CN108022215B - Motion artifact elimination method based on data consistency and image artifact decomposition technology - Google Patents
Motion artifact elimination method based on data consistency and image artifact decomposition technology Download PDFInfo
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Abstract
The invention discloses a motion artifact eliminating method based on data consistency and image artifact decomposition technology, belonging to a medical image processing method, comprising the following steps: a) collecting multi-channel data; b) obtaining self-calibration data through multi-channel data to generate NkGroup convolution kernels based on data consistency; c) according to the NkForming convolution kernel, performing convolution on the collected multichannel data to obtain NkGrouping multi-channel data satisfying data consistency; d) from the acquired multi-channel data, and the newly generated NkAnd (4) grouping multi-channel data, and calculating a real image and an artifact. The invention does not depend on a specific scanning sequence, can be combined with various other artifact eliminating technologies, and has wide applicability; meanwhile, a data consistency method based on parallel imaging is adopted, so that the signal-to-noise ratio of the image can be well kept while the motion artifact is eliminated; in addition, the invention can decompose the image-artifact without depending on a specific motion model, and can stably and effectively eliminate various motion artifacts in clinical practice.
Description
Technical Field
The invention relates to a medical image processing method, in particular to a motion artifact eliminating method based on data consistency and an image artifact decomposition technology.
Background
The magnetic resonance imaging technique is a technique for performing imaging by utilizing a nuclear magnetic resonance phenomenon of hydrogen protons. Nuclei in the human body containing a single proton, such as the ubiquitous hydrogen nucleus, have a spin motion. The spin motion of the charged nuclei is physically similar to that of the individual small magnets, and the directional distribution of these small magnets is random without the influence of external conditions. When a human body is placed in an external magnetic field, the small magnets are rearranged according to the magnetic lines of the external magnetic field, specifically, the small magnets are arranged in two directions which are parallel or antiparallel to the magnetic lines of the external magnetic field, the direction which is parallel to the magnetic lines of the external magnetic field is called as a positive longitudinal axis, the direction which is antiparallel to the magnetic lines of the external magnetic field is called as a negative longitudinal axis, and the atomic nucleus only has a longitudinal magnetization component which has both a direction and an amplitude.
The magnetic resonance phenomenon is that nuclei in an external magnetic field are excited by Radio Frequency (RF) pulses of a specific Frequency, so that the spin axes of the nuclei deviate from the positive longitudinal axis or the negative longitudinal axis to generate resonance. After the spin axes of the excited nuclei are offset from the positive or negative longitudinal axis, the nuclei have a transverse magnetization component.
After the emission of the radio frequency pulse is stopped, the excited atomic nucleus emits an echo signal, absorbed energy is gradually released in the form of electromagnetic waves, the phase and the energy level of the electromagnetic waves are restored to the state before the excitation, and the image can be reconstructed by further processing the echo signal emitted by the atomic nucleus through space coding and the like.
In the magnetic resonance scanning imaging process, the patient often has autonomous or unconscious movement due to the long detection time. Such motion can cause blurring, artifacts, or image mismatch, which can affect the diagnosis of the patient by the physician. The article "Handbook of MRI pulse sequences" (Bernstein, M.A, King K.F., Xiaohong Joe Zhou) states that the elimination of motion artifacts is one of the major and technical challenges in the field of magnetic resonance imaging.
In order to circumvent, correct or eliminate motion-induced image quality degradation, there are basically two main strategies: prospective and retrospective motion correction techniques are disclosed by reduction motion artifacts in two-dimensional Fourier transform Imaging (MagReson Imaging 1986; 4: 359-376). In the prospective motion correction technology, a certain method, such as a navigation echo method, a respiration triggering method and the like, is used for monitoring the spatial position of an imaging part in real time, and the shape of a pulse sequence is changed in real time according to the detected spatial position information, so that the image error caused by the motion of an object is avoided as much as possible. The prospective motion correction method needs special hardware to support special position monitoring information, and the precision of the position monitoring information can have important influence on the motion correction effect; meanwhile, the correction effect of the non-rigid object motion, especially the high-order motion component, is not obvious enough.
