A K-space NMR image reconstruction method based on convex set projection
By combining the convex set projection algorithm and deep learning methods, a phase correction and amplitude reconstruction module is used for the initial reconstruction of MR images, and a deep learning network is used for deep reconstruction. This solves the problems of computational cost and reconstruction effect in MRI undersampling reconstruction, and achieves fast and efficient MR image reconstruction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HOHAI UNIV
- Filing Date
- 2022-08-04
- Publication Date
- 2026-06-30
AI Technical Summary
Existing MRI techniques suffer from limited reconstruction results and high computational costs in undersampling reconstruction. Traditional methods rely on prior image knowledge but are time-consuming, while deep learning methods rely on data scale and computing power, leading to increased hardware and time costs.
By combining the convex set projection algorithm and deep learning methods, the initial reconstruction of MR images is performed through the phase correction module and the amplitude reconstruction module, the deep reconstruction is performed by combining the deep learning network, and the final reconstruction is achieved through the linear fusion model, thereby reducing the number of iterations and computational costs.
It enables fast and efficient reconstruction of MR undersampled images, reducing time and computational costs while improving reconstruction quality.
Smart Images
Figure CN115272509B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent image processing, and in particular to a method for K-space nuclear magnetic resonance image reconstruction based on convex set projection. Background Technology
[0002] K-space conjugate symmetry (Hermitian symmetry) is an important property in magnetic resonance imaging (MRI). Without changing the hardware and scanning methods of clinical MRI, imaging time can be shortened by measuring only a small portion of the k-space data. However, because Hermitian symmetry is often disturbed, it is difficult to directly recover missing sampled data. The Iterative Projection Convex Sets (POCS) algorithm uses an iterative approach, replacing the phase of the reconstructed image with a low-resolution symmetric phase in each iteration and re-inserting the original measurement data near discontinuities using a cone filter. This means that only the undersampled portion of the k-space changes in each iteration, and after several iterations, it no longer terminates when the last change in the undersampled data occurs. While the POCS algorithm effectively utilizes prior knowledge of the k-space of MR images to achieve undersampled image reconstruction, it suffers from limited reconstruction results and time consumption due to numerous iterative calculations.
[0003] In recent years, deep learning methods (DL) based on convolutional neural networks (CNNs) have proven to be a fast and robust MRI reconstruction method (DL-MRI). DL-MRI methods establish a mapping relationship between input and target using trainable deep learning network structures and train with large amounts of data to obtain a better fitting function, achieving good MR image reconstruction results. However, DL-MRI lacks exploration of the inherent characteristics of MR images and relies too heavily on data scale and large parameter training, both of which hinder the development of MR image reconstruction. Although traditional partial Fourier imaging methods and deep learning reconstruction algorithms can effectively accelerate MRI, these methods have drawbacks in terms of time and computational cost. Traditional methods can better utilize prior knowledge of MR images, but the numerical computation time cost is high, and the quality of reconstructed images is not as good as deep learning methods. DL-MRI uses a large amount of training data to obtain better reconstruction performance, but it is highly dependent on computational power and network complexity. A common improvement method is to increase the number of network layers and design more complex network structures, which increases hardware and time costs. Therefore, this invention proposes a K-space MRI image reconstruction method based on convex set projection to address the shortcomings of traditional methods and existing deep learning methods. Summary of the Invention
[0004] Purpose of the invention: The purpose of this invention is to provide a K-space nuclear magnetic resonance image reconstruction method based on convex set projection, so as to achieve fast and efficient reconstruction of MR undersampled images.
[0005] Technical solution: A method for K-space nuclear magnetic resonance image reconstruction based on convex set projection, comprising the following steps:
[0006] (1) Preliminary reconstruction of MR images based on convex set projection algorithm and deep learning method
[0007]
[0008] in, The nonlinear hypothesis function represents the initial reconstruction of MR images based on the convex set projection algorithm and deep learning method, θ. p These are the corresponding training parameters, k M It is MR undersampled k-space data, k c It is centrally symmetric K-space data, x M It is an MR undersampled image. This is the preliminary reconstruction result of the MR image;
[0009] (2) Perform MR image depth reconstruction based on deep learning method using the preliminary reconstruction results of MR images.
[0010]
[0011] Represents depth reconstruction of MR images based on deep learning methods; θ c These are the corresponding training parameters;
[0012] (3) Fusion output of preliminary reconstruction and depth reconstruction of combined MR images
[0013]
[0014] yes and and The linear hypothesis function between them achieves the fusion output of the preliminary reconstruction and depth reconstruction of the joint MR image, and its corresponding training parameter is θ. l , It is the result of depth reconstruction of MR images. This is the final result of MR image reconstruction.
