A method and system for motion correction in quantitative magnetic resonance imaging based on dictionary matching

Abstract

This invention provides a method and system for motion correction in quantitative magnetic resonance imaging (MRI) based on dictionary matching, comprising: Step S1: generating a dictionary by simulating the evolution of the MRI signal and constructing an optimization problem to be solved; Step S2: performing dictionary matching on the acquired quantitative imaging image sequence to obtain a parameter map and a simulated image sequence; Step S3: registering the acquired image sequence to the simulated image sequence to correct motion; alternately executing steps S2 and S3 to solve the optimization problem until convergence, obtaining the motion-corrected image sequence and parameter map. This invention models the contrast changes of the quantitative imaging image sequence based on MRI physics, thus being more accurate and robust than methods based on image characteristics.

Description

Technical Field

[0001] This invention relates to the field of medical image processing, and more specifically, to a method and system for motion correction in quantitative magnetic resonance imaging based on dictionary matching. Background Technology

[0002] Quantitative magnetic resonance imaging (MMRI) diagnoses and assesses related diseases by quantitatively measuring magnetic resonance parameters such as T1 and T2 in physiological tissues. Compared to traditional contrast-weighted imaging, it is more objective and accurate, and its clinical application is gradually increasing. Commonly used MMRI techniques include: longitudinal relaxation time T1 quantitative imaging, transverse relaxation time T2 quantitative imaging, and apparent transverse relaxation time... Quantitative imaging, multi-parameter magnetic resonance imaging (MRI) fingerprinting, etc. Especially in MRI applications of organs such as the heart and brain, quantitative imaging has gradually become the gold standard.

[0003] Quantitative magnetic resonance imaging (MMRI) requires acquiring a series of weighted images at different time points, and then estimating the parameter values ​​(e.g., T1, T2, ...) at each pixel through pixel-by-pixel curve fitting or dictionary matching. (value), and then form a parameter map. To ensure the accuracy of parameter estimation, each frame of image should be aligned with each other, that is, each pixel should correspond to the same tissue at different time points. However, different images often have motion caused by various factors, which leads to a decrease in quantitative accuracy. For example, in the heart, due to some subjects not holding their breath strictly or having arrhythmia, there are often breathing or heartbeat movements in the actual collected image sequence. Therefore, before estimating the parameter map, it is necessary to perform motion correction or registration on the image sequence. The main difficulties of motion correction in quantitative magnetic resonance imaging include: (1) The contrast difference between each frame of image is very large, and even the contrast of each tissue may be reversed, so that conventional mean square error, normalized mutual information, etc. cannot be used as the difference measure of the registration algorithm. (2) It involves multiple frames of images. If the conventional pairwise registration algorithm is used, the result is greatly affected by the selection of reference images and is not stable enough. In contrast, the groupwise registration algorithm that registers all images at once is more reasonable, but this will increase the difficulty of algorithm design. (3) Because the contrast mechanisms of different quantitative imaging tasks are different, the appearance differences between the acquired images are obvious. Therefore, the method designed for one task is usually not easy to extend to another task.

[0004] Existing motion correction methods for quantitative magnetic resonance imaging (MRI) can be broadly categorized into three types: image characteristic-based methods, curve fitting-based methods, and tissue segmentation-assisted registration methods. Image characteristic-based methods mostly utilize the inherent characteristics of the quantitative imaging image sequence itself to design a difference measure. Representative methods include: pairwise registration algorithms based on normalized image gradient fields, pairwise registration algorithms based on local cross-correlation, group registration algorithms based on principal component analysis, and group registration algorithms based on total correlation. Another type of image characteristic-based method first reduces contrast differences between images through preprocessing techniques such as histogram matching, and then uses conventional mean square error or mutual information as a difference measure for registration. Image characteristic-based methods start from the inherent characteristics of the image itself, so they have a wide range of applications and generally high computational efficiency. However, these methods often make overly simplistic assumptions and do not delve deeply into the physical mechanisms of contrast generation, thus lacking accuracy, especially when contrast changes significantly. In contrast, curve fitting-based methods accurately model contrast changes through the relaxation equations of the magnetic resonance signal. These methods generate a sequence of simulated images with the same contrast as the real images but without motion by performing pixel-by-pixel curve fitting. Then, they correct for breathing or heartbeat movements in the simulated images by registering the real image sequence to the simulated image sequence, thus avoiding direct registration of images with different contrasts. Curve fitting and image registration are performed alternately until convergence, ultimately producing a motion-corrected image sequence and parametric map. Because each frame of the simulated image is determined by all the real images, the deformation of each real image is affected by all the other real images. Therefore, curve fitting-based methods are essentially group registration methods and do not require a pre-specified reference image. However, curve fitting-based methods require alternating curve fitting and image registration, resulting in relatively low computational efficiency, with curve fitting consuming the majority of the time. Furthermore, these methods are not suitable for tasks where relaxation equations are difficult to analyze or fit, such as multi-parameter imaging with complex relaxation equations, like magnetic resonance fingerprinting. Unlike the previous two types of methods, tissue segmentation-based methods first segment the tissue of interest from each frame of images and then indirectly align the images by aligning the segmented tissue labels. However, these methods also have significant drawbacks. First, in images at certain time points, the contrast between different tissues is very weak, making it difficult to accurately segment the tissue of interest from these images. Second, these methods can only guarantee that each frame of the image is aligned at the tissue edges, but cannot guarantee that it is aligned within the tissue itself, so the correction results are not reliable enough for quantitative analysis of the tissue interior. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for motion correction in quantitative magnetic resonance imaging based on dictionary matching.

[0006] A method for motion correction in quantitative magnetic resonance imaging based on dictionary matching, according to the present invention, includes:

[0007] Step S1: Generate a dictionary by simulating the evolution of the magnetic resonance signal and construct the optimization problem to be solved;

[0008] Step S2: Perform dictionary matching on the acquired quantitative imaging image sequence to obtain the parameter map and the simulation image sequence;

[0009] Step S3: Register the acquired image sequence to the simulated image sequence and correct for motion;

[0010] Alternately execute steps S2 and S3 to solve the optimization problem until convergence, and obtain the motion-corrected image sequence and parameter map.

[0011] Preferably, in step S1:

[0012] f(x,t) is the sequence of quantitative imaging images acquired; where x∈Ω is the spatial coordinate of an image pixel, Ω is the set of spatial coordinates of all image pixels, t∈Τ is the time point of image acquisition, and Τ is the set of all image acquisition time points;

[0013] The evolution of magnetic resonance signals is simulated using analytical methods, Bloch equation simulation, or EPG simulation, and a dictionary is generated, denoted as...

[0014]

[0015] Where |Τ| is the number of image acquisition time points, i.e. the number of frames in the image sequence, and N is the number of parameter values. For multi-parameter imaging, the parameter values ​​are combinations of parameter values. D is the set of real numbers; each row of D corresponds to a time point of image acquisition, and each entry d in D... n It involves sampling the simulated signal at a given time point, and each sample corresponds to a parameter; normalization is performed on each entry in the dictionary, letting:

[0016] d n ←d n / ||d n ||2,n=1,2,…,N. (2)

[0017] Where ||·||2 is the l2 norm of the vector; motion correction is achieved by solving the following optimization problem:

[0018]

[0019] in, Let θ be the sparse coding of the image signal at pixel x, where θ is a vector containing all the parameters controlling image deformation. Let x be the image signal at position x after deformation, R(θ) be the regularization term constraining the image deformation, and ||·||0 be the l0 norm of the vector, defined as the number of non-zero elements in the vector.

[0020] Preferably, in step S2:

[0021] Solving for θ in fixed problem (3):

[0022]

[0023] The sparse coding α(x) at each pixel is independent of each other. It is solved pixel by pixel. For any given x∈Ω, the solution is:

[0024]

[0025] Optimal solution α * (x) Analytical expression, the image signal f at x θ (x,:) and each entry d in the dictionary n Perform Euclidean inner products for each entry, and denote the entry with the smallest number among those with the largest inner product value as n. * (x), that is:

[0026]

[0027] Where <·,·> is the Euclidean inner product between vectors;

[0028]

[0029] Among them, [α] * (x)] n For α * The nth component of (x), formulas (6) and (7) show that solving problem (4) involves pixel-wise dictionary matching. Based on the result of the dictionary matching, the parameter value at x is the entry. The corresponding parameter values ​​form a parameter graph; Dα * (x) is f θ (x,:) is a sparse approximation with respect to dictionary D; since Dα * (x) The image signal at each pixel corresponds to an entry in dictionary D, so Dα * (x) and f θ The contrast variation of (x,:) remains consistent; due to Dα * Each frame of (x) is generated based on the same parametric map and does not contain motion; f θ (x,:) represents the real image sequence, and Dα * (x) is f θ Simulated image sequence of (x,:).

[0030] Preferably, in step S3:

[0031] Given a fixed α in problem (3), solve:

[0032]

[0033] Solve problem (8) using the real image sequence f θ (x,:) is registered to the simulated image sequence Dα(x). Since the contrast changes of the two image sequences are consistent, the mean square error is used as the measure of difference. The displacement field determined by the deformation parameter θ is d. θ (x,t), and denote the set of all θs that satisfy the condition that the displacement field has zero mean in the time dimension as:

[0034]

[0035] The regularization term R(θ) constraining image deformation consists of two parts, expressed as:

[0036] R(θ)=δ Θ (θ)+λR smooth (θ). (10)

[0037] Where, δ Θ (θ) is an indicator function with respect to the set Θ, R smooth (θ) represents the spatial smoothing regularization term applied to each frame of the image, and λ is the regularization coefficient used to control the degree of smoothing; when θ∈Θ, δ Θ (θ) = 0; when At that time, δ Θ (θ)=+∞,δ Θ (θ) requires the displacement field d θ The mean of (x,t) in the time dimension is zero to ensure that each frame is registered to an average coordinate system; R smooth (θ) is a regularization term based on the first or second order difference of the displacement field, including the first order diffusion regularization term and the second order thin plate bending energy. The optimal deformation parameter θ is obtained by iteratively solving the problem (8) based on the optimization algorithm. * The optimization algorithms include gradient descent, conjugate gradient, and LBFGS.

[0038] Preferably, steps S2 and S3 are alternately executed to solve problem (3) until convergence, resulting in a motion-corrected image sequence and parameter map. The convergence condition is that the relative change of the loss function in problem (3) is less than a given threshold, or the algorithm reaches the maximum number of pre-set alternations. A coarse-to-fine multi-resolution optimization framework is used to first correct the lower resolution image, and then use the obtained deformation parameters to initialize the higher resolution correction. The algorithm first generates global deformation at low resolution to roughly align the target, and generates local deformation at high resolution for adjustment.

[0039] A dictionary-matching-based motion correction system for quantitative magnetic resonance imaging according to the present invention includes:

[0040] Module M1: Generates a dictionary by simulating the evolution of magnetic resonance signals and constructs the optimization problem to be solved;

[0041] Module M2: Performs dictionary matching on the acquired quantitative imaging image sequence to obtain the parameter map and the simulation image sequence;

[0042] Module M3: Registers the acquired image sequence to the simulated image sequence and corrects motion;

[0043] The optimization problem is solved by alternately executing modules M2 and M3 until convergence, resulting in a motion-corrected image sequence and parametric map.

[0044] Preferably, in module M1:

[0045] f(x,t) is the sequence of quantitative imaging images acquired; where x∈Ω is the spatial coordinate of an image pixel, Ω is the set of spatial coordinates of all image pixels, t∈Τ is the time point of image acquisition, and Τ is the set of all image acquisition time points;

[0046] The evolution of magnetic resonance signals is simulated using analytical methods, Bloch equation simulation, or EPG simulation, and a dictionary is generated, denoted as...

[0047]

[0048] Where |Τ| is the number of image acquisition time points, i.e. the number of frames in the image sequence, and N is the number of parameter values. For multi-parameter imaging, the parameter values ​​are combinations of parameter values. D is the set of real numbers; each row of D corresponds to a time point of image acquisition, and each entry d in D... n It involves sampling the simulated signal at a given time point, and each sample corresponds to a parameter; normalization is performed on each entry in the dictionary, letting:

[0049] d n ←d n / ||d n ||2,n=1,2,…,N. (2)

[0050] Where ||·||2 is the l2 norm of the vector; motion correction is achieved by solving the following optimization problem:

[0051]

[0052] in, Let θ be the sparse coding of the image signal at pixel x, where θ is a vector containing all the parameters controlling image deformation. Let x be the image signal at position x after deformation, R(θ) be the regularization term constraining the image deformation, and ||·||0 be the l0 norm of the vector, defined as the number of non-zero elements in the vector.

