Low-field magnetic resonance diffusion imaging reconstruction method and system

Abstract

The present invention relates to a low-field magnetic resonance diffusion imaging reconstruction method, comprising the steps of: acquiring low-field magnetic resonance K-space data; mapping the acquired K-space data to a standard Cartesian coordinate system using a Gaussian kernel grid interpolation method, weighting each radial sampling point using a Gaussian kernel function to ensure that the data is smoothly distributed on a standard grid; utilizing the interpolated K-space data to reconstruct the image based on image prior constraints, wherein the image prior constraints include: the image's low-rank structure and sparse prior information; and gradually optimizing the parameters of the low-rank and sparse components using a hybrid kernel function, and combining these constraints with the image's low-rank structure and sparse prior information to enhance the image reconstruction effect. The present invention also relates to a low-field magnetic resonance diffusion imaging reconstruction system. The present invention can significantly improve image quality and noise immunity.

Description

Technical Field

[0001] The invention relates to a low-field magnetic resonance diffusion imaging reconstruction method and system. Background Art

[0002] Magnetic resonance imaging (MRI) has become an important tool in medical imaging because it can provide high-resolution soft tissue images without the hazards of ionizing radiation. However, while low-field MRI offers advantages in cost, power consumption, and shielding requirements, its lower magnetic field strength results in weaker signal intensity, further affecting the image signal-to-noise ratio (SNR), especially in diffusion-weighted imaging (DWI). The main challenges of low-field diffusion imaging are the decrease in signal intensity, the limitations of gradient strength, and the gradient switching rate, which greatly restricts the application of low-field MRI in diffusion imaging.

[0003] To address these challenges, researchers have developed various diffusion imaging techniques, including EPI (echo planar imaging) and LSDI (line scan diffusion imaging) sequences. The EPI sequence achieves efficient imaging by rapidly acquiring data across the entire K-space, but it is prone to artifacts in low-field MRI and requires high gradient strength and gradient switching rates. In contrast, the LSDI sequence acquires data line by line and is not limited by gradient strength and gradient switching rates. However, due to its slow scanning speed, it is prone to transverse artifacts and is difficult to use efficiently under low-field conditions. In addition, radial acquisition methods have been explored for diffusion imaging in low-field MRI to address signal-to-noise ratio and sampling efficiency issues.

[0004] The radial acquisition scheme in high-resolution MRI acquires data by radiating from the center of K-space to the edge. This approach reduces artifacts and increases imaging speed through dense sampling of the central portion of K-space and sparse reconstruction techniques. This radial sampling pattern enables high-density sampling of low-frequency regions, ensuring clarity of critical image information.

[0005] Existing low-field magnetic resonance diffusion imaging technology has significant shortcomings in image quality and noise suppression. First, the diffusion imaging sequence (EPI) commonly used in high-field conditions is difficult to overcome the limitations of gradient strength and switching rate under low-field conditions, making it impossible to apply it in low-field magnetic resonance. In addition, the inherent weaker net magnetization and shorter T1 relaxation time of low-field magnetic resonance systems lead to a significant reduction in signal intensity, while thermal noise remains unchanged, making the impact of noise more obvious during image reconstruction, ultimately affecting the quality and diagnostic value of the image. In diffusion imaging, the diffusion gradient signal attenuation in weak magnetic field systems is more serious, further reducing the signal-to-noise ratio and making the acquisition of high-quality images more challenging. Although the existing line scan diffusion imaging (LSDI) can perform complete sampling, it has a long scanning time and is easily affected by motion artifacts and frequency offset effects, resulting in insufficient clarity and stability of the reconstructed image. Summary of the Invention

[0006] In view of this, it is necessary to provide a low-field magnetic resonance diffusion imaging reconstruction method and system, which can significantly improve image quality and noise resistance.

[0007] The present invention provides a low-field magnetic resonance diffusion imaging reconstruction method, which includes the following steps: S1, collecting K-space data of low-field magnetic resonance; S2, using a Gaussian kernel grid interpolation method to map the collected K-space data to a standard Cartesian coordinate system, and weighting each radial sampling point by a Gaussian kernel function to ensure that the data is smoothly distributed on the standard grid; S3, using the interpolated K-space data to reconstruct the image based on image prior constraints, wherein the image prior constraints include: a low-rank structure and sparse prior information of the image; S4, gradually optimizing the parameters of low-rank and sparse components by using a hybrid kernel function, and combining the low-rank structure and sparse prior information of the image to perform constraints, thereby improving the image reconstruction effect.

