Iterative magnetic resonance elastography displacement extraction method and system based on dual data fidelity terms

Abstract

The present invention provides an iterative magnetic resonance elastography displacement extraction method and system with dual data fidelity terms, comprising: Step S1: establishing a phase image model and using cross-phase subtraction to remove background phase; Step S2: designing a data fidelity term to perform principal component extraction equivalent to a Fourier transform; Step S3: designing a gradient data fidelity term to perform phase unwrapping; and Step S4: selecting hyperparameters and performing an iterative solution. By designing new data fidelity terms and gradient data fidelity terms, the present invention simultaneously performs phase unwrapping and Fourier transform in magnetic resonance elastography, addressing the difficulty of extracting displacement from complex, noisy data in magnetic resonance elastography.

Description

Technical Field

[0001] The present invention relates to the field of image processing, and in particular, to a method and system for iterative magnetic resonance elastography displacement extraction using dual data fidelity terms, and more particularly, to a method and system for iterative magnetic resonance elastography displacement extraction using numerical iteration based on dual data fidelity terms. Background Art

[0002] As the first step in processing MRE images, the quality of the extracted wavefield determines the performance of biomechanical property estimation. Because phase images are obtained based on motion-encoded gradients, the magnitude of motion can introduce phase warping effects. Therefore, phase unwarping is often the first step. Traditionally, single image frames are unwarped before performing a time-domain fast Fourier transform (FFT) to extract principal components. Unwarping algorithms, such as the reliability-ranking algorithm and Dilate-Erode-Propagate (DE), operate in a manner similar to search or discrete greedy updates and are prone to failure in complex warping scenarios. Laplace-based estimation (LBE) simultaneously performs phase unwarping and FFT in the frequency domain. LBE is robust to noise and has a high unwarping success rate, but it introduces new background offset noise, which affects biomechanical property estimation. Phase gradient (PG) does not require direct unwarping but is sensitive to noise and must be used in conjunction with a specially designed mechanical property estimation algorithm. Therefore, an accurate and noise-resistant wavefield extraction method that can perform both phase unwarping and FFT is needed.

[0003] Patent document CN104055536A (application number: CN201410171606.1) discloses a method for fusion registration of ultrasound and magnetic resonance images. This method constructs a finite element model of the prostate magnetic resonance image and incorporates biomechanical information of the prostate acquired through ultrasound elastography into the finite element model. Principal component analysis is then used to construct a personalized statistical motion model of the prostate based on the finite element model. This method then aligns the prostate magnetic resonance image with the aforementioned three-dimensional transrectal ultrasound image data. However, this invention does not address the difficulty of extracting displacements from complex, noisy data in magnetic resonance elastography. Summary of the Invention

[0004] In view of the defects in the prior art, the present invention aims to provide a method and system for iterative magnetic resonance elastography displacement extraction with dual data fidelity terms.

[0005] According to the present invention, a dual-data fidelity iterative magnetic resonance elastography displacement extraction method is provided, comprising:

[0006] Step S1: Establish a phase image model and remove the background phase using cross phase subtraction;

[0007] Step S2: Design data fidelity items to complete principal component extraction equivalent to Fourier transform;

[0008] Step S3: Designing gradient data fidelity terms to complete phase unwrapping;

[0009] Step S4: Select hyperparameters and perform iterative solution to extract elastic imaging displacement.

[0010] Preferably, in step S1:

[0011] Step S1.1: Build image model, j-th phase shift The image is represented as:

[0012]

[0013] Where, j = 1, 2, 3, ... J, A is the original complex image, Φ is the phase of A, φ j is the phase shift introduced by imaging, U=U′+i·″ represents the reset shift to be extracted, then

[0014]

[0015] Where U′ is the real part of the reset shift, and U″ is the imaginary part of the reset shift;

[0016] Step S1.2: Remove the background phase using cross-phase subtraction:

[0017]

[0018] Where, (p,q)∈{(x,y)|x <y,1≤x,y≤J};I p is the image acquired under the pth phase shift, I q is the image acquired under the qth phase shift, φ p is the MEG phase distribution under the pth phase offset, φ q is the MEG phase distribution under the qth phase offset.

