Fast Magnetic Resonance Reconstruction Method Based on Framelet Transform

Abstract

The present invention relates to a fast magnetic resonance reconstruction method based on Framelet transform. The method includes: a) obtaining undersampled K-space data and preprocessing the data, and using the obtained data as the input for the subsequent model; b) designing a regularization term according to the sparse characteristics of magnetic resonance images to establish a magnetic resonance reconstruction model; c) using the alternating direction multiplier method to decompose the original problem into several sub-problems and solving them alternately; d) expanding the analytical formula in c) into a neural network and implementing the network model; e) using a supervised training strategy to train the magnetic resonance reconstruction model; f) using the trained model to output the reconstructed magnetic resonance image. The present invention is based on Framelet transform and expands from iterative optimization to deep learning, overcoming the problems of overly simple artificial priors and long iterative time of traditional algorithms, and also avoiding the problems of data-driven model parameter selection and large number of parameters, being able to improve the efficiency of magnetic resonance image reconstruction and obtain better reconstructed images.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and relates to a magnetic resonance image reconstruction method, in particular to a fast magnetic resonance reconstruction method based on Framelet transform. Background Art

[0002] Magnetic resonance imaging is one of the most important imaging methods in current medical imaging technologies. It can accurately obtain physiological functions, anatomical structures, metabolic information, and lesion information of tissues and organs without ionizing radiation. However, according to the imaging principle of magnetic resonance images, the entire imaging scan takes a long time, and the human body often undergoes displacement, resulting in the appearance of motion artifacts in the images. These artifacts can cause image blurring, overlapping, etc., seriously affecting the image quality. In clinical applications, it is necessary to shorten the sampling time to improve the patient experience and reduce equipment costs. To accelerate the magnetic resonance imaging speed, commonly used methods include parallel imaging and compressive sensing.

[0003] The parallel imaging method simultaneously acquires magnetic resonance signals by using a multi-channel receiving coil array. Each receiving coil obtains partial signals in the K-space. These acquired data have different spatial sensitivity information, and the associated information between channels is used to reconstruct the unacquired signals. Parallel imaging is currently mainly divided into two categories: one is the reconstruction based on fast K-space acquisition. Its main idea is to calculate the weight coefficients of the parallel coils from the undersampled K-space data, and use the acquired data to fit the missing K-space data in each coil, so as to obtain the complete K-space data of each coil. Its representative algorithm is GRAPPA; the other is the reconstruction based on the image domain. SENSE is the representative algorithm of this type, and subsequently, a variety of reconstruction algorithms such as the more commonly used SC-SENSE have been developed. This type of technology mainly uses the coil sensitivity information to unfold and combine the aliased images to obtain an image without aliasing artifacts. However, due to its physical space limitations, the number of coils cannot be infinitely stacked, and interference is likely to occur between coils, and algorithms need to be further used to eliminate the interference.

[0004] Compressed sensing is a new type of signal sampling technology that can reconstruct the original image information from random linear measurements far below the Nyquist sampling frequency. It takes advantage of the sparsity of the target image in a specific transform domain or dictionary subspace, compresses the signal into the sparse domain, and then realizes efficient signal acquisition and recovery processing. For the problem of magnetic resonance reconstruction, compressed sensing makes it possible to reconstruct undersampled k-space data. The theory of compressed sensing was first applied to the field of magnetic resonance imaging in CS-MRI. The introduction of the compressed sensing method has largely changed the traditional magnetic resonance imaging method. Traditional sparse prior methods assume that the target image is sparse under specific transforms such as total variation transform, discrete cosine transform, discrete wavelet transform, etc. Taking this as a constraint, an energy function is constructed, and then the reconstruction result is obtained by an optimization method. However, these methods also have many limitations. For example, the complexity of the image result is difficult to be completely represented by a simple sparse basis. Traditional CS-MRI reconstruction methods need to solve complex iterative optimization problems, and the reconstruction process is very time-consuming.

[0005] In recent years, algorithms based on deep learning have achieved a series of successes in the field of computer vision. More and more scholars have begun to try to apply deep learning algorithms to compressed sensing reconstruction and have achieved many results. Wang et al. first used CNN to establish the mapping relationship between undersampled images and high-quality images. Zhu et al. proposed the first work to learn the mapping between sensors and high-quality magnetic resonance images. The model uses fully connected layers and has manifold learning as the theoretical support. U-Net can retain low-level details through direct connections and is widely used in the field of medical images. Min et al. used U-Net as the network architecture to learn the mapping relationship between zero-filled images and clear images. The birth of GAN provides another idea for image processing. Quan et al. and Yang et al. both used the GAN architecture, with U-Net as the generator, and guided the training of the generation network through an updated discriminator. Jo et al. applied a cascaded network to magnetic resonance reconstruction and added a data fidelity operation after each reconstruction to perform frequency domain correction on the reconstruction result. KIKI-net uses cross-domain CNN to reconstruct undersampled k-space data and better reconstructs the detailed information. Yang et al. took a different approach and expanded the iteration of the optimization algorithm into the neural network, proposing ADMM-Net. After that, a series of model-driven magnetic resonance reconstruction algorithms have also been proposed. These methods use magnetic resonance physical knowledge to solve the inverse problem of regularization prior knowledge and often have better generalization and interpretability, and require fewer parameters and shorter training time. Summary of the Invention

[0006] The object of the present invention is to propose a fast magnetic resonance reconstruction method based on Framelet transform, which overcomes the problems of overly simple artificial priors and long iteration time in traditional algorithms, and can also avoid the problems of data-driven model parameter selection and large number of parameters to a certain extent. It belongs to the model-driven method and has a certain improvement in detail characterization.

[0007] The specific technical solution for achieving the object of the present invention is as follows:

[0008] A fast magnetic resonance reconstruction method based on Framelet transform, comprising:

[0009] Step 1: Obtain undersampled K-space data, and preprocess the data to obtain the data as the input of the subsequent model;

[0010] Step 2: Design a regularization term according to the sparse characteristics of magnetic resonance images, and establish a magnetic resonance reconstruction model;

[0011] Step 3: Use the alternating direction multiplier method to decompose the original problem into several sub-problems and solve them alternately;

[0012] Step 4: Expand the analytical formula in Step 3 into a neural network and implement the network model;

[0013] Step 5: Use a supervised training strategy to train the magnetic resonance reconstruction model;

[0014] Step 6: Use the trained model to output the reconstructed magnetic resonance image.

[0015] The specific content of Step 1 includes:

[0016] Obtain undersampled K-space data, and then obtain the coil sensitivity coefficient map of the undersampled data through the SENSE algorithm; next, preprocess the data, separate the real part and the imaginary part of the complex data and splice them as two channels and perform mean-variance normalization; the obtained data is used as the input of the subsequent model.

[0017] The specific content of Step 2 includes:

[0018] Design a regularization term according to the sparse characteristics of magnetic resonance images, establish a magnetic resonance reconstruction model, based on Framelet transform, the model is expressed as:

[0019]

[0020] where, y i is the undersampled K-space data of the i-th coil of the input, X is the reconstructed image, S iIt is the sensitivity coefficient diagram of the i-th coil, F represents the Fourier transform, D is the sampling matrix, ψ0 and ψ1 are the low-pass filter and high-pass filter of the Framelet transform respectively, W is the non-local means filtering, n is the number of coils, and α and β are weight coefficients; the first term in the formula is the fidelity term, and the latter two terms are the regularization terms.

[0021] The specific steps of step 3 include:

[0022] First, let S i X = T i , then T = [T1, T2, ……, T n . Let (ψ0X, ψ1X) = (Z0, Z1) = Z, then the said model is expressed by the augmented Lagrangian function as:

[0023]

[0024] where μ and ρ are weight coefficients, v = (v0, v1), σ is the Lagrange multiplier; next, it is necessary to solve four sub-problems of X, T, Z0, and Z1, and the solution is:

[0025]

[0026]

[0027]

[0028] where

[0029] where I is the all-1 matrix, is the conjugate matrix of S i , soft is the soft threshold function, expressed as soft(ω, λ) = sgn(ω)(|ω| - λ) + , where ω is the variable, λ is the threshold, and the sign(|ω| - λ) + means that it is equal to |ω| - λ when (|ω| - λ) > 0 and equal to 0 when (|ω| - λ) < 0; at the same time, for the update of the Lagrange multiplier:

[0030]

[0031]

[0032] Then, for the solution of the magnetic resonance image, the above 6 formulas are solved alternately.

[0033] The specific steps of step 4 include:

[0034] For the solution of sub-problem Z0, since its closed-form solution involves non-local mean filtering operations and matrix inversion operations after non-local mean filtering, it cannot be directly calculated. The analytical formula is expanded into a neural network, and the network model is implemented.

[0035] Step 5 specifically includes:

[0036] Using a supervised training strategy, train the magnetic resonance reconstruction model. First, initialize the data and parameters input to the network, and then determine the loss function, optimization method, and learning rate to start training; all network weights and hyperparameters in the model will be adaptively determined through learning means.

[0037] Step 6 specifically includes:

[0038] Use the trained model to output the reconstructed magnetic resonance image; after the model convergence training is completed, load the trained weights into the current model, input the undersampled image, and directly output the reconstructed magnetic resonance image, which can greatly reduce the entire imaging time.

[0039] Compared with the prior art, the present invention provides a fast magnetic resonance reconstruction method based on Framelet transform, which has the following beneficial effects:

[0040] 1) The present invention is a model-driven method that unfolds the iterative process of the optimization algorithm into a neural network, which often has better generalization and interpretability, and requires fewer parameters and shorter training time.

[0041] 2) The present invention is based on Framelet transform, obtains the low-frequency information and high-frequency information of the reconstructed image respectively, and separately constrains the low-frequency information and high-frequency information of the image, which can better depict the details.

[0042] 3) The present invention uses non-local U-Net, which can capture more long-distance information, help feature extraction, and improve the magnetic resonance reconstruction effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flowchart of the present invention;

[0044] Figure 2 is a network diagram of the non-local U-Net of the present invention;

[0045] Figure 3 is a flowchart of the update process of the magnetic resonance image of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0046] The following further details the embodiments of the present invention with reference to the accompanying drawings:

[0047] Refer to Figure 1, A fast magnetic resonance reconstruction method based on Framelet transform, comprising the following steps:

[0048] Step 1: Obtain undersampled K-space data and preprocess the data to obtain the data as the input for the subsequent model;

[0049] The specific method of Step 1 is as follows:

[0050] Obtain undersampled K-space data, and then obtain the coil sensitivity coefficient map of the undersampled data through the SENSE algorithm. Thus, the undersampled image can be obtained through the following formula:

[0051]

[0052] where X is the undersampled image, is the conjugate matrix of the i-th coil sensitivity coefficient map, T i is the image domain data after the inverse Fourier transform of the K-space data sampled by the i-th coil, and n is the number of coils. Next, preprocess the data, separate the real part and the imaginary part of the complex data as two channels, splice them together and perform mean-variance normalization, and obtain the data as the input for the subsequent model.

[0053] Step 2: Design a regularization term according to the sparse characteristics of magnetic resonance images and establish a magnetic resonance reconstruction model;

[0054] The specific method of Step 2 is as follows:

[0055] Based on the Framelet transform, the magnetic resonance reconstruction model is expressed as:

[0056]

[0057] where y i is the K-space data undersampled by the i-th coil of the input, X is the reconstructed image, S i is the i-th coil sensitivity coefficient map, F represents the Fourier transform, D is the sampling matrix, ψ0 and ψ1 are the low-pass filter and high-pass filter of the Framelet transform respectively, W is the non-local means filtering, n is the number of coils, and α, β are weight coefficients. The first term in the formula is the fidelity term, and the last two terms are the regularization terms. After the Framelet transform, the low-frequency information and high-frequency information of the reconstructed image are obtained. The low-frequency information and high-frequency information of the image are constrained separately. The low-frequency information uses the regularization constraint based on non-local means, and the high-frequency information is subjected to low-rank constraint.

[0058] Step 3: Use the alternating direction multiplier method to decompose the original problem into several sub-problems and solve them alternately;

[0059] The specific method of Step 3 is as follows:

[0060] First, introduce auxiliary variables. Let S i X = T i , then T = [T1, T2, ……, T n , let (ψ0X, ψ1X) = (Z0, Z1) = Z, then the described model is represented by the augmented Lagrangian function as follows:

[0061]

[0062] where μ and ρ are weight coefficients, v = (v0, v1), and σ are Lagrange multipliers. Next, it is necessary to solve four sub-problems of X, T, Z0, and Z1, and the solutions are as follows:

[0063]

[0064]

[0065]

[0066] where

[0067] where I is the all-ones matrix, is the conjugate matrix of S i , soft is the soft-thresholding function, expressed as soft(ω, λ) = sgn(ω)(|ω| - λ) + , where ω is the variable and λ is the threshold, and the sign(|ω| - λ) + means it equals |ω| - λ when (|ω| - λ) > 0 and equals 0 when (|ω| - λ) < 0; meanwhile, for the update of the Lagrange multiplier:

[0068]

[0069]

[0070] Then, for the solution of the magnetic resonance image, the above 6 equations are solved alternately.

[0071] Step 4: Expand the analytical formula in Step 3 into the neural network and implement the network model;

[0072] The specific method of Step 4 is as follows:

[0073] For the solution of the sub-problem Z0, since its closed-form solution contains non-local mean filtering operations and matrix inversion operations after non-local mean filtering operations and cannot be directly calculated, expand the analytical formula into the neural network and implement the network model. The constraint of Z0 is non-local regularization, where (α(1 - W) T(1 - W)+μ) -1 It cannot be directly calculated because it contains non - local operations. On this basis, a non - local network is implemented for fitting. As Figure 2 shown, it is the non - local U - Net (NL - UNet) network model used in the present invention, which mainly includes two parts. The first part is downsampling for feature extraction, and the second part is upsampling for dimension restoration. It first undergoes a 3×3 convolution operation. After an average pooling operation, the dimension is halved. Next, it passes through the non - local network to extract non - local features, and then another 3×3 convolution operation is performed. The entire downsampling process undergoes 3 pooling operations and 2 non - local operations. In the upsampling part, each time upsampling is performed, it is fused at the same scale with the corresponding number of channels in the feature extraction part. The upsampling method is a 2×2 transposed convolution operation, and the fusion method is concatenation. Then the solution of Z0 is:

[0074]

[0075] where NL - UNet is our network update operation. The entire model process for solving magnetic resonance images is as Figure 3 shown, and finally the magnetic resonance reconstructed image can be obtained.

[0076] Step 5: Use a supervised training strategy to train the magnetic resonance reconstruction model;

[0077] The specific method of step 5 is as follows:

[0078] In the network training of the present invention, the Adam optimizer is used, with the learning rate set to 0.0001, the first - order momentum to 0.9, the second - order momentum to 0.999, and the weight decay coefficient to 10 -7 . During the training process, complex - valued K - space data is used as input, and the real part and the imaginary part are concatenated into two channels. Cartesian sampling is used during training, and training is performed on the acceleration of R = 4 (i.e., retaining 25% of the K - space data and fully sampling 8% of the center lines) and R = 8 (i.e., retaining 12.5% of the K - space data and fully sampling 4% of the center lines) on the dataset. In the present invention, 5 sub - modules are cascaded, and all network weights and hyperparameters in the model will be adaptively determined by learning means. The training Loss function is:

[0079]

[0080] where X out is the magnetic resonance image output by the model, X GT is the label image, and m represents the number of magnetic resonance image pairs in a training batch.

[0081] Step 6: Use the trained model to output the reconstructed magnetic resonance image.

[0082] The specific method of step 6 is as follows:

[0083] Use the trained model to output the reconstructed magnetic resonance image. After the model convergence training is completed, load the trained weights into the current model, input the undersampled image, and directly output the reconstructed magnetic resonance image, which can greatly reduce the entire imaging time.

[0084] The protection scope of the present invention is not limited to the above embodiments. Without departing from the spirit and scope of the inventive concept, the changes and advantages that those skilled in the art can think of are included in the present invention, and the appended claims are taken as the protection scope.

Claims

1. A fast magnetic resonance reconstruction method based on Framelet transform, characterized in that, It includes the following steps: Step 1: Obtain undersampled k-space data, preprocess the data, and use the obtained data as the input of the subsequent model; Step 2: Design a regularization term according to the sparse characteristics of magnetic resonance images, and establish a magnetic resonance reconstruction model; Step 3: Use the alternating direction multiplier method to decompose the original problem into several sub-problems and solve them alternately; Step 4: Expand the analytical formula in Step 3 into a neural network and implement the network model; Step 5: Use a supervised training strategy to train the magnetic resonance reconstruction model; Step 6: Use the trained model to output the reconstructed magnetic resonance image; where: The specific content of Step 2 includes: Design a regularization term according to the sparse characteristics of magnetic resonance images, establish a magnetic resonance reconstruction model, and based on the Framelet transform, the model is expressed as: ； Among them, is the k-space data of the th coil under-sampling, is the reconstructed image, is the th coil sensitivity coefficient map, represents the Fourier transform, is the sampling matrix, and are the low-pass filter and high-pass filter of the Framelet transform respectively, is the non-local means filtering, is the number of coils, , are the weight coefficients; the first term in the formula is the fidelity term, and the last two terms are the regularization terms; The specific content of Step 3 includes: First, let , then , let , then the model is expressed by the augmented Lagrangian function as follows: ； Among them, , are weight coefficients, , are Lagrange multipliers; Next, it is necessary to solve four sub-problems, and the solutions are as follows: ； ； ； , where ; Among them, is an all-ones matrix, is 's conjugate matrix, is a soft threshold function, expressed as where, is a variable, is the threshold, and the symbol means equal to when , and equal to 0 when .

2. The fast magnetic resonance reconstruction method based on Framelet transform according to claim 1, characterized in that, The specific content of Step 1 includes: Obtain undersampled k-space data, then obtain the coil sensitivity coefficient map of the undersampled data through the SENSE algorithm; next, preprocess the data, separate the real part and the imaginary part of the complex data and splice them as two channels and perform mean-variance normalization; the obtained data is used as the input of the subsequent model.

3. A fast magnetic resonance reconstruction method based on Framelet transform according to claim 1, characterized in that The Lagrange multiplier is updated as: ； 。 4. A fast magnetic resonance reconstruction method based on Framelet transform according to claim 1, characterized in that The specific content of Step 4 includes: For the sub-problem Since its closed-form solution involves non-local mean filtering operations and matrix inversion operations after non-local mean filtering, which cannot be directly calculated, the analytical formula is expanded into a neural network and the network model is implemented.

5. A fast magnetic resonance reconstruction method based on Framelet transform according to claim 1, characterized in that, The specific content of Step 5 includes: Use a supervised training strategy to train the magnetic resonance reconstruction model. First, initialize the data and parameters input into the network, and then determine the loss function, optimization method, and learning rate to start training; all network weights and hyperparameters in the model will be adaptively determined by learning means.

6. A method for rapid magnetic resonance reconstruction based on Framelet transform according to claim 1, characterized in that The specific content of Step 6 includes: Use the trained model to output the reconstructed magnetic resonance image; after the model converges and the training is completed, load the trained weights into the current model, input the undersampled image, and directly output the reconstructed magnetic resonance image, and the entire imaging time can be greatly reduced.

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