[0008] Preferably, step S1 includes:

[0009] Step S11: establishing an adaptive K-space sampling model under low field strength conditions;

[0010] Step S12, designing a low-field diffusion imaging sequence;

[0011] Step S13: Acquire K-space data according to the designed sampling trajectory and time sequence.

[0012] Preferably, the step S11 includes:

[0013] The signal acquisition trajectory is determined to be bidirectional radial, the central area of ​​the K space can be repeatedly and densely sampled, while the edge ensures sparseness to reduce the acquisition time, and the final K space sampling model is obtained.

[0014] Preferably, the step S12 includes:

[0015] First, a 90-degree excitation pulse is applied, while slice selection is achieved via G1. Phase errors caused by the slice selection gradient are compensated using the phase compensation gradient G2. Gradients G3 and G13 then control the acquisition direction, allowing for continuous radial sampling at different angles. These gradients, after passing through the center of K-space, continue to extend outward, achieving bidirectional acquisition.

[0016] After the 180-degree focusing pulse, readout gradients G5 and G15 are responsible for data acquisition to ensure signal coverage in the entire K-space. Simultaneously, a diffusion gradient is applied before G3 and G13 to directionally compensate for magnetic field inhomogeneities, capture anisotropic water molecule diffusion information, and ensure reliable diffusion-weighted imaging signals at low fields.

[0017] Gradient G4 was set after the 180-degree pulse to eliminate unwanted echoes and enhance stability, while destruction gradients G6, G7, and G8 were used to suppress secondary echoes, flow signals, and residual spin effects.

[0018] Preferably, the step S2 includes:

[0019] Step S21: Project the collected radial K-space data onto a standard Cartesian grid using the polar coordinate to Cartesian coordinate conversion formula (1), where: is the distance from the sampling point to the center of K space, n represents the nth piece of projection data collected, θ is the step size of the projection angle change for each acquisition, FE represents the position of the abscissa in the standard Cartesian coordinate system with the center of K space as the origin, and PE represents the position of the ordinate;

[0020] (1);

[0021] Step S22: Kernel function-based grid interpolation uses a Gaussian kernel function to weight each non-uniform sampling point so that it is smoothly distributed to nearby grid points to ensure complete K-space coverage.

[0022] Preferably, the step S3 includes:

[0023] Step S31, establishing an optimization problem: during the reconstruction process, the K-space data is decomposed into low-rank and sparse components by solving a convex optimization problem with image prior constraints;

[0024] Step S32, iterative optimization: utilizing the low-rank characteristics and sparse prior of the image, iterative optimization is performed to gradually adjust the weight parameters of the low-rank and sparse components to achieve the best reconstruction effect.

[0025] Preferably, in step S31:

[0026] The optimization formula is as follows:

[0027] (2)

[0028] in, is the nuclear norm of the low-rank component, is the L1 norm of the sparse component, and are the weight parameters of low-rank and sparse terms respectively, is the sampling operator, is the K-space data obtained after interpolation in step S2.

[0029] Preferably, the step S4 includes:

[0030] Step S41: define a hybrid kernel function, use an improved Gaussian-polynomial hybrid kernel function, directly introduce the prior coefficients L and S into the whale optimization algorithm, and gradually adjust the balance between the two during the optimization process to achieve the best reconstruction quality;

[0031] Step S42: Iterative solution, using the whale optimization algorithm to gradually and iteratively adjust the kernel function parameters so that the low-rank and sparse components reach the optimal balance, thereby significantly improving the image clarity and effectively suppressing artifacts.

[0032] Preferably, in step S41:

[0033] The specific formula of the hybrid kernel function is as follows:

[0034] (3).

[0035] The present invention also provides a low-field magnetic resonance diffusion imaging reconstruction system, which includes an acquisition module, an interpolation module, a reconstruction module, and an optimization module, wherein:

[0036] The acquisition module is used to acquire K-space data of low-field magnetic resonance imaging;

[0037] The interpolation module is used to map the collected K-space data into a standard Cartesian coordinate system using a Gaussian kernel grid interpolation method, and weight each radial sampling point using a Gaussian kernel function to ensure that the data is smoothly distributed on the standard grid;

[0038] The reconstruction module is used to use the interpolated K-space data to reconstruct the image based on the image prior constraints, wherein the image prior constraints include: low-rank structure and sparse prior information of the image;

[0039] The optimization module is used to gradually optimize the parameters of low-rank and sparse components by using a hybrid kernel function, and to perform constraints in combination with the low-rank structure and sparse prior information of the image to improve the effect of image reconstruction.

