numerical value conversion means 34.

The filter generation device 50 performs processing by the above means on the blur function f (x) measured by, for example, the X-ray imaging system and the desired ideal function I (x), so that the filter F (x ) Can be generated. When this filter generation device 50 is incorporated into the information processing apparatus 1C, for example, if the filter F (x) is generated in advance and stored in the storage means, the image information O _p (x) generated in another process is stored. The original image can be easily calculated simply by convolution with the numerical filter read from the means. Therefore, the final output image can be quickly output as the original image.

  The information processing apparatus and the filter generation apparatus according to the present invention have been described above based on each embodiment, but the present invention is not limited to these. For example, in each of the above-described embodiments, the case where the Fourier transform is adopted as an example of the frequency transform has been described.

  Further, in the modified example of the second embodiment, the second memory 42 is a quadruple memory. However, the second memory 42 has a number of pixels that is three times wide × three times vertical compared to the first memory 41, It may be a large memory having 4 × horizontal × 4 × vertical pixels. The magnification of the captured image is not limited to 200%, and may be 300% or 400%. In that case, an image of 3 pixels × 3 pixels or an image of 4 pixels × 4 pixels is set on the second memory 42 as the ideal function I (x). Then, at the final stage of processing, a 3 × 3 pixel or a 4 × 4 pixel may be compressed into one pixel. In consideration of cost and the like, the second memory 42 is preferably a quadruple memory.

  In addition, the configuration in which the memory 40 includes the first memory 41 and the second memory 42 is not limited to the modification of the second embodiment, and the information processing apparatuses 1 and 1C and the filter generation apparatus 50 according to the first and third embodiments. Can also be applied.

In each of the embodiments described above, the captured image is a medical X-ray image obtained by imaging a human body. Here, the medical X-ray image may be, for example, a simple X-ray image (an X-ray) such as a chest or a limb, a dental panoramic X-ray image, a mammography (mammography), an X-ray CT image, or the like.
The subject is not limited to the human body, and may be, for example, a naturally occurring object such as a mineral or a product of various industries. In this case, various analyzes and inspections to be broken can be performed.

The captured image input to the information processing apparatus 1 can be applied not only to an image captured using radiation, but also to an image captured using visible light, infrared light, or the like.
For example, in the case of medical images, all medical images other than X-rays, specifically, MRI (magnetic resonance imaging) images, ultrasonic images, endoscopic images, and the like may be used.
Moreover, not only a medical image but all general optical system images, for example, a digital camera system, a microscope image, a satellite image, and the like may be used.

  In each of the above embodiments, the impulse response has been described as being a blur function f (x) measured with respect to the focus of the imaging system, for example. However, the impulse response is not limited to this, and blur caused by lens aberration is not limited to this. The blur function represented may be used.

Further, the target of the digital high resolution processing according to the present invention is not limited to the two-dimensional information of the image, but may be one-dimensional information of a communication system such as radio waves such as radar, sound, and voice.
Further, the impulse response may be a one-dimensional blur function that represents a waveform rounding of the communication system.

  Furthermore, the present invention can be applied to, for example, camera shake correction. When performing processing for camera shake correction (one-dimensional smoothing), the camera is equipped with a gyro sensor, and the detected value of the gyro sensor is measured during the exposure time. By smoothing each captured image during the exposure time by the information processing apparatus according to the invention, it is possible to restore an image in which blur due to camera shake is eliminated.

1, 1B, 1C Information processing apparatus 10, 10B First calculation means 11 Preprocessing means 12 Frequency conversion means 13 First function calculation means 14 Second function calculation means 20, 20B, 20C Second calculation means 21 First phase inversion means 22 second phase inversion means 23 gain correction coefficient calculation means 24 multiplication means 25 second preprocessing means 30, 30B, 30C third calculation means 31, 31B information generation means (inverse frequency conversion means)
32, 32B, 32C Post-processing means 33 Inverse frequency conversion means 34 Numerical value conversion means 35 Convolution calculation means 40 Memory 41 First memory 42 Second memory 50 Filter generation device

Claims (6)