[0053] Preferably, in module M2:

[0054] Solving for θ in fixed problem (3):

[0055]

[0056] The sparse coding α(x) at each pixel is independent of each other. It is solved pixel by pixel. For any given x∈Ω, the solution is:

[0057]

[0058] Optimal solution α * (x) Analytical expression, the image signal f at x θ (x,:) and each entry d in the dictionary n Perform Euclidean inner products for each entry, and denote the entry with the smallest number among those with the largest inner product value as n. * (x), that is:

[0059]

[0060] Where <·,·> is the Euclidean inner product between vectors;

[0061]

[0062] Among them, [α] * (x)] n For α * The nth component of (x), formulas (6) and (7) show that solving problem (4) involves pixel-wise dictionary matching. Based on the result of the dictionary matching, the parameter value at x is the entry. The corresponding parameter values ​​form a parameter graph; Dα * (x) is f θ (x,:) is a sparse approximation with respect to dictionary D; since Dα * (x) The image signal at each pixel corresponds to an entry in dictionary D, so Dα * (x) and f θ The contrast variation of (x,:) remains consistent; due to Dα * Each frame of (x) is generated based on the same parametric map and does not contain motion; f θ (x,:) represents the real image sequence, and Dα * (x) is fθ Simulated image sequence of (x,:).

[0063] Preferably, in module M3:

[0064] Given a fixed α in problem (3), solve:

[0065]

[0066] Solve problem (8) using the real image sequence f θ (x,:) is registered to the simulated image sequence Dα(x). Since the contrast changes of the two image sequences are consistent, the mean square error is used as the measure of difference. The displacement field determined by the deformation parameter θ is d. θ (x,t), and denote the set of all θs that satisfy the condition that the displacement field has zero mean in the time dimension as:

[0067]

[0068] The regularization term R(θ) constraining image deformation consists of two parts, expressed as:

[0069] R(θ)=δ Θ (θ)+λR smooth (θ). (10)

[0070] Where, δ Θ (θ) is an indicator function with respect to the set Θ, R smooth (θ) represents the spatial smoothing regularization term applied to each frame of the image, and λ is the regularization coefficient used to control the degree of smoothing; when θ∈Θ, δ Θ (θ) = 0; when At that time, δ Θ (θ)=+∞,δ Θ (θ) requires the displacement field d θ The mean of (x,t) in the time dimension is zero to ensure that each frame is registered to an average coordinate system; R smooth (θ) is a regularization term based on the first or second order difference of the displacement field, including the first order diffusion regularization term and the second order thin plate bending energy. The optimal deformation parameter θ is obtained by iteratively solving the problem (8) based on the optimization algorithm. * The optimization algorithms include gradient descent, conjugate gradient, and LBFGS.

[0071] Preferably, module M2 and module M3 are alternately executed to solve problem (3) until convergence, and the motion-corrected image sequence and parameter map are obtained. The convergence condition is that the relative change of the loss function in problem (3) is less than a given threshold, or the algorithm reaches the maximum number of pre-set alternations. A coarse-to-fine multi-resolution optimization framework is used to first correct the lower resolution image, and then use the obtained deformation parameters to initialize the higher resolution correction. The algorithm first generates global deformation at low resolution to roughly align the target, and generates local deformation at high resolution for adjustment.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] 1. This invention is based on magnetic resonance physics modeling to quantitatively model the contrast changes of imaging image sequences, so it is more accurate and robust than methods based on image characteristics.

[0074] 2. This invention generates simulated image sequences and parameter maps based on dictionary matching, which is more efficient than curve fitting-based methods and is suitable for tasks where signal relaxation equations are difficult to analyze or fit.

[0075] 3. This invention alternates between dictionary matching and image registration, which is equivalent to alternately solving an optimization problem. Therefore, it is not only intuitive but also has a rigorous mathematical basis. Attached Figure Description

[0076] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0077] Figure 1 A flowchart of motion correction for quantitative magnetic resonance imaging based on dictionary matching, according to an embodiment of the present invention;

[0078] Figure 2 This is a schematic diagram illustrating the motion correction principle of quantitative magnetic resonance imaging based on dictionary matching in this invention.

[0079] Figure 3 This is a schematic diagram of motion correction results for T2 quantitative cardiac magnetic resonance imaging based on dictionary matching, according to an embodiment of the present invention.

[0080] Figure 4 This is a schematic diagram of motion correction results for cardiac magnetic resonance T1 quantitative imaging based on dictionary matching, according to an embodiment of the present invention. Detailed Implementation

[0081] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0082] Example 1:

[0083] To address the limitations of existing methods, this invention proposes a dictionary-matching-based motion correction method for quantitative magnetic resonance imaging (MRI). This method generates a dictionary by simulating the evolution of the MRI signal and models contrast changes accordingly, thus achieving higher accuracy than image-characteristic-based methods. Furthermore, compared to curve fitting, dictionary matching is not only more computationally efficient but also applicable to tasks where relaxation equations are difficult to analyze or fit, such as MRI fingerprinting. Therefore, this method is more practical and general than curve fitting-based methods. This invention discloses a dictionary-matching-based motion correction method and system for quantitative magnetic resonance imaging (MRI), comprising: Step S1: Generating a dictionary by simulating the evolution of the MRI signal and constructing an optimization problem to be solved. Step S2: Performing dictionary matching on the acquired quantitative imaging image sequence to obtain a parameter map and a simulated image sequence. Step S3: Registering the acquired image sequence to the simulated image sequence to correct motion in the former. Step S4: Solving the optimization problem in S1 by alternately executing S2 and S3 until convergence, obtaining the motion-corrected image sequence and parameter map.

[0084] According to the present invention, a motion correction method for quantitative magnetic resonance imaging based on dictionary matching is provided, such as... Figures 1-2 As shown, it includes:

[0085] Step S1: Generate a dictionary by simulating the evolution of the magnetic resonance signal and construct the optimization problem to be solved;

[0086] Specifically, in step S1:

[0087] f(x,t) is the sequence of quantitative imaging images acquired; where x∈Ω is the spatial coordinate of an image pixel, Ω is the set of spatial coordinates of all image pixels, t∈Τ is the time point of image acquisition, and Τ is the set of all image acquisition time points;

[0088] The evolution of magnetic resonance signals is simulated using analytical methods, Bloch equation simulation, or EPG simulation, and a dictionary is generated, denoted as...