[0040] This application uses a special bidirectional radial acquisition sequence to ensure dense repeated sampling of the low-frequency part of the K space and sparse sampling of the high-frequency area, thereby enhancing the stability of the fixed components and the signal strength of the diffusion components. During the reconstruction process, the K space is completed by interpolation of the kernel function. At the same time, the image low rank and sparse priors are used for constraints, and the low rank and sparse coefficients are optimized by the whale optimization algorithm (WOA) to balance the energy difference between the low-frequency and high-frequency components, effectively suppressing artifacts and enhancing the clarity of the image. This maximizes the accuracy and noise resistance of the reconstructed image. Ultimately, this application significantly improves the image quality of low-field diffusion imaging and enhances its reliability and applicability in clinical diagnosis. The beneficial effects of this application specifically include:

[0041] (1) Experimental improvement of bidirectional radial sampling sequence design: In low-field MRI diffusion imaging, in order to improve the acquisition efficiency, this application designs a bidirectional radial sampling sequence (SEDWPR). This sequence allows the radial trajectory to pass from one side of the K space to the other side, passing through the central area multiple times, thereby achieving high-density low-frequency signal acquisition. Through experimental comparison with traditional unidirectional radial acquisition, the bidirectional design of this application increases low-frequency redundancy, effectively improves the image's ability to resist motion artifacts, enhances sampling consistency in low-field MRI, and provides more stable data support for subsequent reconstruction.

[0042] (2) Improvement of data acquisition efficiency: Based on experimental comparison, bidirectional radial sampling can cover the main area of ​​K space with fewer acquisition times, effectively reducing the dependence on phase encoding. By achieving dense sampling in the low-frequency region, the K space filling efficiency is optimized. The results show that this method significantly reduces the scanning time in a low-field environment, improves the overall imaging efficiency, and further improves the reconstruction accuracy by using compressed sensing reconstruction.

[0043] (3) Experimental verification of anti-artifact capability: In low-field magnetic resonance imaging, motion artifacts and non-uniform sampling artifacts are common image quality challenges. This application uses a bidirectional radial sampling sequence design so that each trajectory passes through the center of the K space from multiple angles. Experimental results show that this sampling strategy significantly enhances the image's anti-motion artifact capability. At the same time, through comparative experiments, it is verified that under different motion conditions, the image quality of this application is more stable, further improving the reliability of low-field magnetic resonance imaging.

[0044] (4) Experimental optimization of grid interpolation reconstruction. To address the non-uniform distribution caused by radial sampling, this application introduces a Gaussian kernel grid interpolation method to smoothly map radial data to a standard Cartesian grid. Experiments show that Gaussian weighted interpolation balances the weight of each radial point, making the K-space data coverage more complete. Comparative experiments show that compared with other interpolation methods, Gaussian kernel interpolation significantly reduces non-uniform sampling artifacts and improves image reconstruction accuracy.

[0045] (5) Experimental verification of low-field diffusion imaging sequence optimization. In low-field environments, traditional diffusion imaging methods have poor imaging effects due to limited gradient strength and switching rate. To this end, this application designs a diffusion-weighted imaging sequence suitable for low-field environments. By precisely controlling the time sequence and gradient combination, the gradient utilization rate under limited conditions is maximized. Experimental verification shows that the diffusion imaging quality of this application design under low-field conditions is superior to that of traditional methods, especially in terms of signal-to-noise ratio and image clarity. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of the low-field magnetic resonance diffusion imaging reconstruction method of the present invention;

[0047] Figure 2 A schematic diagram of spatial data sampling provided by an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of a kernel function interpolation method provided in an embodiment of the present invention;

[0049] Figure 4 This is a hardware architecture diagram of the low-field magnetic resonance diffusion imaging reconstruction system of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] See Figure 1 FIG. 2 is a flowchart of a preferred embodiment of the low-field magnetic resonance diffusion imaging reconstruction method of the present invention.

