A method for reconstruction of magnetic resonance images based on high frequency preservation

Abstract

This invention discloses a method for reconstructing magnetic resonance images based on high-frequency fidelity. The method includes: a) undersampling the fully sampled K-space data; b) designing a high-frequency fidelity term to establish a model; c) decomposing the problem into multiple sub-problems using a variable splitting method and solving them iteratively; d) expanding the solution of the sub-problems into an end-to-end neural network and solving them using the network model; e) supervising the model using ground truth images; and f) selecting the optimal model based on a validation set and inputting test data into the model to obtain the reconstructed magnetic resonance image. Compared with existing technologies, this invention explicitly constrains the high-frequency information of the image restoration, expands the iterative solution algorithm into a neural network, effectively solves the problem of poor restoration of image details and texture structure, better preserves the details of the magnetic resonance image, facilitates disease diagnosis by doctors, is simple in method, has good results, and has promising application prospects.

Description

Technical Field

[0001] This invention relates to the field of magnetic resonance imaging technology, and in particular to a method for rapid reconstruction of magnetic resonance images based on high-frequency fidelity. Background Technology

[0002] Magnetic resonance imaging (MRI) is a widely used medical imaging technique that provides detailed images of human organs and physiological structures. Unlike computed tomography (CT), MRI is radiation-free, meaning it does not expose patients to ionizing radiation. MRI images are derived from the frequency domain, also known as K-space. However, acquiring K-space data is a time-consuming process that can cause patient discomfort and may lead to motion artifacts, negatively impacting image quality. Therefore, there is a pressing need to reduce acquisition time. Two common methods to accelerate MRI acquisition are increasing the number of coils and reducing the amount of data acquired. The former, known as parallel imaging (PI), focuses on reconstructing high-quality MRI images from multi-coil K-space data. The latter, undersampled MRI reconstruction, primarily recovers high-quality MRI images from undersampled K-space data.

[0003] As previously mentioned, PI involves acquiring patient data using multiple receiving coils, each covering a portion of the field of view. The individual signals from the coils are then combined to form a single image of the entire field of view. PI can operate in the image domain or the K-space domain. In the image domain, it uses a sensitivity coding (SENSE) method, which involves transforming the signal to the image domain via an inverse Fourier transform and performing artifact removal using a pre-computed coil sensitivity map (such as ESPIRiT). In the K-space domain, PI is modeled as an interpolation process inspired by the Generalized Automatic Calibration Partial Parallel Acquisition (GRAPPA) method. On the other hand, undersampled MRI reconstruction involves acquiring fewer data points using undersampled masks (such as Cartesian masks, radial masks, or spiral masks). However, this can lead to aliasing artifacts in undersampled MRI images. To obtain clean, high-quality MRI images, reconstruction algorithms are required. Compressed sensing (CS) is a traditional MRI reconstruction method that utilizes the sparsity of MRI images in the transform domain, such as wavelets or discrete cosine transforms, to recover aliased MRI images. The combination of PI and CS is called PI-CS, which can simultaneously acquire undersampled data from multiple coils, resulting in faster MRI acquisition compared to PI or CS alone. However, PI-CS requires careful selection of hyperparameters, and manually adjusting hyperparameters can be challenging to obtain optimal results.

[0004] Deep learning (DL) has achieved remarkable success in computer vision due to its powerful representation capabilities. This success has also spurred the development of DL-based magnetic resonance imaging (MRI) reconstruction algorithms, which have shown significant advantages. Wang et al. were the first to use multi-layer convolutional neural networks (CNNs) to learn the mapping between MR images obtained from zero-padding and fully sampled K-space data. Since then, CNN-based MRI reconstruction algorithms have rapidly emerged. While CNNs have great potential in this field, Transformer models have attracted considerable attention due to their ability to capture long-range dependencies in various tasks, including computer vision. In recent years, researchers have proposed Transformer-based MRI reconstruction methods and achieved promising results. Unlike CNNs, Transformers have a stronger ability to model complex relationships. However, DL-based MRI methods, whether CNN-based or transformer-based, generally lack interpretability, making it challenging to analyze the contributions of different network modules. Furthermore, as the networks become deeper, overfitting also becomes a problem for these methods.

[0005] Existing magnetic resonance imaging reconstruction algorithms are not good at restoring image details and texture structures. They suffer from problems such as difficulty in manually designing priors and long iteration times, and cannot better preserve the details of magnetic resonance images to facilitate doctors' diagnosis of diseases. Summary of the Invention

[0006] The purpose of this invention is to provide a high-frequency fidelity magnetic resonance image reconstruction method to address the shortcomings of existing technologies. It adopts a model-driven high-frequency fidelity method, which allows the model to explicitly constrain the high-frequency information of the recovered image. The iterative solution algorithm is expanded into a neural network, which effectively solves the problem of poor recovery of image details and texture structure by traditional algorithms. It better preserves the details of magnetic resonance images, making it easier for doctors to diagnose diseases. The method is simple, has good results, and has good application prospects.