Retrospective motion correction techniques, the motion location information of the object is also recorded by certain techniques, such as navigator echoes or gating triggering methods. But does not change the shape of the scan sequence in real time. Because the image of the object and the corresponding position information are recorded, the generated image can be post-processed, the motion information of the object is used for correcting the primarily generated image, and the image quality reduction caused by motion is eliminated.
Pipe proposed the PROPELLER (periodic Rotated overlaying parallel Lines with Enhanced Reconstruction) technique in 1999 J.G.Pipe. The technology is based on the data acquisition of K space at unequal intervals, and the data acquisition time is reduced, as shown in figure 1; estimating a motion form and correcting motion artifacts by utilizing over-sampled data of an overlapped area of a K space central data band; and converting the non-Cartesian data into Cartesian data by using a gridding algorithm, and performing inverse Fourier transform to finally generate a reconstructed image. The method has a remarkable effect on eliminating rigid motion artifacts, and has been successfully applied to cranial magnetic resonance imaging. However, this method is mainly directed to rigid moving objects, and the correction effect on the movement of non-rigid moving objects, such as abdominal, vascular fluctuation, swallowing, etc., is not obvious, and the over-sampling is necessary due to the requirement, so that the scanning time is prolonged.
In 1993, Qing-San Xiang et al proposed a method of eliminating motion artifacts by two scans using coherence of motion information. In this method, an image containing a motion artifact (hereinafter referred to as an acquired image) can be decomposed into a complex image containing no motion (hereinafter referred to as a target image) and a complex image containing only a motion artifact (hereinafter referred to as an artifact). In the two independent scanning processes, under the condition that the motion states of the scanning objects are consistent, the sequence of the K space (namely data space) of image acquisition is modified, so that after the two independent scanning processes, the phase of a complex image only containing a motion artifact caused by motion is changed, but a target image not containing the motion artifact has no influence, therefore, as long as the phase change of the artifact caused by the motion can be estimated, the size of the artifact and the size of the target image can be directly obtained by an analytical method.
The phase change of the artifact due to motion ranges between 0-2 pi for each pixel. The whole imaging range is divided into a plurality of small areas, the phase of each pixel in each small area is continuously adjusted, at the moment, the gradient energy corresponding to each small area is changed, and when the gradient energy of the area is minimum, the phase in the small area can be confirmed to be the most accurate. The artifact and the size of the target image can be directly obtained from the artifact phase value at this time. The method based on the image-artifact decomposition has the advantages that special hardware is not needed for detecting the motion condition of an imaged object, modeling of the motion form of the object is not needed, and both rigid motion and non-rigid motion can be applied; however, the method has too strict requirements on the form of motion, and the motion mode of the imaging object in two independent acquisitions is basically consistent, which is difficult to guarantee in practice; at the same time, this method requires changing the filling order of the K space (data space), which significantly changes the image contrast based on the echo train sequence.
The effect of the motion of the object in the final image can be specifically analyzed by the frequency of the motion. In theory, any one motion frequency introduces two symmetric artifacts in the image, whose positions in the image are determined by the frequency (effective motion frequency) of this motion in K-space (data space). Generally, the smaller the effective motion frequency, the less noticeable the dispersion of artifacts introduced by motion in the image, whereas the larger the effective motion frequency, the more noticeable the dispersion of artifacts introduced by motion in the image. The motion in clinical applications often contains multiple frequencies of motion, and the motion at each frequency may also enhance or cancel each other, eventually resulting in very complex artifact shapes. Although the actual motion frequency is complex, the effective motion frequency of the motion in the K space can be changed by changing the filling mode of the K space, so as to modify the display mode of the motion artifact in the image.