[0052] Step S1, collects K-space data of low-field magnetic resonance. That is: in a low-field magnetic resonance environment, use a bidirectional radial diffusion imaging sequence to collect K-space data. Through this strategy, sufficient sampling coverage is ensured in the low-frequency region to obtain sufficient low-frequency information for accurate reconstruction; at the same time, sparse sampling is used in the high-frequency region to reduce the amount of data collected and optimize the acquisition efficiency. This sampling method reduces the sampling time and data volume while ensuring the quality of reconstruction, improves the overall signal-to-noise ratio, and ensures that the image still has good clarity and detail performance under low-field conditions. Specifically:

[0053] In K-space data acquisition, this application designs a bidirectional radial sampling sequence suitable for low-field diffusion imaging, ensuring high-density low-frequency repeated sampling and sparse sampling in the edge area. Figure 2 This embodiment uses multi-angle projection to achieve each radial trajectory passing through the center of K space, thereby enhancing the redundancy of low-frequency data and reducing the amount of peripheral sampling, effectively reducing data acquisition time. The specific steps are as follows:

[0054] Step S11, establishing a K-space sampling model: Under low field strength conditions, the present invention establishes an adaptive K-space sampling model, determines that the trajectory of signal acquisition is bidirectional radial, the central area of ​​the K-space can be repeatedly and densely sampled, and at the same time, the edge ensures sparseness to reduce acquisition time. The final K-space sampling model is as follows: Figure 2 As shown in (c), it shows how the projection trajectories at multiple angles evenly cover the entire K space.

[0055] Step S12, designing a low-field diffusion imaging sequence: To adapt to the hardware limitations of the low-field MRI system, the present invention designs a bidirectional radial diffusion imaging sequence. Figure 2In the sequence design shown in (a), a 90-degree excitation pulse is first applied via radiofrequency (RF). Simultaneously, slice selection is achieved via G1 in the slice selection gradient (GS), and phase compensation gradient G2 compensates for the phase error caused by the slice selection gradient. Next, gradients G3 and G13 are applied to the X-axis readout gradient (GR) and Y-axis readout gradient (GP), respectively. G3 and G13 control the prephasing direction of the acquired signal, allowing for continuous radial sampling of echo signals at varying angles. These gradients, after passing through the center of k-space, continue to extend outward, achieving bidirectional acquisition.

[0056] After the 180-degree focusing pulse, readout gradients G5 and G15 are applied to the X-axis readout gradient (GR) and Y-axis readout gradient (GP), respectively. G5 and G15 control echo signal data acquisition. The areas of these two gradients are twice those of G3 and G13, ensuring signal coverage throughout K-space. Furthermore, to accommodate the diffusion effects of low-field imaging, the present invention applies diffusion gradients (such as G20 and G23, G21 and G24, and G22 and G25) before G3 and G13. These diffusion gradients directionally compensate for magnetic field inhomogeneities, capturing information about anisotropic water molecule diffusion and ensuring reliable diffusion-weighted imaging signals at low fields.

[0057] In addition, gradient G4 is set after the 180-degree pulse to eliminate unwanted echoes and enhance stability, while destruction gradients G6, G7, and G8 are used to suppress secondary echoes, flow signals, and residual spin effects. By applying a diffusion gradient before G3 and G13, phase error propagation is minimized, simplifying frequency encoding, improving resistance to motion artifacts, and enhancing system stability.

[0058] Step S13, K-space data acquisition: According to the designed sampling trajectory and time sequence, a 0.16T low-field magnetic resonance system is used to acquire K-space data. High-density sampling in the central area ensures complete signal acquisition and provides an accurate reference for subsequent reconstruction, while downsampling in the peripheral area effectively reduces the amount of data, creating conditions for rapid imaging. In this process, the gradient field usually changes continuously in a smooth manner, without the need for frequent direction switching, thus reducing the system's recovery time and stabilization time, effectively shortening the overall acquisition time. Finally, the data collected at each angle is stored as a column, such as Figure 2 As shown in (b).

[0059] In other embodiments, the sampling angle is calculated to adapt to various clinical needs. For example, when clinical diagnosis requires high resolution, the low-frequency sampling density is increased and the reconstruction algorithm is optimized to ensure complete image details. In emergency or rapid imaging, the sampling density can be reduced and the sampling speed can be increased to meet clinical timeliness.

[0060] Step S2: K-space data grid interpolation. To obtain complete K-space data due to the non-uniformity of radial sampling, a Gaussian kernel grid interpolation method is used to map the acquired sparse priors to a standard Cartesian coordinate system. Each radial sampling point is weighted using a Gaussian kernel function to ensure a smooth distribution of data on a standard grid, ensuring accuracy and consistency during subsequent image reconstruction.