[0007] The specific technical solution for achieving the objective of this invention is: a magnetic resonance image reconstruction method based on high-frequency fidelity, characterized in that the method specifically includes the following steps:

[0008] Step 1: Undersample the fully sampled K-space data for data preprocessing;

[0009] Step 2: Design high-frequency fidelity terms based on the magnetic resonance image reconstruction model and establish the model;

[0010] Step 3: Use the variable splitting method to decompose the problem into multiple subproblems and solve them iteratively in an alternating manner;

[0011] Step 4: Use the variable splitting method to decompose the problem into multiple subproblems, and solve them iteratively in alternating ways;

[0012] Step 5: Use a supervised strategy to train the model using ground truth images;

[0013] Step 6: Select the best model based on the performance of the validation set, and input the test data into the model to obtain the reconstructed magnetic resonance image;

[0014] Step 1 specifically includes: applying a mask to the complete K-space data to obtain undersampled K-space data, normalizing the mean and variance of the obtained data, and then obtaining the estimated coil sensitivity map through the SENSE algorithm. The obtained data and the estimated sensitivity map are used as inputs to the subsequent model.

[0015] Step 2 specifically includes: establishing a magnetic resonance reconstruction model as shown in equation (a) below by adding a designed high-frequency fidelity term:

[0016]

[0017] Among them, the operator I is the identity matrix. To extract high-frequency information from an image in the image domain, a Gaussian high-pass filter is used here; β is the penalty weight, and n c The total number of coils, For the reconstructed image, For the undersampled K-space data of the i-th coil, This is the coil sensitivity diagram for the i-th coil. For inverse Fourier transform, the operator Where M is the sampling mask. This represents the inverse Fourier transform; φ(x) is the regularization term with respect to x. This is the joint prior distribution term for the images of each coil.

[0018] Step 3 specifically includes:

[0019] 3-1: Introduce auxiliary splitting variables u and v i ,make Furthermore, by adding a penalty term, the model transforms into the following equation (b) with respect to x, u, v. i Subproblems:

[0020]

[0021] in, The image is a multi-channel coil image, and γ1 and γ2 are penalty weights.

[0022] 3-2: The three subproblems after variable splitting are solved iteratively in an alternating manner, resulting in u as shown in equation (c) below. k , and x k Three sub-problems in form:

[0023]

[0024] Where, k∈{1,2,...,N} s} represents k iterations.

[0025] Step 4: Expand the analytical expression into the neural network and solve it using the network model.

[0026] Because it contains implicit regularization terms or implicit prior terms, regarding u k and The subproblems can be solved using a network model, x k In essence, it is about u k and The weighted average of the results of the sub-problems can be calculated using network training of the weighted weights.

[0027] Step 5 specifically includes: first, determining the loss function, learning rate, and optimizer, and then initializing the parameters in the model; the penalty weights in the model are all adaptively determined through learning methods.

[0028] Step 6 specifically includes: using the trained model to output the reconstructed magnetic resonance image; after the model training converges, saving the model weights; during inference, loading the model weights, then inputting the undersampled image, and outputting the reconstructed magnetic resonance image.

[0029] Compared with existing technologies, this invention explicitly constrains the high-frequency information of image restoration and expands the iterative solution algorithm into a neural network. It effectively solves the problem of poor restoration of image details and texture structure by traditional algorithms, better preserves the details of magnetic resonance images, facilitates doctors' diagnosis of diseases, and is simple to use with good results, showing promising application prospects. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the process of the present invention;

[0031] Figure 2 A schematic diagram of the magnetic resonance image update process. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0033] Example 1

[0034] See Figure 1A high-frequency fidelity magnetic resonance rapid reconstruction method includes the following steps:

[0035] Step 1: Obtain undersampled K-space data, preprocess the data, and use the obtained data as input for subsequent models.

[0036] Step 1 specifically includes:

[0037] 1-1: Obtain undersampled K-space data, and use the SENSE algorithm to estimate the sensitivity map S. i Therefore, the undersampled image shown in equation (d) can be obtained.

[0038]

[0039] in, The sensitivity diagram S of the i-th coil i The conjugate transpose of . For undersampled images, For the undersampled K-space data of the i-th coil, n c The total number of coils, This is the inverse Fourier transform.

[0040] 1-2: Yes Perform mean-variance normalization and then use it as the initial input to the model.

[0041] Step 2: Design high-frequency fidelity terms and establish a magnetic resonance reconstruction model.

[0042] Step 2 specifically includes: establishing a magnetic resonance reconstruction model based on the high-frequency fidelity term, expressed by the following equation (a):

[0043]

[0044] Among them, the operator I is the identity matrix. This method extracts high-frequency information from images in the image domain using a Gaussian high-pass filter. By explicitly adding a high-frequency fidelity term, the model pays more attention to recovering high-frequency information during image reconstruction. β is the penalty weight, and the operator... Where M is the sampling mask. This represents the inverse Fourier transform; φ(x) is the regularization term with respect to x. This is the joint prior distribution term for the images of each coil.

[0045] Step 3: Use the variable splitting method to decompose the problem into multiple subproblems and solve them iteratively in turn.

[0046] Step 3 specifically includes:

[0047] 3-1: Introduce auxiliary splitting variables u and v i ,make Furthermore, by adding a penalty term, the model transforms into the form shown in equation (b) below with respect to x, u, v. i Subproblems:

[0048]

[0049] in, The image is a multi-channel coil image, and γ1 and γ2 are penalty weights.

[0050] 3-2: The three subproblems after variable splitting, solved iteratively in an alternating manner, can be written in the form of the following equation (c):

[0051]

[0052] Where, k∈{1,2,...,N} s} represents k iterations.

[0053] Step 4: Expand the analytical expression into the neural network and solve it using the network model.

[0054] Because it contains implicit regularization terms or implicit prior terms, regarding u k and The subproblems can be solved using a network model, x k In essence, it is about u k and The weighted average of the results of the sub-problems can be calculated using network training of the weighted weights.

[0055] Step 5: Use a supervised strategy to train the model using ground truth images.

[0056] The specific method of step 5 includes: the model uses the Adam optimizer, the learning rate is set to 0.0005, the model involves complex data input, the real and imaginary parts are concatenated into two channels, the undersampling mask used during training is Cartesian sampling, and the training loss function is as follows (e):

[0057]

[0058] Where, x out The model outputs a reconstructed magnetic resonance image, x gt Here, N represents the ground truth image, and N represents the size of a training batch.

[0059] Step 6: Output the reconstructed magnetic resonance image.

[0060] The specific method of step 6 includes: after the model training converges, saving the best model, loading the model weights into the model, inputting undersampled K data, and outputting the reconstructed magnetic resonance image.

[0061] The scope of protection of this invention is not limited to the above embodiments. Any variations and advantages that can be conceived by those skilled in the art without departing from the spirit and scope of the inventive concept are included in this invention and are protected by the appended claims.

Claims

1. A method of magnetic resonance image reconstruction based on high frequency fidelity, characterized by: The method specifically includes the following steps: Step 1: Data Preprocessing Undersampled K-space data is obtained by using masks with different acceleration factors, and the mean and variance are normalized. Then, the estimated coil sensitivity map is obtained by the SENSE algorithm. The obtained data and the estimated sensitivity map are used as inputs for subsequent models. Step 2: Construction of the magnetic resonance image reconstruction model Design a high-frequency fidelity term and establish a magnetic resonance image reconstruction model; Step 3: Iterative solution of the model The model is decomposed into multiple sub-problems using the variable splitting method, and then solved iteratively in alternating ways. Step 4: Solving the subproblems The solution to the subproblem is expanded into an end-to-end neural network, and the network model is used to solve it; Step 5: Model Training A supervised strategy was used to train the magnetic resonance image reconstruction model using ground-based ground images. Step 6: Image Reconstruction The best model is selected based on the performance on the validation set. The test data is then input into the trained magnetic resonance image reconstruction model to obtain the reconstructed magnetic resonance image. Step 2 specifically includes: adding a designed high-frequency fidelity term and establishing a magnetic resonance image reconstruction model using the following equation (a): Among them, the operator ; It is the identity matrix; This is an operator for extracting high-frequency information from an image in the image domain; β is the penalty weight; n c This represents the total number of coils. The reconstructed image; This represents the undersampled K-space data for the i-th coil; This is the coil sensitivity diagram for the i-th coil; Inverse Fourier Transform; Operator ,in For sampling mask; This is the inverse Fourier transform; For about Regular terms; This is the joint prior distribution term for the images of each coil; Step 3 specifically includes: 3-1: Introduce auxiliary splitting variables u and v i ,make A penalty term is added to transform the magnetic resonance image reconstruction model into the form shown in equation (b) below with respect to x, u, v. i Subproblems: wherein, is a multi-channel coil image; γ1 and γ2 are penalty weights; 3-2: The three subproblems after variable splitting are solved through alternating iterations, resulting in the following equation (c). , and The three sub-problems are in the form of: wherein represents sub-iterations.

2. The high-frequency-fidelity-based magnetic resonance image reconstruction method of claim 1, characterized in that: Step 4 expands the analytical expression into a neural network and uses the network model to... and Solving subproblems; solving using network training and weighted weights. That is to and Calculate the weighted average of the results of the subproblems.

3. The high-fidelity-based magnetic resonance image reconstruction method of claim 1, characterized in that: Step 5 specifically includes: determining the loss function, learning rate, and optimizer, and then initializing the parameters in the magnetic resonance image reconstruction model; and adaptively determining the penalty weights in the magnetic resonance image reconstruction model through learning methods.

4. The high-fidelity-based magnetic resonance image reconstruction method of claim 1, characterized in that: Step 6 specifically includes: using the trained model to output the reconstructed magnetic resonance image; saving the model weights after the model training converges; during inference, loading the model weights, then inputting the undersampled image, and outputting the reconstructed magnetic resonance image.

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