[0089]

[0090] Where |Τ| is the number of image acquisition time points, i.e. the number of frames in the image sequence, and N is the number of parameter values. For multi-parameter imaging, the parameter values ​​are combinations of parameter values. D is the set of real numbers; each row of D corresponds to a time point of image acquisition, and each entry d in D... n It involves sampling the simulated signal at a given time point, and each sample corresponds to a parameter; normalization is performed on each entry in the dictionary, letting:

[0091] d n ←d n / ||d n ||2,n=1,2,…,N. (2)

[0092] Where ||·||2 is the l2 norm of the vector; motion correction is achieved by solving the following optimization problem:

[0093]

[0094] in, Let θ be the sparse coding of the image signal at pixel x, where θ is a vector containing all the parameters controlling image deformation. Let x be the image signal at position x after deformation, R(θ) be the regularization term constraining the image deformation, and ||·||0 be the l0 norm of the vector, defined as the number of non-zero elements in the vector.

[0095] Step S2: Perform dictionary matching on the acquired quantitative imaging image sequence to obtain the parameter map and the simulation image sequence;

[0096] Specifically, in step S2:

[0097] Solving for θ in fixed problem (3):

[0098]

[0099] The sparse coding α(x) at each pixel is independent of each other. It is solved pixel by pixel. For any given x∈Ω, the solution is:

[0100]

[0101] Optimal solution α * (x) Analytical expression, the image signal f at x θ (x,:) and each entry d in the dictionary n Perform Euclidean inner products for each entry, and denote the entry with the smallest number among those with the largest inner product value as n. * (x), that is:

[0102]

[0103] Where <·,·> is the Euclidean inner product between vectors;

[0104]

[0105] Among them, [α] * (x)] n For α * The nth component of (x), formulas (6) and (7) show that solving problem (4) involves pixel-wise dictionary matching. Based on the result of the dictionary matching, the parameter value at x is the entry. The corresponding parameter values ​​form a parameter graph; Dα * (x) is f θ (x,:) is a sparse approximation with respect to dictionary D; since Dα * (x) The image signal at each pixel corresponds to an entry in dictionary D, so Dα * (x) and f θ The contrast variation of (x,:) remains consistent; due to Dα * Each frame of (x) is generated based on the same parametric map and does not contain motion; f θ (x,:) represents the real image sequence, and Dα * (x) is f θ Simulated image sequence of (x,:).

[0106] Step S3: Register the acquired image sequence to the simulated image sequence and correct for motion;

[0107] Specifically, in step S3:

[0108] Given a fixed α in problem (3), solve:

[0109]

[0110] Solve problem (8) using the real image sequence f θ (x,:) is registered to the simulated image sequence Dα(x). Since the contrast changes of the two image sequences are consistent, the mean square error is used as the measure of difference. The displacement field determined by the deformation parameter θ is d. θ (x,t), and denote the set of all θs that satisfy the condition that the displacement field has zero mean in the time dimension as:

[0111]

[0112] The regularization term R(θ) constraining image deformation consists of two parts, expressed as:

[0113] R(θ)=δ Θ (θ)+λR smooth (θ). (10)

[0114] Where, δ Θ (θ) is an indicator function with respect to the set Θ, R smooth (θ) represents the spatial smoothing regularization term applied to each frame of the image, and λ is the regularization coefficient used to control the degree of smoothing; when θ∈Θ, δ Θ (θ) = 0; when At that time, δ Θ (θ)=+∞,δ Θ (θ) requires the displacement field d θ The mean of (x,t) in the time dimension is zero to ensure that each frame is registered to an average coordinate system; R smooth (θ) is a regularization term based on the first or second order difference of the displacement field, including the first order diffusion regularization term and the second order thin plate bending energy. The optimal deformation parameter θ is obtained by iteratively solving the problem (8) based on the optimization algorithm. * The optimization algorithms include gradient descent, conjugate gradient, and LBFGS.

[0115] Specifically, steps S2 and S3 are executed alternately to solve problem (3) until convergence, resulting in a motion-corrected image sequence and parameter map. The convergence condition is that the relative change of the loss function in problem (3) is less than a given threshold, or the algorithm reaches the maximum number of pre-set alternations. A coarse-to-fine multi-resolution optimization framework is used to first correct the lower resolution image, and then the obtained deformation parameters are used to initialize the higher resolution correction. The algorithm first generates global deformation at low resolution to roughly align the target, and then generates local deformation at high resolution for adjustment.

[0116] Alternately execute steps S2 and S3 to solve the optimization problem until convergence, and obtain the motion-corrected image sequence and parameter map.

[0117] Example 2:

[0118] Example 2 is a preferred embodiment of Example 1, and is used to illustrate the present invention in more detail.

[0119] The present invention also provides a dictionary-matching-based motion correction system for quantitative magnetic resonance imaging (QMRI). The dictionary-matching-based QMRI motion correction system can be implemented by executing the process steps of the dictionary-matching-based QMRI motion correction method. That is, those skilled in the art can understand the dictionary-matching-based QMRI motion correction method as a preferred embodiment of the dictionary-matching-based QMRI motion correction system.

[0120] A dictionary-matching-based motion correction system for quantitative magnetic resonance imaging according to the present invention includes:

[0121] Module M1: Generates a dictionary by simulating the evolution of magnetic resonance signals and constructs the optimization problem to be solved;

[0122] Specifically, in module M1:

[0123] f(x,t) is the sequence of quantitative imaging images acquired; where x∈Ω is the spatial coordinate of an image pixel, Ω is the set of spatial coordinates of all image pixels, t∈Τ is the time point of image acquisition, and Τ is the set of all image acquisition time points;

[0124] The evolution of magnetic resonance signals is simulated using analytical methods, Bloch equation simulation, or EPG simulation, and a dictionary is generated, denoted as...

[0125]

[0126] Where |Τ| is the number of image acquisition time points, i.e. the number of frames in the image sequence, and N is the number of parameter values. For multi-parameter imaging, the parameter values ​​are combinations of parameter values. D is the set of real numbers; each row of D corresponds to a time point of image acquisition, and each entry d in D... n It involves sampling the simulated signal at a given time point, and each sample corresponds to a parameter; normalization is performed on each entry in the dictionary, letting:

[0127] d n ←d n / ||d n ||2,n=1,2,…,N. (2)

[0128] Where ||·||2 is the l2 norm of the vector; motion correction is achieved by solving the following optimization problem:

[0129]

[0130] in, Let θ be the sparse coding of the image signal at pixel x, where θ is a vector containing all the parameters controlling image deformation. Let x be the image signal at position x after deformation, R(θ) be the regularization term constraining the image deformation, and ||·||0 be the l0 norm of the vector, defined as the number of non-zero elements in the vector.