[0019] Preferably, in step S2:

[0020] Solve the principal component extraction equivalent to Fourier transform by designing data fidelity terms:

[0021]

[0022] in, Loss DC1 It is to solve the loss terms introduced by Fourier transform and data consistency.

[0023] Preferably, in step S3:

[0024] Step S3.1: Extract unwrapped phase gradient data from the warped raw data using the phase gradient method

[0025] Step S3.2: Obtain the gradient of the estimated U′ and U″ to obtain the phase gradient fidelity term to solve the wrapping problem:

[0026]

[0027] Among them, Loss unwrapping To solve the loss term introduced by unwinding, To extract the gradient along the x direction from the warped original data to the unwarped U′, To extract the gradient along the y direction from the warped original data to the unwarped U′, To extract the gradient along the x direction from the warped original data to the unwarped U″, is the gradient along the y direction extracted from the warped original data to the unwarped U″.

[0028] Preferably, in step S4:

[0029] Step S4.1: The final loss function is:

[0030]

[0031] Step S4.2: Select the λ hyperparameter for iterative update.

[0032] According to the present invention, a dual-data fidelity iterative magnetic resonance elastography displacement extraction system is provided, comprising:

[0033] Module M1: Establish phase image model and remove background phase using cross phase subtraction;

[0034] Module M2: Design data fidelity items to complete principal component extraction equivalent to Fourier transform;

[0035] Module M3: Design gradient data fidelity terms to complete phase unwrapping;

[0036] Module M4: Select hyperparameters and perform iterative solution to extract elastic imaging displacement.

[0037] Preferably, in the module M1:

[0038] Module M1.1: Build image model, j-th phase shift The image is represented as:

[0039]

[0040] Where, j = 1, 2, 3, ... J, A is the original complex image, Φ is the phase of A, φ j is the phase shift introduced by imaging, U=U′+i·″ represents the reset shift to be extracted, then

[0041]

[0042] Where U′ is the real part of the reset shift, and U″ is the imaginary part of the reset shift;

[0043] Module M1.2: Using cross-phase removal to remove background phase:

[0044]

[0045] Where, (p,q)∈{(x,y)|x <y,1≤x,y≤J};I p is the image acquired under the pth phase shift, I q is the image acquired under the qth phase shift, φ p is the MEG phase distribution under the pth phase offset, φ q is the MEG phase distribution under the qth phase offset.

[0046] Preferably, in the module M2:

[0047] Solve the principal component extraction equivalent to Fourier transform by designing data fidelity terms:

[0048]

[0049] in, Loss DC1 It is to solve the loss terms introduced by Fourier transform and data consistency.

[0050] Preferably, in the module M3:

[0051] Module M3.1: Extracting unwrapped phase gradient data from warped raw data using the phase gradient method

[0052] Module M3.2: Obtain the gradient of the estimated U′ and U″ to obtain the phase gradient fidelity term to solve the winding problem:

[0053]

[0054] Among them, Loss unwrapping To solve the loss term introduced by unwinding, To extract the gradient along the x direction from the warped original data to the unwarped U′, To extract the gradient along the y direction from the warped original data to the unwarped U′, To extract the gradient along the x direction from the warped original data to the unwarped U″, is the gradient along the y direction extracted from the warped original data to the unwarped U″.

[0055] Preferably, in the module M4:

[0056] Module M4.1: The final loss function is:

[0057]

[0058] Module M4.2: Select the λ hyperparameter for iterative update.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] The present invention solves the problem of difficult displacement extraction of complex noisy data in magnetic resonance elastography by designing new data fidelity terms and gradient data fidelity terms, and simultaneously completing phase unwrapping and Fourier transform in magnetic resonance elastography. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0062] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0063] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0064] Example 1:

[0065] According to the invention, a dual data fidelity iterative magnetic resonance elastography displacement extraction method is provided. Figure 1 Shown, including:

[0066] Step S1: Establish a phase image model and remove the background phase using cross phase subtraction;

[0067] Specifically, in step S1:

[0068] Step S1.1: Build image model, j-th phase shift The image is represented as:

[0069]

[0070] Where, j = 1, 2, 3, ... J, A is the original complex image, Φ is the phase of A, φ j is the phase shift introduced by imaging, U=U′+i·″ represents the reset shift to be extracted, then

[0071]

[0072] Where U′ is the real part of the reset shift, and U″ is the imaginary part of the reset shift;

[0073] Step S1.2: Remove the background phase using cross-phase subtraction:

[0074]

[0075] Where, (p,q)∈{(x,y)|x <y,1≤x,y≤J};I p is the image acquired under the pth phase shift, I q is the image acquired under the qth phase shift, φ p is the MEG phase distribution under the pth phase offset, φ q is the MEG phase distribution under the qth phase offset.