In 1985, Bailes et al proposed a "low frequency rearrangement" method in "rearranged phase encoding (ROPE) - -aggregate for reproducing rearrangement activities in MRimaging" (J.Comp.Asst.Tomogr.9: 835-838). In this method, signals with similar movement positions are arranged as close as possible in K-space, so that the effective movement frequency in K-space is very low. In this way, the motion-generated artifacts are limited to a small distance from the location where the motion occurs; in 1986, Haaceke et al proposed a "center rearrangement" method in "Reducing motion artifacts in two-dimensional Fourier transform Imaging (MagReson Imaging 1986; 4: 359-376)". The method acquires the central part of K space with the largest influence on the image contrast in the stationary phase of respiratory motion as much as possible, acquires the part with smaller influence on the contrast in the period with more motion, and simultaneously arranges signals with similar motion positions in the similar K space as much as possible. This method can provide a more stable motion suppression effect; in 1998, Jhooti et al proposed a "high frequency rearrangement" method in "Hybrid Ordered Phasing (HOPE): An improved approach for rearrangement efficiency reduction" (J.Magn.Reson. imaging 8: 968-. In this method, signals with widely differing motion positions are arranged as close as possible in K-space, so that the effective motion frequency in K-space is very high. In this way, motion-generated artifacts are spread out to a location that is far from the location where the motion occurs. These artifacts can be spread out of the object if a larger imaging field of view FOV is used. The above method based on K-space rearrangement can reduce the degree of artifacts to some extent, but cannot achieve the expected effect when the motion mode is not ideal, for example, the motion amplitude and frequency suddenly change.
Magnetic Resonance Imaging (MRI) is increasingly used to eliminate motion artifacts because of the direct relationship between the effect of motion on the image and the duration of motion, as disclosed in "Simultaneous acquisition of spatial harmonics (SMASH)" (MagnReson Med 1997; 38: 591-603) "," sensing coding for fast MRI "(MagnReson Med 1999; 42: 952-962)", "Generalized SMASH imaging" (MagnReson Med 2002; 47: 160-170) ", and the like. "Artifact reduction in moving-table acquisition using parallel imaging and multiple averaging" (MagReson Med 2007; 57: 226-. Under the condition of multi-channel phased array acquisition, the coding capability provided by a parallel imaging technology is considered, normally sampled data has a larger redundancy characteristic, and based on the characteristic, a plurality of schemes based on data consistency and data elimination are applied to the suppression and elimination of motion artifacts. In 2002, M.Bydder et al, at "Detection and subtraction of motion artifacts by regeneration of K-space" (MagnReson Med2002 Apr; 47(4):677-86), proposed a method for Detection and elimination of motion artifacts by K-space data regeneration techniques. The method divides the fully acquired K-space data into two parts of odd lines and even lines, and respectively carries out parallel imaging processing on the two parts. And respectively detecting the difference between the data acquired at the specific position and the data generated based on the parallel imaging, and determining whether the signal meets the requirement of overall consistency according to the difference, and determining whether the signal is rejected or retained. The method of SMASH Navigators DavidAtkinson, Mark Bydder, Joseph V.Hajnal, Derek Hill, David Larkman ISMRM2002p2395 adopts a parallel imaging technology of K space, and further expands the data consistency of signals. The method "CARE: Coil-based Artifact reduction ISMR M2004 exact number 96" uses an optimized objective function to describe the consistency of the signals. The method 'Data correlation and Combination Operation (COA) for movement of host images reduction' (MagnReson Med 2010; 64: 157-. The methods fully utilize the parallel imaging technology to ensure the consistency of the acquired data, but actually, the input data of the parallel imaging contains motion artifacts, so that the data consistency is poor; meanwhile, the judgment of data consistency needs a relatively stable reference object, and is difficult to obtain accurately in practice. Methods for eliminating motion artifacts based on data consistency still face many challenges for clinically realistic complex motion scenarios.