[0131] Module M2: Performs dictionary matching on the acquired quantitative imaging image sequence to obtain the parameter map and the simulation image sequence;

[0132] Specifically, in module M2:

[0133] Solving for θ in fixed problem (3):

[0134]

[0135] The sparse coding α(x) at each pixel is independent of each other. It is solved pixel by pixel. For any given x∈Ω, the solution is:

[0136]

[0137] Optimal solution α * (x) Analytical expression, the image signal f at x θ (x,:) and each entry d in the dictionary n Perform Euclidean inner products for each entry, and denote the entry with the smallest number among those with the largest inner product value as n. * (x), that is:

[0138]

[0139] Where <·,·> is the Euclidean inner product between vectors;

[0140]

[0141] Among them, [α] * (x)] n For α * The nth component of (x), formulas (6) and (7) show that solving problem (4) involves pixel-wise dictionary matching. Based on the result of the dictionary matching, the parameter value at x is the entry. The corresponding parameter values ​​form a parameter graph; Dα * (x) is f θ (x,:) is a sparse approximation with respect to dictionary D; since Dα * (x) The image signal at each pixel corresponds to an entry in dictionary D, so Dα * (x) and f θ The contrast variation of (x,:) remains consistent; due to Dα * Each frame of (x) is generated based on the same parametric map and does not contain motion; f θ (x,:) represents the real image sequence, and Dα * (x) is f θ Simulated image sequence of (x,:).

[0142] Module M3: Registers the acquired image sequence to the simulated image sequence and corrects motion;

[0143] Specifically, in module M3:

[0144] Given a fixed α in problem (3), solve:

[0145]

[0146] Solve problem (8) using the real image sequence fθ (x,:) is registered to the simulated image sequence Dα(x). Since the contrast changes of the two image sequences are consistent, the mean square error is used as the measure of difference. The displacement field determined by the deformation parameter θ is d. θ (x,t), and denote the set of all θs that satisfy the condition that the displacement field has zero mean in the time dimension as:

[0147]

[0148] The regularization term R(θ) constraining image deformation consists of two parts, expressed as:

[0149] R(θ)=δ Θ (θ)+λR smooth (θ). (10)

[0150] Where, δ Θ (θ) is an indicator function with respect to the set Θ, R smooth (θ) represents the spatial smoothing regularization term applied to each frame of the image, and λ is the regularization coefficient used to control the degree of smoothing; when θ∈Θ, δ Θ (θ) = 0; when At that time, δ Θ (θ)=+∞,δ Θ (θ) requires the displacement field d θ The mean of (x,t) in the time dimension is zero to ensure that each frame is registered to an average coordinate system; R smooth (θ) is a regularization term based on the first or second order difference of the displacement field, including the first order diffusion regularization term and the second order thin plate bending energy. The optimal deformation parameter θ is obtained by iteratively solving the problem (8) based on the optimization algorithm. * The optimization algorithms include gradient descent, conjugate gradient, and LBFGS.

[0151] Specifically, the algorithm alternately executes module M2 and module M3 to solve problem (3) until convergence, and obtains the motion-corrected image sequence and parameter map. The convergence condition is that the relative change of the loss function in problem (3) is less than a given threshold, or the algorithm reaches the maximum number of pre-set alternations. Using a coarse-to-fine multi-resolution optimization framework, the lower resolution image is corrected first, and then the higher resolution correction is initialized with the obtained deformation parameters. The algorithm first generates global deformation at low resolution to roughly align the target, and generates local deformation at high resolution for adjustment.

[0152] The optimization problem is solved by alternately executing modules M2 and M3 until convergence, resulting in a motion-corrected image sequence and parametric map.

[0153] Example 3:

[0154] Example 3 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0155] The following describes in detail, with reference to the accompanying drawings, an embodiment of applying the present invention to motion correction in cardiac magnetic resonance T2 quantitative imaging. Specifically, this embodiment includes the following steps:

[0156] Step S1: Acquire a T2 quantitative imaging (amplitude) image sequence f(x,t) based on T2 prep. Where x∈Ω are the spatial coordinates of image pixels (Ω is the set of all image pixel spatial coordinates), and t∈T are the image acquisition time points (T is the set of all image acquisition time points). The signal relaxation equation for this imaging task is:

[0157] s(t)=A·exp(-t / T2). (1)

[0158] Where A is a parameter related to proton density, and T2 is the transverse relaxation time. The parameter T2 is sampled with a starting point of 20ms, an ending point of 170ms, and a step size of 1ms. Then, a dictionary is constructed based on the signal relaxation equation (1), denoted as...

[0159]

[0160] Where |Τ| is the number of image acquisition time points (i.e., the number of frames in the image sequence), and N is the number of T2 values. In this embodiment, |Τ| = 4, N = 151. Each row of D corresponds to an image acquisition time point (called echo time, EchoTime, TE), and each entry (column) of D d n All are samples of the signal relaxation equation (1) at a given time point, and all correspond to a T2 value. Normalize each entry in the dictionary, that is, let...

[0161] d n ←d n / ||d n ||2,n=1,2,…,N. (3)

[0162] Where ||·||2 is the l2 norm of the vector. According to formula (3), for a given T2 value, taking any positive real number for A will produce the same entry, so there is no need to sample A when constructing the dictionary. This method achieves motion correction by solving the following optimization problem:

[0163]

[0164] in, This represents the sparse coding of the image signal at pixel x, where θ represents all parameters controlling image deformation (considered as a vector). Let x be the image signal at position x after deformation, R(θ) be the regularization term constraining the image deformation, and ||·||0 be the l0 norm of the vector, defined as the number of non-zero elements in the vector. In this invention, steps S2, S3, and S4 are the three steps for solving problem (4).

[0165] Step S2: Fix θ in problem (4) and solve.

[0166]

[0167] Since the sparse coding α(x) at each pixel is independent, problem (5) can be solved pixel by pixel. The image signal f at x... θ (x,:) and each entry d in the dictionary n Perform Euclidean inner products on each entry, and denote the smallest number among the entries with the largest inner product value as n. * (x), that is

[0168]

[0169] Where <·,·> represent the Euclidean dot product (dot product) of vectors. Therefore, the optimal solution is obtained.

[0170]

[0171] Among them, [α] * (x)] n For α * The nth component of (x). Formulas (6) and (7) show that solving problem (5) is actually performing pixel-by-pixel dictionary matching. Based on the result of dictionary matching, the T2 value at x should be the entry The corresponding T2 values ​​can be used to construct a T2 graph. Dα * (x) is f θ (x,:) is a sparse approximation with respect to dictionary D. Note that due to Dα * (x) The image signal at each pixel corresponds to an entry in dictionary D, so Dα * (x) and f θ The contrast variation of (x,:) remains consistent; due to Dα * Each frame of image (x) is generated based on the same T2 image, so it does not contain motion. Hereinafter, f is referred to as... θ (x,:) represents the real image sequence, and Dα is correspondingly called... * (x) is f θ Simulated image sequence of (x,:).

[0172] Step S3: Fix α in problem (4) and solve.

[0173]

[0174] Solving problem (8) actually involves processing the real image sequence f θ (x,:) is registered to the simulated image sequence Dα(x). Since the contrast changes of the two image sequences are consistent, it is reasonable to use the mean squared error as a measure of difference. This embodiment uses a free-form deformation (FFD) model as the deformation model for the registration algorithm. The FFD model controls the displacement of pixels by moving control points and B-spline interpolation. The resulting displacement field is relatively flexible and smooth, suitable for characterizing the local morphological changes of soft tissues such as myocardium. For the FFD model, the deformation parameter θ is the displacement of its control point grid. Let the displacement field determined by θ be d. θ (x,t), and denote the set of all θs that satisfy the condition that the displacement field has zero mean in the time dimension as (x,t).

[0175]

[0176] The regularization term R(θ) for constraining image deformation consists of two parts and can be expressed as follows:

[0177] R(θ)=δ Θ (θ)+λR smooth (θ). (10)

[0178] Where, δ Θ 9θ) is an indicator function with respect to the set Θ, R smooth (θ) represents the sum of the bending energies of the thin plate in each frame of the image, and λ is the regularization coefficient used to control the smoothness. δ Θ (θ) requires the displacement field d θ The mean of (x,t) in the time dimension is zero to ensure that all images are registered to an average coordinate system. For the FFD model, since there is a linear relationship between the displacement field and the control point displacement, this constraint can be transformed into the control point grid having a mean of zero in the time dimension. The gradient projection algorithm is used to iteratively solve problem (8) to obtain the optimal deformation parameter θ. * With the initial displacement of the control points set to zero, this optimization algorithm is equivalent to centering the gradient of the control point grid in the time dimension before each update of the gradient descent algorithm.

[0179] Step S4: Solve problem (4) by alternately executing steps S2 and S3 until convergence, obtaining the motion-corrected image sequence and T2 map. The convergence condition is that the relative change of the loss function in problem (4) is less than a given threshold, or the algorithm reaches the pre-set maximum number of alternations. Step S4 also uses a coarse-to-fine multi-resolution optimization framework, that is, first correcting the image with half the resolution, and then initializing the correction of the original resolution image with the obtained deformation parameters.

[0180] Figure 3 This is a schematic diagram of the results of this embodiment. The two rows of this diagram correspond to two subjects respectively. The first and second columns show the average T2 quantitative imaging images before and after motion correction, and the third and fourth columns show the T2 images before and after motion correction. In the average image before correction, the edges of the left ventricular myocardium are blurred, and there is even partial absence of left ventricular myocardium (as shown by the arrow), indicating significant motion in the image sequence. The T2 image before correction also shows partial absence of left ventricular myocardium (as shown by the arrow). After motion correction, the left ventricular myocardium in both the average and T2 images becomes relatively intact, and the edges are clearer, indicating that the motion in the image sequence has been effectively compensated for.

[0181] Example 4:

[0182] Example 4 is a preferred example of Example 1, which is used to illustrate the present invention in more detail.

[0183] The following describes in detail, with reference to the accompanying drawings, an embodiment of applying the present invention to motion correction in cardiac magnetic resonance T1 quantitative imaging. Specifically, this embodiment includes the following steps:

[0184] Step S1: Acquire a T1 quantitative imaging (amplitude) image sequence f(x,t) based on MOLLI. Where x∈Ω are the spatial coordinates of image pixels (Ω is the set of all image pixel spatial coordinates), and t∈T are the image acquisition time points (T is the set of all image acquisition time points). The signal relaxation equation for this imaging task is:

[0185]

[0186] Where A and B are parameters related to proton density. T1 represents the apparent longitudinal relaxation time. Depending on whether contrast agent was injected, T1 can be divided into native T1 (without contrast agent injection) and post T1 (with contrast agent injection). Combining the native T1 map, post T1 map, and hematocrit (obtained through blood tests), the extracellular volume fraction (ECV) of the myocardium can be calculated and used for the diagnosis of diseases such as myocardial fibrosis and myocardial edema. The parameter B / A was sampled with a starting value of 1.5, an ending value of 3, and a step size of 0.05. For native T1, the parameter was sampled with a starting value of 200ms, an ending value of 2200ms, and a step size of 2ms. Sampling was performed; for post T1, parameters were adjusted with a starting time of 100ms, an ending time of 800ms, and a step size of 2ms. Sampling is performed. Then, a dictionary is constructed based on the signal relaxation equation (1), denoted as...

[0187]

[0188] Where |Τ| is the number of image acquisition time points (i.e., the number of frames in the image sequence), and N is the B / A value and The number of value combinations. In this embodiment, for native T1, |T| = 8, N = 31031; for post T1, |T| = 9, N = 10881. Each row of D corresponds to an image acquisition time point (called Inversion Time, TI), and each entry (column) of D d n Both are samplings of the signal relaxation equation (1) at a given time point, and both correspond to a B / A value and Combinations of values. Normalize each entry in the dictionary individually, that is, let...

[0189] d n ←d n / ||d n ||2,n=1,2,…,N. (3)

[0190] Where ||·||2 is the l2 norm of the vector. According to formula (3), for a given B / A value and Since any combination of values ​​for A will produce the same entry regardless of whether A is a positive real number, sampling of A is unnecessary when constructing the dictionary. This invention achieves motion correction by solving the following optimization problem:

[0191]

[0192] in, This represents the sparse coding of the image signal at pixel x, where θ represents all parameters controlling image deformation (considered as a vector). Let x be the image signal at position x after deformation, R(θ) be the regularization term constraining the image deformation, and ||·||0 be the l0 norm of the vector, defined as the number of non-zero elements in the vector. In this invention, steps S2, S3, and S4 are the three steps for solving problem (4).