[0076] Step S2: Design data fidelity items to complete principal component extraction equivalent to Fourier transform;

[0077] Specifically, in step S2:

[0078] Solve the principal component extraction equivalent to Fourier transform by designing data fidelity terms:

[0079]

[0080] in, Loss DC1 It is to solve the loss terms introduced by Fourier transform and data consistency.

[0081] Step S3: Designing gradient data fidelity terms to complete phase unwrapping;

[0082] Specifically, in step S3:

[0083] Step S3.1: Extract unwrapped phase gradient data from the warped raw data using the phase gradient method

[0084] Step S3.2: Obtain the gradient of the estimated U′ and U″ to obtain the phase gradient fidelity term to solve the wrapping problem:

[0085]

[0086] Among them, Loss unwrapping To solve the loss term introduced by unwinding, To extract the gradient along the x direction from the warped original data to the unwarped U′, To extract the gradient along the y direction from the warped original data to the unwarped U′, To extract the gradient along the x direction from the warped original data to the unwarped U″, is the gradient along the y direction extracted from the warped original data to the unwarped U″.

[0087] Step S4: Select hyperparameters and perform iterative solution to extract elastic imaging displacement.

[0088] Specifically, in step S4:

[0089] Step S4.1: The final loss function is:

[0090]

[0091] Step S4.2: Select the λ hyperparameter for iterative update.

[0092] Example 2:

[0093] Example 2 is a preferred example of Example 1 and is used to illustrate the present invention in more detail.

[0094] The present invention also provides an iterative magnetic resonance elastography displacement extraction system for dual data fidelity items. The iterative magnetic resonance elastography displacement extraction system for dual data fidelity items can be implemented by executing the process steps of the iterative magnetic resonance elastography displacement extraction method for dual data fidelity items. That is, those skilled in the art can understand the iterative magnetic resonance elastography displacement extraction method for dual data fidelity items as a preferred embodiment of the iterative magnetic resonance elastography displacement extraction system for dual data fidelity items.

[0095] According to the present invention, a dual-data fidelity iterative magnetic resonance elastography displacement extraction system is provided, comprising:

[0096] Module M1: Establish phase image model and remove background phase using cross phase subtraction;

[0097] Specifically, in the module M1:

[0098] Module M1.1: Build image model, j-th phase shift The image is represented as:

[0099]

[0100] Where, j = 1, 2, 3, ... J, A is the original complex image, Φ is the phase of A, φ j is the phase shift introduced by imaging, U=U′+i·″ represents the reset shift to be extracted, then

[0101]

[0102] Where U′ is the real part of the reset shift, and U″ is the imaginary part of the reset shift;

[0103] Module M1.2: Using cross-phase removal to remove background phase:

[0104]

[0105] Where, (p,q)∈{(x,y)|x <y,1≤x,y≤J};I p is the image acquired under the pth phase shift, I q is the image acquired under the qth phase shift, φ p is the MEG phase distribution under the pth phase offset, φ q is the MEG phase distribution under the qth phase offset.

[0106] Module M2: Design data fidelity items to complete Fourier transform;

[0107] Specifically, in the module M2:

[0108] Solve the Fourier transform problem by designing data fidelity terms:

[0109]

[0110] in, Loss DC1 This is to solve the loss term introduced by FFT and data consistency.