[0061] Since radial sampling results in incomplete K-space sampling, this embodiment uses a kernel function interpolation method, such as Figure 3 As shown in Figure 2, the collected radial data is mapped to a standard Cartesian grid. Specifically:

[0062] Step S21, polar coordinate to Cartesian coordinate conversion, projecting the collected radial K-space data onto a standard Cartesian grid using the polar coordinate to Cartesian coordinate conversion formula (1), where: is the distance from the sampling point to the center of K space, n represents the nth piece of projection data collected, θ is the step size of the projection angle change for each data collection, FE represents the position of the horizontal coordinate in the standard Cartesian coordinate system with the center of K space as the origin, and PE represents the position of the vertical coordinate.

[0063] (1)

[0064] Step S22: Grid interpolation based on kernel function, using Gaussian kernel function to weight each non-uniform sampling point so that it is smoothly distributed to nearby grid points to ensure complete K-space coverage, such as Figure 3 For each regular grid point, the weights of adjacent sampling points are accumulated to achieve complete K-space coverage and high-precision reconstruction, as shown in (a). Figure 3 As shown in (b).

[0065] In step S3, image reconstruction is performed based on the image prior constraints. Specifically, the prior constraints can effectively separate the image's structural information from noise characteristics, achieving a clearer image restoration. By using appropriate prior information to adjust the reconstruction model, adapting it to data collected from different angles and requirements, the algorithm's versatility and reconstruction quality are improved.

[0066] This embodiment utilizes the low-rank structure and sparse prior information of the image for reconstruction to improve the image's noise resistance and detail restoration effect. The low-rank components are used to capture the stable background information of the image, while the sparse components extract dynamic features.

[0067] Specifically:

[0068] Step S31: Establish an optimization problem. During the reconstruction process, the K-space data is decomposed into low-rank and sparse components by solving a convex optimization problem with image prior constraints to minimize the reconstruction error. The optimization formula is as follows:

[0069] (2)

[0070] in, is the nuclear norm of the low-rank component, is the L1 norm of the sparse component, and are the weight parameters of low-rank and sparse terms respectively, is the sampling operator, is the K-space data obtained after interpolation in step S2. This prior constraint model effectively enhances the image restoration capability in low-field imaging environments.

[0071] Step S32, iterative optimization. Using the low-rank characteristics and sparse priors of the image, iterative optimization is performed to gradually adjust the weight parameters of the low-rank and sparse components. and , in order to achieve the best reconstruction effect.

[0072] Step S4: Whale Optimization Algorithm (WOA) parameter tuning: WOA uses a hybrid kernel function to gradually optimize the parameters of low-rank and sparse components, incorporating constraints based on the image's low-rank characteristics and sparse prior information to enhance image reconstruction. This significantly improves the reconstructed image's noise immunity and detail restoration, resulting in higher clarity and diagnostic value. This optimization strategy achieves optimal reconstruction quality in various imaging scenarios, further enhancing the clinical value of images.

[0073] Based on the use of image prior information, this embodiment uses the Whale Optimization Algorithm (WOA) to further optimize the low-rank structure and coefficient components. The specific steps are as follows:

[0074] Step S41: Define a hybrid kernel function. Use an improved Gaussian-polynomial hybrid kernel function to directly introduce the prior coefficients L and S into the WOA. During the optimization process, gradually adjust the balance between the two to achieve the best reconstruction quality. The specific formula is as follows:

[0075] (3)

[0076] Step S42: Iterative solution. Through WOA, kernel function parameters are adjusted step by step to achieve an optimal balance between low-rank and sparse components, thereby significantly improving image clarity and effectively suppressing artifacts. The reconstruction error is gradually reduced over multiple iterations to achieve high-quality image reconstruction.

[0077] See Figure 4 FIG. 1 is a hardware architecture diagram of a low-field magnetic resonance diffusion imaging reconstruction system 10 of the present invention. The system includes: an acquisition module 101, an interpolation module 102, a reconstruction module 103, and an optimization module 104.