Disclosure of Invention
The invention aims to provide a method based on data consistency and image-artifact decomposition, on one hand, the method does not depend on a specific scanning sequence, can be combined with a plurality of other artifact elimination technologies, and has wide applicability; meanwhile, a data consistency method based on parallel imaging is adopted, so that the signal-to-noise ratio of the image can be well kept while the motion artifact is eliminated; finally, the invention decomposes the image-artifact without depending on a specific motion model, and can stably and effectively eliminate various motion artifacts in clinical practice.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses a motion artifact elimination method based on data consistency and image artifact decomposition technology, which comprises the following steps:
a) collecting multi-channel data A;
b) obtaining self-calibration data through multi-channel data to generate NkGroup convolution kernels based on data consistency;
c) according to the NkForming convolution kernels, and performing convolution on the acquired multichannel data A to obtain NkGrouping multi-channel data B satisfying data consistency;
d) based on the collected multi-channel data A and the newly generated NkMultiple with group satisfying data consistencyChannel data B, calculating a real image and an artifact;
in the step a), multichannel data A is acquired through a multichannel receiving coil, and the data size is represented as: n is a radical ofx*Ny*NcIn which N isxNumber of lines representing acquired data, NyNumber of columns representing data, NcRepresents the number of receiving channels;
in the step b), the self-calibration data size is represented as: n is a radical ofa*Ny*NcIn which N isaTo self-calibrate the width of the data, the default phase encoding direction is along the row direction, and the data-consistency-based convolution kernel is solved by the following equation
The size of each set of convolution kernels is a four-dimensional array: wx*Wy*Nc*NcRepresents NcA Wx*Wy*NcThree-dimensional convolution kernels, each channel corresponding to a three-dimensional convolution kernel, so that in general a four-dimensional convolution kernel,
wherein J represents the number of signals contained in the target convolution kernel, L represents the number of receive channels, Sl(kr) Represents the position k in the channel lrSignal strength of Sl′(kr-Δkj) Represents the position k in the channel lr-ΔkjSignal strength of, Δ kjIs a signal Sl′Relative to the signal SlOffset, convolution kernel weight in the receive channel
Is a weighting factor for channel l', S in equation (1)l(kr) And Sl′(kr-Δkj) Is a known amount;
in the step c), the acquired multichannel data A is substituted into the equation (1)The convolution of the rows is performed such that,
and Sl′(kr-Δkj) Calculating multi-channel data B meeting the data consistency for a known quantity through convolution calculation;
in the step d), the calculation is carried out by the following equation:
I′0＝I0+g0(2)
Is＝I0+gs,s＝1,2,...,k (3)
wherein, I0Representing complex images containing no artifacts, g0Represents an artifact due to motion, I'0Representing images containing motion artefacts after direct acquisition, gsIs an artifact processed by data consistency, IsIs data containing artifacts after being processed by data consistency,
is the response function of motion artifacts to a convolution kernel based on data consistency, AsIs amplitude, θsIs phase, is known
In the case of (2) to (4), the complex image I containing no artifact can be obtained by solving the equation system0The solution result is represented as (5).
Preferably, in the step d), before solving equation (5), the response function of the motion artifact corresponding to the convolution kernel needs to be determined, that is, the response function is
According to renAn input three-dimensional convolution kernel, i.e. Wx*Wy*NcThe corresponding response function calculation method is calculated by the following equation:
wherein W is Wx*Wy*NcThe IFFT stands for the inverse fourier transform operator.
Preferably, in the step d), in the process of solving the equation (5), when the condition number of the equation set is greater than 50, an image artifact removing step based on signal-to-noise ratio optimization and artifact minimization is added.
Further, the image artifact elimination based on signal-to-noise ratio optimization and artifact minimization: limiting solution IcIs calculated from the following equation:
wherein, IcIs based on an image with optimal signal-to-noise ratio and minimized artifacts, IiIs the ith multi-channel data generated based on data consistency, WiIs the weight of the ith data,
is the standard deviation over a range around the pixel location in the image.
Further, an iterative process is added, namely newly generated multi-channel data is regarded as acquired data, and the processes b), c) and d) are executed again, so that the suppression of the artifacts is gradually converged.
The purpose of generating multiple sets of data satisfying data consistency from input raw data is multifaceted. On the one hand, the motion modulation artifacts contained in the newly generated data based on the data consistency are different, and these differences are due to the particularity of the motion artifacts and cannot be predicted in advance; second, the multiple sets of data themselves impose data consistency, and therefore, the effects of motion artifacts are relatively reduced relative to the originally acquired data (since motion-induced artifacts tend to not satisfy data consistency, but are suppressed during regeneration). Therefore, data generating methods satisfying data consistency may be included, such as SENSE, GRAPPA, SPIRiT, and the like.
Equations (2) - (4) are a set of over-determined equations that can be solved using a variety of methods, such as the generalized inverse matrix method, the conjugate iteration method, etc. Meanwhile, the characteristics of newly generated data meeting data consistency are considered, and certain limitation can be better made on the final solution. The solution of the constraint solution is a multi-group data synthesis based on the region variance. The reason why the region variance is adopted as the determination weight is that the variance of data with physically large artifacts or noise is necessarily large, and therefore, a smaller weight should be given; while data with less artifacts or noise, whose variance is necessarily smaller, should be given more weight. Similarly, other calculations for determining weights based on the amount of data of image features may be employed, such as the total variation or entropy of the image, etc.
The invention has the following beneficial effects:
1. the invention does not depend on a specific scanning sequence and a specific reconstruction method, so the method has wide applicability and can be combined with various clinical scanning sequences and specific reconstruction methods;
2. the method generates the final image based on the data consistency, can better inhibit the motion artifact, and better ensures the signal-to-noise ratio of the final image;
3. the method does not depend on a specific motion model for image-artifact decomposition, and can be suitable for rigid and non-rigid motion and high-order motion modes, so that the motion artifact under clinically variable scanning conditions can be stably and effectively eliminated.
4. By the iterative process, the suppression of the artifact can be gradually converged.
Drawings
FIG. 1 is a schematic diagram of a K-space-based unequal interval data acquisition with reduced data acquisition time;
FIG. 2 is a flow chart of a method for motion artifact removal based on data consistency and ghost removal;
FIG. 3 is an image synthesis based on signal-to-noise optimization and artifact minimization;
in fig. 1, M0(K) represents the object offset position corresponding to the K-space acquisition line, the horizontal axis represents the acquisition position of K-space, and the vertical axis represents the object offset position corresponding to the time of acquiring the K-space data; m1(K) represents the object offset position corresponding to the K space acquisition line after convolution processing;
in FIG. 3, the size of the region is Kr*KrFor determining the weight W of the position of the black dot in the areaiSelecting all points in the region, and determining the standard deviation of the points
Substituting into equations (7) and (8).
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings.
As shown in fig. 2, the method for eliminating motion artifacts based on data consistency and image artifact decomposition technique according to the present invention comprises the following steps:
a) multi-channel data is collected. And receiving data by adopting a multi-channel receiving coil. The sample data may come from a variety of scan sequences. The data size may be expressed as: n is a radical ofx*Ny*Nc. Wherein N isxNumber of lines representing acquired data, NyNumber of columns representing data, NcRepresenting the number of receive channels. As shown in fig. 1M0(K), due to the motion of the object, the offset position of the object changes during the K-space data acquisition, which is equivalent to the modulation of the motion of the data in K-space, which is the root cause of the motion artifact that eventually appears in the image.
b) Based onGenerating N self-calibration data from the multi-channel datakThe groups are based on a convolution kernel of data consistency.