[0111] Module M3: Design gradient data fidelity terms to complete phase unwrapping;

[0112] Specifically, in the module M3:

[0113] Module M3.1: Extracting unwrapped phase gradient data from warped raw data using the phase gradient method

[0114] Module M3.2: Obtain the gradient of the estimated U′ and U″ to obtain the phase gradient fidelity term to solve the winding problem:

[0115]

[0116] Among them, Loss unwrapping To solve the loss term introduced by unwinding, To extract the gradient along the x direction from the warped original data to the unwarped U′, To extract the gradient along the y direction from the warped original data to the unwarped U′, To extract the gradient along the x direction from the warped original data to the unwarped U″, is the gradient along the y direction extracted from the warped original data to the unwarped U″.

[0117] Module M4: Select hyperparameters and perform iterative solution to extract elastic imaging displacement.

[0118] Specifically, in the module M4:

[0119] Module M4.1: The final loss function is:

[0120]

[0121] Module M4.2: Select the λ hyperparameter for iterative update.

[0122] Example 3:

[0123] Example 3 is a preferred example of Example 1 and is used to illustrate the present invention in more detail.

[0124] Aiming at the problem of displacement extraction in magnetic resonance elastography, a numerical iteration method using dual data fidelity terms is proposed to simultaneously complete phase unwrapping and Fourier transform. This method can effectively solve the problem of displacement extraction in noisy and complex scenes.

[0125] A method for extracting displacement from magnetic resonance elastography based on numerical iteration of dual data fidelity terms is proposed. The method mainly includes data preprocessing, design of data fidelity terms and gradient data fidelity terms, and iterative updating. Specifically,

[0126] Step S1: Establish a phase image model and use cross-phase to remove the background phase, and design a new data fidelity term to complete the Fourier transform.

[0127] Step S2: Design a new gradient data fidelity term to complete phase unwrapping.

[0128] Step S3: Select appropriate hyperparameters and perform iterative solution.

[0129] The step S1 comprises the following steps:

[0130] Step S1.1: Establish an image model. The jth (j=1…J) phase offset The image can be represented as

[0131]

[0132] Where, is the original complex image, Φ is the phase of A, φ j is the phase shift introduced by imaging, U=U′+i·U″, then

[0133]

[0134] Wherein, U′ is the real part of the reset shift, and U″ is the imaginary part of the reset shift.

[0135] Step S1.2: Use cross-phase division to remove the background phase:

[0136] Where, (p,q)∈{(x,y)|x <y,1≤x,y≤J};I p is the image acquired under the pth phase shift, I q is the image acquired under the qth phase shift, φ p is the MEG phase distribution under the pth phase offset, φ q is the MEG phase distribution under the qth phase offset;

[0137] Step S1.3: Solve the Fourier transform problem with the newly designed data fidelity term:

[0138] in

[0139] Loss DC1 In order to solve the loss term Data Consistency (DC) introduced by FFT and data consistency.

[0140] The step S2 comprises the following steps:

[0141] Step S2.1: Extract unwrapped phase gradient data from the warped raw data using the phase gradient method

[0142] Step S3.2: Obtain the gradient of the estimated U′ and U″ to obtain the phase gradient fidelity term to solve the wrapping problem:

[0143]

[0144] Among them, Loss unwrapping In order to solve the loss term introduced by unwinding, To extract the gradient along the x direction from the warped original data to the unwarped U′, To extract the gradient along the y direction from the warped original data to the unwarped U′, To extract the gradient along the x direction from the warped original data to the unwarped U″, is the gradient along the y direction extracted from the warped original data to the unwarped U″.

[0145] The step S3 comprises the following steps:

[0146] Step S3.1: The final loss function is

[0147]

[0148] Step S3.2: Select an appropriate λ hyperparameter for iterative update.

[0149] Those skilled in the art will appreciate that, in addition to implementing the system, device, and various modules provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like by logically programming the method steps. Therefore, the system, device, and various modules provided by the present invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; the modules for implementing various functions can also be considered both software programs for implementing the method and structures within the hardware component.

[0150] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A dual-data fidelity iterative magnetic resonance elastography displacement extraction method, characterized in that: include: Step S1: Establish a phase image model and remove the background phase using cross phase subtraction; Step S2: Design data fidelity items to complete principal component extraction equivalent to Fourier transform; Step S3: Designing gradient data fidelity terms to complete phase unwrapping; Step S4: Select hyperparameters and perform iterative solution to extract elastic imaging displacement; In step S1: Step S1.1: Establish phase image model, j-th phase offset The complex image of is represented as: Where, j = 1, 2, 3, ... J, A is the original complex image, Φ is the phase of A, φ j is the phase shift introduced by imaging, U=U′+i·U″ represents the reset shift to be extracted, then Where U′ is the real part of the reset shift, and U″ is the imaginary part of the reset shift; Step S1.2: Remove the background phase using cross-phase subtraction: Where, (p,q)∈{(x,y)|x <y,1≤x,y≤J};I p is the image acquired under the pth phase shift, I q is the image acquired under the qth phase shift, φ p is the MEG phase distribution under the pth phase offset, φ q is the MEG phase distribution under the qth phase offset.

2. The iterative magnetic resonance elastography displacement extraction method based on dual data fidelity terms according to claim 1, characterized in that: In step S2: Solve the principal component extraction equivalent to Fourier transform by designing data fidelity terms: in, Loss DC1 It is to solve the loss terms introduced by Fourier transform and data consistency.

3. The iterative magnetic resonance elastography displacement extraction method based on dual data fidelity terms according to claim 2, characterized in that: In step S3: Step S3.1: Extract unwrapped phase gradient data from the warped raw data using the phase gradient method Step S3.2: Obtain the gradient of the estimated U′ and U″ to obtain the phase gradient fidelity term to solve the wrapping problem: Among them, Loss DC2 To solve the loss term introduced by unwinding, To extract the gradient along the x direction from the warped original data to the unwarped U′, To extract the gradient along the y direction from the warped original data to the unwarped U′, To extract the gradient along the x direction from the warped original data to the unwarped U″, is the gradient along the y direction extracted from the warped original data to the unwarped U″.

4. The iterative magnetic resonance elastography displacement extraction method based on dual data fidelity terms according to claim 3, characterized in that: In step S4: Step S4.1: The final loss function is: Step S4.2: Select the λ hyperparameter for iterative update.

5. A dual-data fidelity iterative magnetic resonance elastography displacement extraction system, characterized in that: include: Module M1: Establish phase image model and remove background phase using cross phase subtraction; Module M2: Design data fidelity items to complete principal component extraction equivalent to Fourier transform; Module M3: Design gradient data fidelity terms to complete phase unwrapping; Module M4: Select hyperparameters and perform iterative solution to extract elastic imaging displacement; In the module M1: Module M1.1: Establish phase image model, j-th phase offset The complex image of is represented as: Where, j = 1, 2, 3, ... J, A is the original complex image, Φ is the phase of A, φ j is the phase shift introduced by imaging, U=U′+i·U″ represents the reset shift to be extracted, then Where U′ is the real part of the reset shift, and U″ is the imaginary part of the reset shift; Module M1.2: Using cross-phase removal to remove background phase: Where, (p,q)∈{(x,y)|x <y,1≤x,y≤J};I p is the image acquired under the pth phase shift, I q is the image acquired under the qth phase shift, φ p is the MEG phase distribution under the pth phase offset, φ q is the MEG phase distribution under the qth phase offset.

6. The dual data fidelity iterative magnetic resonance elastography displacement extraction system according to claim 5, characterized in that: In the module M2: Solve the principal component extraction equivalent to Fourier transform by designing data fidelity terms: in, Loss DC1 It is to solve the loss terms introduced by Fourier transform and data consistency.

7. The dual data fidelity iterative magnetic resonance elastography displacement extraction system according to claim 6, characterized in that: In the module M3: Module M3.1: Extracting unwrapped phase gradient data from warped raw data using the phase gradient method Module M3.2: Obtain the gradient of the estimated U′ and U″ to obtain the phase gradient fidelity term to solve the winding problem: Among them, Loss DC2 To solve the loss term introduced by unwinding, To extract the gradient along the x direction from the warped original data to the unwarped U′, To extract the gradient along the y direction from the warped original data to the unwarped U′, To extract the gradient along the x direction from the warped original data to the unwarped U″, is the gradient along the y direction extracted from the warped original data to the unwarped U″.

8. The dual data fidelity iterative magnetic resonance elastography displacement extraction system according to claim 7, characterized in that: In the module M4: Module M4.1: The final loss function is: Module M4.2: Select the λ hyperparameter for iterative update.

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