[0015] The preliminary reconstruction of the MR image in step (1) includes a phase correction module and an amplitude reconstruction module based on the POCS algorithm.
[0016] The phase correction module based on the POCS algorithm uses the POCS algorithm to decompose the MR undersampled image into two parts: phase and amplitude. It also introduces the phase information of the centrally symmetric MR image as the reference phase and designs a deep learning network architecture model to realize the phase correction of the MR undersampled image, as shown in formula (2).
[0017]
[0018] in, It is the corrected phase of the MR undersampled image, φ C It is the phase of a centrally symmetric MR image, φ M It is the phase of the MR undersampled image. It is a linearly trainable network layer, θ φ yes Trainable parameters in the network.
[0019] The amplitude reconstruction module iteratively updates the phase of the MR undersampled image after correction with the amplitude of the MR undersampled image to achieve preliminary reconstruction of the MR image, as shown in formula (3):
[0020]
[0021] in, yes With x M and The nonlinear hypothesis function between them This is the preliminary reconstruction result of the MR image, x M It is the initial undersampled MR image. It is the corrected phase of the MR undersampled image, θ p These are the corresponding training parameters.
[0022] The iterative update step of correcting the phase of the MR undersampled image and updating the amplitude of the MR undersampled image can be expressed as formula (4) after the (n+1)th iteration:
[0023]
[0024] in, It is the magnitude of the MR-updated image after the nth iteration. It is the MR update image after the (n+1)th iteration. It is the corrected MR image phase.
[0025] Step (2) MR image depth reconstruction uses DL-MRI image reconstruction technology to achieve MR undersampled image depth reconstruction based on the preliminary reconstruction of the MR undersampled image. The formula is as follows:
[0026]
[0027] in, It is the result of depth reconstruction of MR images. This represents a nonlinear hypothesis function relating the preliminary reconstruction results of an MR image to the depth reconstruction results of an MR image. This is the preliminary reconstruction result of the MR image, θ c yes Trainable parameters.
[0028] Step (3) Design a trainable linear fusion model to achieve linear fusion of the preliminary reconstruction results and depth reconstruction results of the MR image, and obtain the final K-space MRI image reconstruction result based on convex set projection; the specific process is shown in formula (6):
[0029]
[0030] in, yes and and The linear hypothesis function between them These are the preliminary reconstruction results of the MR images. It is the result of depth reconstruction of MR images. This is the result of K-space NMR image reconstruction based on convex set projection, and its corresponding training parameter is θ. l .
[0031] Beneficial effects: This invention proposes a k-space MRI reconstruction method based on convex set projection, which changes the current mainstream MRI deep learning reconstruction method. It transforms the traditional iterative update solution mode into two steps: image verification and image reconstruction. The use of an end-to-end deep learning network for solving the problem reduces time and computational costs, enabling fast and efficient reconstruction of undersampled MR images. Attached Figure Description
[0032] Figure 1 This is a schematic diagram illustrating the principle of the present invention;
[0033] Figure 2 The image shows the effect of reconstructing MRI images according to the present invention, and compares it with other algorithms. Detailed Implementation
[0034] The technical solution of the present invention will be further described below with reference to the accompanying drawings.
[0035] like Figure 1As shown, this invention provides a technical solution: a K-space nuclear magnetic resonance image reconstruction method based on convex set projection (POCS) algorithm, comprising: an MR image preliminary reconstruction module based on convex set projection (POCS) algorithm and deep learning method, an MR image depth reconstruction module based on deep learning method, and a fusion output module for joint MR image preliminary reconstruction and depth reconstruction. The MR image preliminary reconstruction module based on POCS algorithm and deep learning method includes a phase correction module and an amplitude reconstruction module based on the POCS algorithm. The phase correction module based on the POCS algorithm introduces the phase of the MR centrosymmetric sampled image as a reference phase and designs a deep learning network architecture model to achieve phase correction of the MR undersampled image. The amplitude reconstruction module based on the POCS algorithm uses an iterative approach to provide more prior image knowledge to the MR image depth reconstruction module based on the deep learning method. The MR image depth reconstruction based on the deep learning method can select from a variety of advanced deep learning-based MR undersampled image reconstruction algorithms. The fusion output module for joint MR image preliminary reconstruction and depth reconstruction linearly fuses the MR image preliminary reconstruction results based on POCS algorithm and deep learning method with the MR image depth reconstruction results based on deep learning method. This invention provides a highly efficient and accurate MR undersampled image reconstruction method by utilizing the iterative approach of the POCS algorithm to provide more prior image knowledge for the POCS-based K-space MR image reconstruction method.
[0036] Figure 1 Description of each part: (A) Flowchart of the K-space NMR image reconstruction method based on convex set projection proposed in this invention. (B) POCS Network. It consists of a phase correction network (f phase It consists of a magnitude reconstruction module (POCS) and a magnitude reconstruction module (k). c and k M These represent centrally sampled K-space data and undersampled K-space data, respectively. DC is the data consistency layer, used to enhance data consistency in the POCS method. (C) POCS algorithm execution flowchart, where K-space is the complete K-space data, IDFT is the inverse Fourier transform operation, |x L (m,n)| and |x M (m,n) represents the amplitude of the center-sampled MR image and the amplitude of the undersampled MR image, respectively, and ∠x L (m,n) and ∠x M (m,n) represent the phase of the MR image at the center and the phase of the undersampled MR image, respectively. pocs (m,n) is the output of the POCS algorithm.
[0037] like Figure 1 As shown in (A), the K-space MRI image reconstruction method based on convex set projection adopts an end-to-end network design structure, using the original K-space data as input and the reconstructed image as output; the POCS Network module, DL-MRINetwork module, and Linear Fusion Network module correspond to the formula (1) respectively. and The mapping relationship;
[0038] Figure 1 In (B), k c and k M This involves using simulated sampling masks to accelerate sampling (4x and 8x) and center sampling for MR k-space data, resulting in undersampled K-space and centrosymmetric K-space data. Then, a two-dimensional inverse Fourier transform is used to convert the frequency domain of the undersampled MR image and the centrosymmetric sampled MR image to the time domain. The specific process is as follows:
[0039] Assumption This represents a fully sampled 2D complex K-space data, and This is the MR image corresponding to the K-space, where M represents the sampling mask. The MR K-space undersampling process and the generation of the undersampled image can be represented as follows:
[0040]
[0041] in, It is the inverse Fourier transform, k M It is undersampled k-space data, x M It is an MR undersampled image;
[0042] The aforementioned MR K spatial centrosymmetric sampling process and centrosymmetric sampling image generation can be represented as follows:
[0043]
[0044] in, It is the inverse Fourier transform, k C It is centrally symmetric sampled k-space data, x C It is an MR centrally symmetric sampled image. This represents a fully sampled 2D complex K-space data;
[0045] like Figure 1 (B) shows the initial reconstruction module of MR images based on the Projection Convex Sets (POCS) algorithm and deep learning method. In the figure, f phase The trainable module is responsible for implementing formula (2) The mapping relationship, the phase φ of the centrally symmetric MR imageC It was introduced as a reference phase to realize the phase φ of the MR undersampled image. M Phase correction; POCS is a reconstruction module based on the POCS algorithm, and its execution flowchart is as follows. Figure 1 (C) shows the DC module, which is the data consistency layer module. Figure 1 The operation process of (B) is as follows:
[0046] First, the phase information of the undersampled K-space image and the phase information of the centrally symmetric K-space image are extracted and fused using a deep learning-based method. Then, using the POCS reconstruction algorithm and the corrected MR image phase information, a small number of iterations are performed to achieve the initial reconstruction of the MR image based on the POCS algorithm and deep learning method, providing more prior knowledge of the image for the verification network. Finally, a data consistency layer operation is performed to increase the consistency of the initial MR image reconstruction data, thus completing the initial MR image reconstruction.
[0047] like Figure 1 As shown in (B), the MR image depth reconstruction module based on deep learning methods utilizes the currently advanced MR image reconstruction network structure based on deep learning methods to complete MR image depth reconstruction; the DL-MRI network proposed in this invention can integrate various mainstream reconstruction network structures (K-space-image, image-image, etc.).
[0048] like Figure 1 As shown in (B), the fusion output module for the joint preliminary reconstruction and depth reconstruction of MR images uses a deep learning network method to design a linear fusion network structure to achieve linear fusion of the preliminary reconstruction results and the depth reconstruction results of MR images, and obtains the final K-space nuclear magnetic resonance image reconstruction result based on convex set projection.
[0049] Figure 2 The .U-Net and POCS-Unet are representative image visualizations on the test dataset with random and equispaced masks at 4x and 8x speedup, respectively. The Ground Truth is a true MR fully sampled image.
[0050] The images used in the experiments were obtained from the publicly available human MR database (FastMRI), and were cropped to 320×320 pixels after data preprocessing. Two undersampling masks with simulated acceleration factors of 4 (center sampling rate of 0.08) and 8 (center sampling rate of 0.04) were used in the experiments, and both random sampling and equidistant sampling methods were employed. The deep learning-based MR image depth reconstruction module used the classic U-Net network as a benchmark network. The test platform consisted of an Intel Xeon(R) CPU E5-2650 v4@2.20GHz and an NVIDIA GeForce RTX 2080 Ti GPU. Deep learning was performed using the PyTorch framework for modeling, training, and testing. The single-image reconstruction results under different sampling masks are shown in the attached figure. Figure 2 As shown, the method used in this invention has a better reconstruction effect than the benchmark DL-MRI reconstruction network.
Claims
1. A method for K-space magnetic resonance image reconstruction based on convex set projection, characterized in that, Includes the following steps: (1) Preliminary reconstruction of MR images based on convex set projection algorithm and deep learning method （1a） wherein, represents a nonlinear hypothesis function to implement MR image preliminary reconstruction based on a convex set projection algorithm and a deep learning method, is a corresponding training parameter, is MR undersampled K-space data, is central symmetric K-space data, is an MR undersampled image, is an MR image preliminary reconstruction result; (2) Perform MR image depth reconstruction based on deep learning method using the preliminary reconstruction results of MR images. （1b） This represents depth reconstruction of MR images based on deep learning methods. These are the corresponding training parameters; (3) Fusion output of preliminary reconstruction and depth reconstruction of combined MR images （1c） yes and and The linear hypothesis function between them achieves the fusion output of the preliminary reconstruction and depth reconstruction of the joint MR image, and its corresponding training parameters are: , It is the result of depth reconstruction of MR images. This is the final result of MR image reconstruction; The preliminary reconstruction of the MR image in step (1) includes a phase correction module and an amplitude reconstruction module based on the POCS algorithm; The phase correction module based on the POCS algorithm uses the POCS algorithm to decompose the MR undersampled image into two parts: phase and amplitude. It also introduces the phase information of the centrally symmetric MR image as the reference phase and designs a deep learning network architecture model to realize the phase correction of the MR undersampled image, as shown in formula (2). （2） in, It is the corrected phase of the MR undersampled image. It is a centrally symmetric MR image phase. It is the phase of the MR undersampled image. It is a linearly trainable network layer. yes Trainable parameters in the network; The amplitude reconstruction module iteratively updates the phase of the MR undersampled image after correction with the amplitude of the MR undersampled image to achieve preliminary reconstruction of the MR image, as shown in formula (3): （3） in, yes and and The nonlinear hypothesis function between them These are the preliminary reconstruction results of the MR images. It is the initial undersampled MR image. It is the corrected phase of the MR undersampled image. These are the corresponding training parameters.
2. The method for K-space nuclear magnetic resonance image reconstruction based on convex set projection according to claim 1, characterized in that, The step of iteratively updating the phase of the MR undersampled image and the amplitude of the MR undersampled image, the first step... After the next iteration, it can be expressed as formula (4): （4） in, It is the magnitude of the MR-updated image after the nth iteration. It is the first After the next iteration, the MR image is updated. It is the corrected MR image phase.
3. The method for K-space nuclear magnetic resonance image reconstruction based on convex set projection according to claim 1, characterized in that, Step (2) MR image depth reconstruction uses DL-MRI image reconstruction technology to achieve MR undersampled image depth reconstruction based on the preliminary reconstruction of the MR undersampled image. The formula is as follows: （5） in, It is the result of depth reconstruction of MR images. This represents a nonlinear hypothesis function relating the preliminary reconstruction results of an MR image to the depth reconstruction results of an MR image. These are the preliminary reconstruction results of the MR images. yes Trainable parameters.
4. The method for K-space nuclear magnetic resonance image reconstruction based on convex set projection according to claim 1, characterized in that, Step (3) Design a trainable linear fusion model to achieve linear fusion of the preliminary reconstruction results and the depth reconstruction results of the MR image, and obtain the final K-space nuclear magnetic resonance image reconstruction results based on convex set projection; The specific process is shown in formula (6): （6） in, yes and and The linear hypothesis function between them These are the preliminary reconstruction results of the MR images. It is the result of depth reconstruction of MR images. This is the result of K-space NMR image reconstruction based on convex set projection, and its corresponding training parameters are: .