[0193] Step S2: Fix θ in problem (4) and solve.

[0194]

[0195] Since the sparse coding α(x) at each pixel is independent, problem (5) can be solved pixel by pixel. The image signal f at x... θ (x,:) and each entry d in the dictionary n Perform Euclidean inner products on each entry, and denote the smallest number among the entries with the largest inner product value as n. * (x), that is

[0196]

[0197] Where <·,·> represent the Euclidean dot product (dot product) of vectors. Therefore, the optimal solution is obtained.

[0198]

[0199] Among them, [α] * (x)] n For α * The nth component of (x). Formulas (6) and (7) show that solving problem (5) is actually performing pixel-by-pixel dictionary matching. Based on the result of the dictionary matching, the B / A value at x is... The value should be an entry. The corresponding B / A value and Values, from which a B / A diagram can be formed and Figure. Dα * (x) is f θ (x,:) is a sparse approximation with respect to dictionary D. Note that due to Dα * (x) The image signal at each pixel corresponds to an entry in dictionary D, so Dα * (x) and f θ The contrast variation of (x,:) remains consistent; due to Dα * Each frame of image (x) is based on the same B / A diagram and The graph is generated, so it does not contain motion. Hereinafter, f is called f. θ (x,:) represents the real image sequence, and Dα is correspondingly called... * (x) is f θ Simulated image sequence of (x,:).

[0200] Step S3: Fix α in problem (4) and solve.

[0201]

[0202] Solving problem (8) actually involves processing the real image sequence f θ (x,:) is registered to the simulated image sequence Dα(x). Since the contrast changes of the two image sequences are consistent, it is reasonable to use the mean squared error as a measure of difference. This embodiment uses a free-form deformation (FFD) model as the deformation model for the registration algorithm. The FFD model controls the displacement of pixels by moving control points and B-spline interpolation. The resulting displacement field is relatively flexible and smooth, suitable for characterizing the local morphological changes of soft tissues such as myocardium. For the FFD model, the deformation parameter θ is the displacement of its control point grid. Let the displacement field determined by θ be d. θ (x,t), and denote the set of all θs that satisfy the condition that the displacement field has zero mean in the time dimension as (x,t).

[0203]

[0204] The regularization term R(θ) for constraining image deformation consists of two parts and can be expressed as follows:

[0205] R(θ)=δ Θ (θ)+λR smooth (θ). (10)

[0206] Where, δ Θ (θ) is an indicator function with respect to the set Θ, R smooth (θ) represents the sum of the bending energies of the thin plate in each frame of the image, and λ is the regularization coefficient used to control the smoothness. δ Θ (θ) requires the displacement field d θ The mean of (x,t) in the time dimension is zero to ensure that all images are registered to an average coordinate system. For the FFD model, since there is a linear relationship between the displacement field and the control point displacement, this constraint can be transformed into the control point grid having a mean of zero in the time dimension. The gradient projection algorithm is used to iteratively solve problem (8) to obtain the optimal deformation parameter θ. * With the initial displacement of the control points set to zero, this optimization algorithm is equivalent to centering the gradient of the control point grid in the time dimension before each update of the gradient descent algorithm.

[0207] Step S4: Solve problem (4) by alternately executing steps S2 and S3 until convergence, obtaining the motion-corrected image sequence, B / A diagram, and... The T1 graph is then calculated using formula (1). The convergence condition is that the relative change of the loss function in problem (4) is less than a given threshold, or the algorithm reaches the maximum number of pre-set alternations. Step S4 also uses a coarse-to-fine multi-resolution optimization framework, that is, first correcting the image with half the resolution, and then initializing the correction of the original resolution image with the obtained deformation parameters.

[0208] Figure 4 This is a schematic diagram of the results of this embodiment. The first and second rows of the diagram show the native T1 and post-T1 results for the first subject, respectively; the third and fourth rows show the native T1 and post-T1 results for the second subject, respectively; the first and second columns show the average T1 quantitative imaging images before and after motion correction; and the third and fourth columns show the T1 images before and after motion correction, respectively. In the average image before correction, the edges of the left ventricular myocardium are relatively blurred, and there are obvious artifacts (as shown by the arrows), indicating strong motion in the image sequence. Due to the influence of motion, artifacts and partial missing left ventricular myocardium also appear in the T1 image before correction (as shown by the arrows). After motion correction, the quality of the T1 image is significantly improved, with the left ventricular myocardium appearing more complete, the edges of the left ventricular myocardium becoming clearer, and artifacts significantly reduced.

[0209] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0210] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A dictionary matching based magnetic resonance quantitative imaging motion correction method, characterized in that, include: Step S1: Generate a dictionary by simulating the evolution of the magnetic resonance signal and construct the optimization problem to be solved; Motion correction is achieved by solving the following optimization problem: in, For pixels Sparse coding of image signals, All parameters controlling image deformation are represented by a vector. After deformation Image signal at the location, To constrain the regularization term of image deformation, For vectors Norm, defined as the number of non-zero elements in a vector; Step S2: Perform dictionary matching on the acquired quantitative imaging image sequence to obtain the parameter map and the simulation image sequence; In step S2: Fixed problem (3) in Solution: Sparse coding at each pixel Independently of each other, pixel-wise solving for any given Solving: Optimal solution Parse the expression, Image signal at the location With each entry in the dictionary Perform Euclidean inner products for each entry, and denote the entry with the smallest number among those with the largest inner product value as... ,Right now: wherein is the Euclidean inner product between vectors; in, for The Each component, formulas (6) and (7) show that solving problem (4) involves pixel-by-pixel dictionary matching, based on the results of the dictionary matching. The parameter value at that location is the entry. The corresponding parameter values ​​form a parameter graph; for About dictionaries The sparse approximation; due to The image signal at each pixel corresponds to a dictionary. One of the entries, so and The contrast variation remains consistent; due to Each frame of the image is generated based on the same parametric map and does not contain motion; It is a real image sequence. for Simulated image sequence; Step S3: Register the acquired image sequence to the simulated image sequence and correct for motion; In step S3: Fixed problem (3) in , the solution is: Solving problem (8) will register the real image sequence to the simulated image sequence Since the contrast of the two image sequences varies consistently, the mean square error is used as the measure of difference; the displacement field determined by the morphing parameters is and the set of all that satisfy the condition that the mean of the displacement field in the time dimension is zero is denoted as: Regularization term constraining image deformation consists of two parts, denoted as: in, For about sets Indicator functions, To apply a spatial smoothing regularization term to each frame of the image, Here is the regularization coefficient used to control the degree of smoothness; when hour, ;when hour, , Requirement of displacement field The mean value in the time dimension is zero to ensure that each frame of the image is registered to an average coordinate system; It is based on the first or second order difference regularization term of the displacement field, including the first order diffusion regularization term and the second order thin plate bending energy. The optimal deformation parameters are obtained by iteratively solving the problem (8) based on the optimization algorithm. The optimization algorithms include gradient descent, conjugate gradient, and LBFGS. Alternately execute steps S2 and S3 to solve the optimization problem until convergence, and obtain the motion-corrected image sequence and parameter map.

2. The dictionary matching based magnetic resonance quantitative imaging motion correction method of claim 1, wherein, In step S1: is a sequence of quantitative imaging images acquired; wherein, is a spatial coordinate of an image pixel, is a set of spatial coordinates of all image pixels, is a time point of image acquisition, is a set of all image acquisition time points; The evolution of magnetic resonance signals is simulated using analytical methods, Bloch equation simulation, or EPG simulation, and a dictionary is generated, denoted as... in, This represents the number of image acquisition time points, i.e., the number of frames in the image sequence. The parameter value is the number of parameter values, and the parameter value for multi-parameter imaging is a combination of parameter values. It is the set of real numbers; Each row corresponds to a time point in the image acquisition process. Each entry It involves sampling the simulated signal at a given time point, and each sample corresponds to a parameter; normalization is performed on each entry in the dictionary, letting: wherein is a vector norm.

3. The method for motion correction in quantitative magnetic resonance imaging based on dictionary matching according to claim 1, characterized in that: Alternately execute steps S2 and S3 to solve problem (3) until convergence, and obtain the motion-corrected image sequence and parameter map. The convergence condition is that the relative change of the loss function in problem (3) is less than a given threshold, or the algorithm reaches the maximum number of pre-set alternations. Use a coarse-to-fine multi-resolution optimization framework to first correct the lower resolution image, and then use the obtained deformation parameters to initialize the higher resolution correction. The algorithm first generates global deformation at low resolution to align the target, and generates local deformation at high resolution for adjustment.

4. A dictionary matching based magnetic resonance quantitative imaging motion correction system, characterized by, include: Module M1: Generates a dictionary by simulating the evolution of magnetic resonance signals and constructs the optimization problem to be solved; Motion correction is achieved by solving the following optimization problem: in, For pixels Sparse coding of image signals, All parameters controlling image deformation are represented by a vector. After deformation Image signal at the location, To constrain the regularization term of image deformation, For vectors Norm, defined as the number of non-zero elements in a vector; Module M2: Performs dictionary matching on the acquired quantitative imaging image sequence to obtain the parameter map and the simulation image sequence; In module M2: Fixed problem (3) Solution: Sparse coding at each pixel Independently of each other, pixel-wise solving for any given , solving: Optimal solution Parse the expression, Image signal at the location With each entry in the dictionary Perform Euclidean inner products for each entry, and denote the entry with the smallest number among those with the largest inner product value as... ,Right now: wherein is the Euclidean inner product between vectors; in, for The Each component, formulas (6) and (7) show that solving problem (4) involves pixel-by-pixel dictionary matching, based on the results of the dictionary matching. The parameter value at that location is the entry. The corresponding parameter values ​​form a parameter graph; for About dictionaries The sparse approximation; due to The image signal at each pixel corresponds to a dictionary. One of the entries, so and The contrast variation remains consistent; due to Each frame of the image is generated based on the same parametric map and does not contain motion; It is a real image sequence. for Simulated image sequence; Module M3: Registers the acquired image sequence to the simulated image sequence and corrects motion; In module M3: Fixed problem (3) in , the solution is: Solve problem (8) using the real image sequence Registered to simulated image sequence Since the contrast changes of the two image sequences are consistent, the mean squared error is used as a measure of difference; the deformation parameter The determined displacement field is And all conditions that satisfy the condition that make the displacement field mean zero in the time dimension. The set is denoted as: Regularization term constraining image deformation consists of two parts, denoted as: in, For about sets Indicator functions, To apply a spatial smoothing regularization term to each frame of the image, Here is the regularization coefficient used to control the degree of smoothness; when hour, ;when hour, , Requirement of displacement field The mean value in the time dimension is zero to ensure that each frame of the image is registered to an average coordinate system; It is based on the first or second order difference regularization term of the displacement field, including the first order diffusion regularization term and the second order thin plate bending energy. The optimal deformation parameters are obtained by iteratively solving the problem (8) based on the optimization algorithm. The optimization algorithms include gradient descent, conjugate gradient, and LBFGS. The optimization problem is solved by alternately executing modules M2 and M3 until convergence, resulting in a motion-corrected image sequence and parametric map.

5. The dictionary matching based magnetic resonance quantitative imaging motion correction system of claim 4, wherein, In module M1: is a sequence of quantitative imaging images acquired; wherein, is a spatial coordinate of an image pixel, is a set of spatial coordinates of all image pixels, is a time point of image acquisition, is a set of all image acquisition time points; The evolution of magnetic resonance signals is simulated using analytical methods, Bloch equation simulation, or EPG simulation, and a dictionary is generated, denoted as... wherein is the number of time points of image acquisition, i.e. the number of frames of the image sequence, is the number of parameter values, parameter values being a combination of parameter values for multi-parameter imaging; is the set of real numbers; each row of corresponds to a time point of image acquisition, each entry of corresponds to a parameter value, is a sample of the simulated signal at the given time point and all correspond to one parameter; normalizing each entry of the dictionary separately, let wherein is a vector of norms.

6. The motion correction system for quantitative magnetic resonance imaging based on dictionary matching according to claim 4, characterized in that: Alternately execute module M2 and module M3 to solve problem (3) until convergence, and obtain the motion-corrected image sequence and parameter map. The convergence condition is that the relative change of the loss function in problem (3) is less than the given threshold, or the algorithm reaches the maximum number of pre-set alternations. Use a coarse-to-fine multi-resolution optimization framework to first correct the lower resolution image, and then use the obtained deformation parameters to initialize the higher resolution correction. The algorithm first generates global deformation at low resolution to roughly align the target, and generates local deformation at high resolution for adjustment.

Images