The self-calibration data is from the central position of the multi-channel data collected in the above steps, and the data size can be expressed as: n is a radical ofa*Ny*Nc. Wherein N isaTo self-calibrate the width of the data, the default phase encoding direction is along the row direction. The convolution kernel based on data consistency can be solved by the following equation:
wherein J represents the number of signals contained in the target convolution kernel, L represents the number of receive channels, Sl(kr) Represents the position k in the channel lrSignal strength of Sl′(kr-Δkj) Represents the position k in the channel lr-ΔkjSignal strength of, Δ kjIs a signal Sl′Relative to the signal SlOffset, convolution kernel weight in the receive channel
Is the weighting factor for channel l'. Each set of convolution kernels
The size of (d) is a four-dimensional array: wx*Wy*Nc*Nc。
In this step, S in equation (1)l(kr) And Sl′(kr-Δkj) Considered as a known quantity, a convolution kernel
The convolution kernel can be calculated for the unknown quantity by solving the linear equation above.
c) According to the NkForming convolution kernel, performing convolution on the collected multichannel data to obtain NkThe group satisfies the multi-channel data of data consistency. GeneratingThe method of satisfying data consistency still satisfies equation (1) above. In this step, the process is carried out,
and Sl′(kr-Δkj) All the data are known quantities, and multi-channel data meeting the data consistency can be obtained through convolution calculation.
d) From the acquired multi-channel data, and the newly generated NkThe real image and artifact are calculated by combining multi-channel data, and the following equations can be used for calculation:
I′0＝I0+g0(2)
Is＝I0+gs,s＝1,2,...,k (3)
wherein, I0Representing complex images containing no artifacts, g0Represents an artifact due to motion, I'0Representing images containing motion artefacts after direct acquisition, gsIs an artifact processed by data consistency, IsIs data containing artifacts after being processed by data consistency,
is the response function of motion artifacts to a convolution kernel based on data consistency, AsIs amplitude, θsIs the phase. In the prior art are known
In the case of (2) to (4), the complex image I containing no artifact can be obtained by solving the equation system0. The solution results are expressed as follows:
e) before solving the above equation, it is necessary to determine the response function of the motion artifact corresponding to the convolution kernel,namely, it is
According to any input three-dimensional convolution kernel, the corresponding response function calculation method can be calculated by the following equation:
wherein W is a size of Wx*Wy*NcThe IFFT stands for the inverse fourier transform operator.
f) Image artifact removal based on signal-to-noise optimization and artifact minimization. In the process of solving the equation set (5), if the condition number of the equation set is greater than 50, the matrix is close to the singular matrix, and the solved result has larger deviation. Therefore, the obtained result needs to be limited. Limiting solution IcCan be calculated using the following equation:
wherein, IcIs based on an image with optimal signal-to-noise ratio and minimized artifacts, IiIs the ith multi-channel data generated based on data consistency, WiIs the weight of the ith data,
is the standard deviation over a range around the pixel location in the image.
g) In the process of solving the synthesis of the multiple groups of images, S groups with the size of N are inputx*Ny*NcThe output is a set of size Nx*Ny*NcThe image of (2). Wherein, each pixel after synthesis has a component from the S-set result, and the size of the component is from the weight size in the synthesis formula (7). As shown in fig. 3, for each input image pixelWeight, dependent on the variance of the image in the area around the pixel: the larger the variance is, the smaller the corresponding weight is, and the smaller the variance is, the larger the corresponding weight is. The physical significance of the synthesis method is that when an input image region contains more artifacts or noises, the variance of the image region is larger, and the image region should have smaller weight; conversely, when an input image region contains less artifacts or noise, the variance of the image region is smaller, and the input image region should have a larger weight. In this solution, the artifacts and various signal noises caused by the motion are treated equally and can be optimized simultaneously.
In the above-mentioned steps f) -g), in the multi-group image synthesis method based on region support, Kr*KrThe constructed region forms a support region for the center point of the region, and the variance of the image of the region determines the weighting required in the synthesis process.
h) And (3) adding an iterative process, namely considering newly generated multi-channel data as acquired data, and re-executing the processes from b) to g), wherein the suppression of the artifact is gradually converged.
The present invention is capable of other embodiments, and various changes and modifications may be made by one skilled in the art without departing from the spirit and scope of the invention.
Claims (5)
1. A motion artifact elimination method based on data consistency and image artifact decomposition technology is characterized by comprising the following steps:
a) collecting multi-channel data A;
b) obtaining self-calibration data through multi-channel data to generate NkGroup convolution kernels based on data consistency;
c) according to the NkForming convolution kernels, and performing convolution on the acquired multichannel data A to obtain NkGrouping multi-channel data B satisfying data consistency;
d) based on the collected multi-channel data A and the newly generated NkGroup satisfaction data consistencyCalculating a real image and an artifact by using the multi-channel data B;
in the step a), multichannel data A is acquired through a multichannel receiving coil, and the data size is represented as: n is a radical ofx*Ny*NcIn which N isxNumber of lines representing acquired data, NyNumber of columns representing data, NcRepresents the number of receiving channels;
in the step b), the self-calibration data size is represented as: n is a radical ofa*Ny*NcIn which N isaTo self-calibrate the width of the data, the default phase encoding direction is along the row direction, and the data-consistency-based convolution kernel is solved by the following equation
The size of each set of convolution kernels is a four-dimensional array: wx*Wy*Nc*Nc，
Wherein J represents the number of signals contained in the target convolution kernel, L represents the number of receive channels, Sl(kr) Represents the position k in the channel lrSignal strength of Sl′(kr-Δkj) Represents the position k in the channel lr-ΔkjSignal strength of, Δ kjIs a signal Sl′Relative to the signal SlOffset, convolution kernel weight in the receive channel
Is a weighting factor for channel l', S in equation (1)l(kr) And Sl′(kr-Δkj) Is a known amount;
in the step c), the collected multichannel data A is substituted into equation (1) for convolution,
and Sl′(kr-Δkj) Calculating multi-channel data B meeting the data consistency for a known quantity through convolution calculation;
in the step d), the calculation is carried out by the following equation:
I′0＝I0+g0(2)
Is＝I0+gs,s＝1,2,...,k (3)
wherein, I0Representing complex images containing no artifacts, g0Represents an artifact due to motion, I'0Representing images containing motion artefacts after direct acquisition, gsIs an artifact processed by data consistency, IsIs data containing artifacts after being processed by data consistency,
is the response function of motion artifacts to a convolution kernel based on data consistency, AsIs amplitude, θsIs phase, is known
In the case of (2) to (4), the complex image I containing no artifact can be obtained by solving the equation system0The solution result is represented as (5).
2. The method of claim 1, wherein the motion artifact removal method is based on data consistency and image artifact decomposition techniques, and wherein:
in said step d), before solving equation (5), it is necessary to determine the response function of the motion artifact corresponding to the convolution kernel, i.e.
According to any input three-dimensional convolution kernel, the corresponding response function calculation method is calculated by the following equation:
wherein W is Wx*Wy*NcThe IFFT stands for the inverse fourier transform operator.
3. The method of claim 1, wherein the motion artifact removal method is based on data consistency and image artifact decomposition techniques, and wherein: in the step d), in the process of solving the equation (5), when the condition number of the equation system is more than 50, an image artifact eliminating step based on signal-to-noise ratio optimization and artifact minimization is added.
4. The method of claim 3 for motion artifact removal based on data consistency and image artifact decomposition techniques, wherein: the image artifact elimination based on signal-to-noise ratio optimization and artifact minimization comprises the following steps: limiting solution IcIs calculated from the following equation:
wherein, IcIs based on an image with optimal signal-to-noise ratio and minimized artifacts, IiIs the ith multi-channel data generated based on data consistency, WiIs the weight of the ith data,
is the standard deviation over a range around the pixel location in the image.
5. The method of any of claims 1-4 for motion artifact removal based on data consistency and image artifact decomposition techniques, wherein: and (4) adding an iterative process, namely considering newly generated multi-channel data as acquired data, and re-executing the processes b), c) and d), so that the suppression of the artifact is gradually converged.
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