Information that can be expressed by convolution integral of the one-dimensional or two-dimensional impulse response set based on the measurement and the original information of the target, and the target recording information obtained from the target is frequency-converted on the memory First computing means for obtaining a spectrum of the target recording information;
A second calculation means for performing processing for inverting the sign of the spectrum of the target recording information in a frequency section selected in advance by comparing the impulse response with the ideal function;
Third computing means for calculating, as the original information, information in the real space restored by inverse frequency transforming the spectrum of the target recording information subjected to the processing;
An information processing apparatus comprising:   The information processing apparatus according to claim 1, wherein the impulse response is a blur function that represents one of a focal blur of an X-ray imaging system, a blur caused by lens aberration, and a waveform rounding of a communication system. The first calculation means includes
First function calculating means for calculating a first function by frequency-converting the blur function on a memory;
A second function calculating means for calculating a second function by performing frequency conversion on a memory of the ideal function set in advance by approximating a delta function or a delta function;
The second calculation means includes
A frequency interval different from the sign of the second function is selected in the first function, and the phase of the first function is changed to the phase of the second function by inverting the sign of the first function in the selected frequency interval. First phase inversion means for performing a process for matching
A second phase inversion means for performing a process of inverting the sign of the spectrum of the target recording information in the frequency section selected by the first phase inversion means;
Gain correction coefficient calculation means for calculating a gain correction coefficient as a result of dividing the second function by the first function with the sign inverted at a plurality of predetermined frequencies,
Multiplying means for multiplying the spectrum of the target recording information with the sign inverted by the gain correction coefficient,
3. The information according to claim 2, wherein the third computing unit calculates information in the restored real space as the original information by performing inverse frequency conversion on a spectrum of the target recording information multiplied by the gain correction coefficient. Processing equipment. The first calculation means includes
First function calculating means for calculating a first function by frequency-converting the blur function on a memory;
A second function calculating means for calculating a second function by performing frequency conversion on a memory of the ideal function set in advance by approximating a delta function or a delta function;
The second calculation means includes
A frequency interval different from the sign of the second function is selected in the first function, and the phase of the first function is changed to the phase of the second function by inverting the sign of the first function in the selected frequency interval. First phase inversion means for performing a process for matching
A second phase inversion means for performing a process of inverting the sign of the spectrum of the target recording information in the frequency section selected by the first phase inversion means;
Gain correction coefficient calculating means for calculating a gain correction coefficient as a result of dividing the second function by the first function with the sign inverted at a plurality of predetermined frequencies,
The third calculation means includes
Information generating means for generating information in real space by performing inverse frequency conversion on the spectrum of the target recording information with the sign inverted;
Reverse frequency conversion means for performing reverse frequency conversion of the gain correction coefficient;
Numerical conversion means for converting the inverse frequency converted gain correction coefficient into a numerical filter having a predetermined size in real space;
The information processing apparatus according to claim 2, further comprising: a convolution operation unit that calculates information obtained by convolving the information in the generated real space and the numerical filter as the original information. The target recording information is a captured image of a predetermined subject,
The memory includes a first memory that stores an image having a predetermined number of pixels, and a second memory that stores an image having a number of pixels that is four or more times the predetermined number of pixels.
The first calculation means transfers the captured image and the blur function from the first memory to the second memory, and 1 pixel of the captured image and the blur function is 2 × 2 pixels on the second memory. Each of the images enlarged in number is frequency-converted, and the frequency-converted image of 2 pixels × 2 pixels set on the second memory as the ideal function,
The second calculation means and the third calculation means perform calculation using a function obtained by frequency-converting the image enlarged on the second memory,
The third calculation means calculates an image obtained by compressing 2 × 2 pixels into one pixel in an image restored by inverse frequency conversion on the second memory as an original image of the subject. Item 5. The image processing apparatus according to Item 4. First function calculating means for calculating a first function by frequency-converting a blur function representing a one-dimensional or two-dimensional impulse response set based on measurement on a memory;
A second function calculating means for calculating a second function by performing frequency conversion on a memory of a delta function or an ideal function set in advance approximating the delta function;
A frequency interval different from the sign of the second function is selected in the first function, and the phase of the first function is changed to the phase of the second function by inverting the sign of the first function in the selected frequency interval. Phase inversion means for performing processing to match
Gain correction coefficient calculation means for calculating a gain correction coefficient as a result of dividing the second function by the first function with the sign inverted at a plurality of predetermined frequencies,
Reverse frequency conversion means for performing reverse frequency conversion of the gain correction coefficient;
Numerical conversion means for converting the inverse frequency converted gain correction coefficient into a numerical filter having a predetermined element size in real space;
A filter generation device comprising: