Reference driving undersampling magnetic resonance image reconstruction method based on denoising regularization and depth image prior

Abstract

The invention discloses a reference driving undersampling magnetic resonance (MR) image reconstruction method based on denoising regularization (RED) and depth image prior. The method does not depend on a large-scale clinical data set, a constraint reconstruction model based on denoising regularization and depth image prior is constructed, and the reconstruction of the target MR image under the under-sampling data can be realized only through the driving of a high-resolution reference image similar to the structure of the target image to be reconstructed. The method comprises the specific steps of selection of a single magnetic resonance reference image, denoising engine training of reference driving, depth image prior network construction based on U-Net, construction of a constraint optimization model combining k-space data fidelity and RED regularization, sub-problem decomposition and iterative updating based on an ADMM algorithm, and data correction and reconstruction output. According to the method, the structure prior is introduced into the deep network by using the reference image, the learning efficiency is improved, the dependence on the training data is reduced, the high-quality reconstruction of the MR image under the under-sampling data can be realized, the detail structure and the texture feature are effectively reserved, and the reconstruction precision and the visual quality are remarkably improved. The method is suitable for clinical MRI rapid reconstruction and other imaging applications, and has high practical value.

Description

Technical Field

[0001] The present invention relates to the field of magnetic resonance imaging (MRI) image reconstruction, and in particular to an under-sampling MRI image reconstruction method that combines deep image prior (DIP) with denoising regularization (RED) and introduces reference image driving. Background Art

[0002] Currently, magnetic resonance imaging has the advantages of being radiation-free and having high soft tissue contrast, but it takes a long time to acquire data, often requiring acceleration through undersampling and reconstruction algorithms. Deep learning-based reconstruction methods require large-scale, high-quality clinical datasets for pre-training. However, in practical applications, high-quality training data is difficult to obtain due to limitations in patient privacy and data acquisition requirements. In existing technologies, deep image priors (DIPs) have attracted attention as a method that can solve inverse problems without pre-training. However, they do not fully utilize image structural information, resulting in limited improvement in reconstruction performance. Introducing display regularization into DIP can further improve reconstruction performance, but the reconstruction process involves the derivation of the regularization term. For complex, non-convex cases, it often faces problems such as poor convergence and robustness, low algorithm efficiency, and difficulty in obtaining a global optimal solution.

[0003] Therefore, there is an urgent need for a method that does not rely on clinical datasets, can effectively utilize MR image structure priors, has flexible and efficient regularization, and can achieve rapid reconstruction of high-quality MR images under undersampling conditions. Summary of the Invention

[0004] The present invention provides a reference-driven magnetic resonance image reconstruction method based on denoising regularization and deep image prior. The main technical solution is to use only a reference image with a similar structure to drive an untrained deep image prior network. Therefore, without the need for large-scale fully sampled data pre-training, a constrained reconstruction model is constructed by combining deep image prior (DIP) and denoising regularization (RED), and high-precision, detail-preserving, fast MR image reconstruction is achieved from undersampled k-space data.

[0005] To solve the problems of long acquisition time and limited data acquisition in existing magnetic resonance imaging, the technical solution of the present invention mainly includes the following steps and technical features:

[0006] 1. Data acquisition and reference image selection

[0007] Undersampling is used to obtain the k-space data of the target image, and a high-resolution reference image with similar anatomical structure to the target image is selected.

[0008] 2. Reference-driven denoising engine training

[0009] The present invention designs a denoising engine training scheme driven by reference images: a pre-constructed convolutional neural network (CNN) is used as the denoising engine, and its training process is only based on a single reference image I. r Drive, by minimizing the objective function shown in formula (1), the denoising engine training is completed through iterative solution. r ) with reference image I r In practical applications, the target image and the reference image are from the same part of the same patient, with the same acquisition scene and acquisition parameters. Therefore, using the reference image to train the denoising engine can fully utilize the structural similarity and introduce structural prior information.

[0010] 3. Build a constrained optimization model

[0011] A constrained optimization model is constructed as shown in Equation (2), whose objective function includes a data fidelity term (ensuring the consistency of the k-space between the reconstruction and the actual measurement data) and a RED regularization term (using the trained denoising engine to constrain image smoothness and structural information).

[0012] 4. Decompose the sub-problems and use ADMM to update them alternately

[0013] The present invention transforms the constrained optimization problem in formula (2) into a penalty problem using the augmented Lagrangian method (AL), and adopts the ADMM iterative algorithm to decompose the original problem into three sub-problems:

[0014] Network parameter update subproblem: Fix the current image estimate and update the deep network parameters through backpropagation and Adam optimization algorithm so that the network output gradually approaches the target image while retaining the structural prior provided by the reference image.

[0015] Image update subproblem: Under fixed network parameters, a fixed-point strategy is adopted to solve the RED regularization subproblem and update the image reconstruction result I.

[0016] Lagrange multiplier update: Update the multiplier variables according to the ADMM framework to ensure a balance between data fidelity terms and regularization terms.

[0017] 5. Constructing a deep image prior network

[0018] The encoder-decoder network structure based on U-Net is adopted, which is equipped with multi-layer convolutional layers, batch normalization layers, LeakyReLU activation functions and jump connections to fully capture image features of different scales.

[0019] Different from the traditional deep image prior (DIP) method, the present invention uses the reference image as the network input to provide structural prior information, rather than relying solely on random noise. This enables the network to have better image structure information in the initialization stage, facilitating subsequent iterative optimization.

[0020] 6. Post-processing and reconstructed image output

[0021] After the iteration, the k-space data of the reconstructed image is corrected to ensure that the error is only concentrated in the unsampled data.

[0022] The final output magnetic resonance reconstruction image has high fidelity in terms of details, texture and edge information, and can better reflect the actual anatomical structure, meeting clinical diagnostic requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 The overall workflow of the Ref-DRED method is detailed in two parts: the left side shows the reference-driven denoising engine training process, and the right side shows the reference-driven reconstruction process based on RED regularization and DIP. This figure intuitively illustrates the implementation process of the present invention and the dual driving role of the reference image in both the denoising engine training and reconstruction phases, serving as the network input and introducing a structural prior.

[0024] Figure 2 The U-Net structure adopted in the present invention is demonstrated, including encoder and decoder, skip connection, batch normalization layer, convolution layer and activation function.

[0025] Figure 3 This figure shows a comparison of images reconstructed from brain image 1 at a 30% sampling rate (Cartesian sampling template). The first row shows the ground truth of the target image, the comparison method, and the reconstruction result of the present invention. The second row shows the corresponding error image, and the third row shows a local magnification. The comparison methods used are: zero padding, classic DIP, and DIP with the reference image as input (abbreviated as DIP+Ref). Figure 4 This figure shows a comparison of the reconstructed images of brain image 2 at a 25% sampling rate (Cartesian sampling template). The first row shows the ground truth of the target image, the comparison method, and the reconstruction result of the present invention. The second row shows the corresponding error image, and the third row shows a local magnification.

[0026] Depend on Figure 3-4 The visual reconstruction results show that the reconstruction results of the present invention are closer to the target MR image. In particular, the locally enlarged image shows that it has obvious advantages in preserving structural details and texture features. The corresponding error image also proves that the reconstruction results of the present invention have the smallest error.

[0027] Figure 5The quantitative indicators of the comparison method and the present invention at sampling rates of 10%, 15%, 20%, 25%, 30% and 40% are compared using a Cartesian sampling template at different sampling rates. The evaluation indicators include relative error RelErr, peak signal-to-noise ratio PSNR, and structural similarity index SSIM. Figure 6 The quantitative evaluation of the reconstruction results of the comparison method and the present invention under variable density (20% sampling rate) and radial undersampling mask (30% sampling rate) is demonstrated.

[0028] Figure 5-6 The data comparison in shows that, with the same number of sampled data, for the three groups of MR data, the reconstruction results obtained by the present invention have the highest SSIM and PSNR values ​​and the lowest RelErr, that is, the present invention can reconstruct more accurate reconstruction results. DETAILED DESCRIPTION

[0029] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention, but the protection scope of the present invention should not be limited thereto.

[0030] Example: Reference-driven denoising engine training and reconstruction process

[0031] 1. Acquire undersampled k-space data of the target image from the MRI scanner and select a reference image with similar anatomical structure to the target image.

[0032] 2. Use the reference image to train the denoising engine.

[0033] 3. Construct the objective function: The objective function includes the data fidelity term.

[0034] 4. Use the ADMM method to decompose the objective function into network parameter optimization, image update, and Lagrange multiplier update subproblems, and update them alternately and iteratively:

[0035] Network parameter optimization: Use the Adam algorithm to back-propagate and update the deep network parameters.

[0036] Make the network output gradually close to the target image. In this step, the reference image is used as the input of the deep network.

[0037] A randomly initialized U-Net structure is used.

[0038] Image update: Fix the network parameters and solve the RED regularization subproblem using a fixed-point strategy to obtain an intermediate reconstructed image.

[0039] Lagrange multiplier update: Update the multipliers according to the ADMM framework to maintain data consistency.

[0040] 5. When the iteration reaches the preset maximum number or meets the convergence criterion, the iteration is stopped, and the network output is subjected to k-space data correction and inverse Fourier transform to finally obtain the reconstructed image.

Claims

1. A reference-driven undersampled MR image reconstruction method based on denoising regularization (RED) and deep image prior (DIP), characterized in that: The following steps are involved: (1) Provide a reference MR image that is anatomically similar to the target image as a driver; (2) Constructing a neural network model as a denoising engine, using a single reference image to drive the denoising engine training and constructing the denoising regularization term; (3) Construct a constrained reconstruction model that includes k-space data fidelity terms and denoising regularization; (4) Using the ADMM algorithm, the constrained reconstruction problem is decomposed into three sub-problems: network parameter optimization, image update, and Lagrange multiplier update, and an alternating iterative update strategy is designed; (5) constructing a U-net model, inputting the reference image into an untrained U-net network, introducing a structural prior, and driving the optimization of network parameters; (6) The output is k-space data corrected and reconstructed to obtain the target MR image.

2. The method according to claim 1(1), wherein Select a single reference MR image I r And use it to implement a dual driving strategy: first, it serves as the input of the denoising engine to drive the training of the denoising engine; The second is to serve as the input of the deep prior network, used to introduce structural prior information into the network and learning process, improve learning efficiency and reduce dependence on training data.

3. The method according to claim 1(2), wherein: Reference Image I r is used to train a convolutional neural network (CNN) that acts as a denoising engine D(·). In this step, the training process does not rely on a large amount of pre-training data, but only on the single reference image I r Driven by minimizing the objective function shown in formula (1) The denoising engine training is completed after 3000 iterations. In the above formula, D(Θ|I r ) means that Θ is the parameter and I r For input.

4. The method according to claim 1(3), wherein: Based on the deep image prior framework, the target MR image reconstruction problem is transformed into a constrained optimization problem as shown in Equation (2): Among them, F U is the under-sampled Fourier transform operator, y is the under-sampled k-space data obtained by measurement, and λ is the regularization parameter. r ) represents the network parameter θ, and the reference image I r The first term in Equation (2) is the data fidelity term, which ensures the consistency between the k-space data of the reconstructed result and the measured value. The second term is the RED regularization term, where D(·) is the denoising engine trained in the previous step. By adding a denoising prior, the reconstruction is further constrained, improving the accuracy and stability of the reconstruction result.

5. The method according to claim 1(4), characterized in that The constrained optimization problem in formula (2) is transformed into a penalty problem using the augmented Lagrangian method (AL), and the alternating direction multiplier method (ADMM) is used to decompose the overall problem into three sub-problems: network parameter optimization, image update, and Lagrangian multiplier update. The formula is described as follows: (1) Introduce the Lagrange multiplier vector u and construct an augmented objective function for the original problem, as shown in formula (3): Where μ is the ADMM penalty parameter. (2) Using the alternating update strategy, the complex optimization problem shown in formula (3) is decomposed into three simple sub-problems and solved alternately and iteratively. For the iteration index k: Formula (4) is the network parameter update sub-problem, which is obtained by using Adam and back propagation after 100 iterations. k; Equation (5) is the image update subproblem. Using the fixed-point strategy, the derivative of the objective function with respect to I is set to zero to obtain the current optimal solution. Formula (6) is the Lagrange multiplier update function. After the predetermined number of iterations K=30 updates, the network parameters after training are obtained. And the corresponding network output is the reconstructed MR image.

6. The method according to claim 1(5), wherein: The U-net structure is used to construct an untrained deep network as f(θ|I r ), which uses the reference image I r As the network input, by introducing structural prior information, the optimization of network parameters is driven. The specific network structure and parameter settings are as follows: (1) The network structure adopts the U-net model based on the encoder-decoder architecture. Its overall network shape is similar to the "hourglass structure", and jump connections are set between the encoder layer and the decoder layer to integrate feature information at different levels. (2) Network input: The reference image I r Directly input U-net to embed the prior information of anatomical structure into the network during the forward transmission process, thereby improving the efficiency of network parameter learning. (3) Network hyperparameter settings: (a) Maximum network depth: L = 6; (b) Number of upsampling channels: n u =[32,32,64,128,128,128]; (c) Number of downsampling channels: n d =[32,32,64,128,128,128]; (d) Number of filters in skip connection: n s =[16,16,16,16,16,16]; (e) Convolution kernel size: k is used in both upsampling and downsampling paths. d =k u =[3,3,3,3,3,3]; (f) The convolution step size of each layer is k s =[1,1,1,1,1,1]; (g) Batch normalization (BN) and leaky rectified linear unit (LeakyReLU) are used to improve training stability; (h) The upsampling strategy uses bilinear interpolation, and the downsampling adopts pooling operation. During the entire reconstruction process, the untrained U-net model uses the structural prior in the reference image to update the network parameters through backpropagation and Adam optimization algorithm, so that the model output is more consistent with the actual structural characteristics of the target image.

7. The method according to claim 1(6), characterized in that After the aforementioned alternating iterative updates, the k-space data is corrected for consistency using a data correction operator. The corrected data is then inverse Fourier transformed to produce the final reconstructed target MRI image. This step ensures that the final reconstruction strictly preserves the sampled data information obtained from the original measurement.

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