[0078] The acquisition module 101 is used to acquire K-space data of low-field magnetic resonance. That is: in a low-field magnetic resonance environment, a bidirectional radial diffusion imaging sequence is used to acquire K-space data. Through this strategy, sufficient sampling coverage is ensured in the low-frequency region to obtain sufficient low-frequency information for accurate reconstruction; at the same time, sparse sampling is used in the high-frequency region to reduce the amount of data collected and optimize the acquisition efficiency. This sampling method reduces the sampling time and data volume while ensuring the quality of reconstruction, improves the overall signal-to-noise ratio, and ensures that the image still has good clarity and detail performance under low-field conditions. Specifically:

[0079] In K-space data acquisition, this application designs a bidirectional radial sampling sequence suitable for low-field diffusion imaging, ensuring high-density low-frequency repeated sampling and sparse sampling in the edge area. Figure 2 This embodiment uses multi-angle projection to ensure that each radial trajectory passes through the center of the K space, thereby enhancing the redundancy of low-frequency data and reducing the amount of peripheral sampling, effectively reducing data acquisition time. Specifically, it includes:

[0080] The acquisition module 101 establishes a K-space sampling model: Under low field strength conditions, the present invention establishes an adaptive K-space sampling model, determines that the trajectory of signal acquisition is bidirectional radial, and the central area of ​​the K-space can be repeatedly and densely sampled, while the edge ensures sparseness to reduce acquisition time. The final K-space sampling model is as follows Figure 2 As shown in (c), it shows how the projection trajectories at multiple angles evenly cover the entire K space.

[0081] The acquisition module 101 designs a low-field diffusion imaging sequence: To adapt to the hardware limitations of the low-field MRI system, the present invention designs a bidirectional radial diffusion imaging sequence. Figure 2 In the sequence design shown in (a), a 90-degree excitation pulse is first applied via radiofrequency (RF). Slice selection is achieved using G1 in the slice selection gradient (GS), and phase compensation gradient G2 compensates for phase errors caused by the slice selection gradient. Next, gradients G3 and G13 are applied to the X-axis readout gradient (GR) and Y-axis readout gradient (GP), respectively. G3 and G13 control the prephasing direction of the acquired signal, allowing for continuous radial sampling of echo signals at varying angles. These gradients, after passing through the center of k-space, continue to extend outward, achieving bidirectional acquisition.

[0082] After the 180-degree focusing pulse, readout gradients G5 and G15 are applied to the X-axis readout gradient (GR) and Y-axis readout gradient (GP), respectively. G5 and G15 control echo signal data acquisition. The areas of these two gradients are twice those of G3 and G13, ensuring signal coverage throughout K-space. Furthermore, to accommodate the diffusion effects of low-field imaging, the present invention applies diffusion gradients (such as G20 and G23, G21 and G24, and G22 and G25) before G3 and G13. These diffusion gradients directionally compensate for magnetic field inhomogeneities, capturing information about anisotropic water molecule diffusion and ensuring reliable diffusion-weighted imaging signals at low fields.

[0083] In addition, gradient G4 is set after the 180-degree pulse to eliminate unwanted echoes and enhance stability, while destruction gradients G6, G7, and G8 are used to suppress secondary echoes, flow signals, and residual spin effects. By applying a diffusion gradient before G3 and G13, phase error propagation is minimized, simplifying frequency encoding, improving resistance to motion artifacts, and enhancing system stability.

[0084] The acquisition module 101 performs K-space data acquisition: according to the designed sampling trajectory and time sequence, a 0.16T low-field magnetic resonance system is used to acquire K-space data. High-density sampling in the central area ensures complete signal acquisition and provides an accurate reference for subsequent reconstruction, while downsampling in the peripheral area effectively reduces the amount of data, creating conditions for rapid imaging. In this process, the gradient field usually changes continuously in a smooth manner, without the need for frequent direction switching, thus reducing the system's recovery time and stabilization time, effectively shortening the overall acquisition time. Finally, the data collected at each angle is stored as a column, such as Figure 2 As shown in (b).

[0085] Interpolation module 102 performs grid interpolation of k-space data. Specifically, due to the non-uniformity of radial sampling, a Gaussian kernel grid interpolation method is used to map the acquired sparse priors to a standard Cartesian coordinate system to obtain complete k-space data. Each radial sampling point is weighted using a Gaussian kernel function to ensure a smooth distribution of data on a standard grid, ensuring accuracy and consistency during subsequent image reconstruction.

[0086] Since radial sampling results in incomplete K-space sampling, this embodiment uses a kernel function interpolation method, such as Figure 3 As shown in Figure 2, the collected radial data is mapped to a standard Cartesian grid. Specifically:

[0087] The interpolation module 102 performs polar coordinate to Cartesian coordinate conversion, and projects the acquired radial K-space data onto a standard Cartesian grid using the polar coordinate to Cartesian coordinate conversion formula (1), where: is the distance from the sampling point to the center of K space, n represents the nth piece of projection data collected, θ is the step size of the projection angle change for each data collection, FE represents the position of the horizontal coordinate in the standard Cartesian coordinate system with the center of K space as the origin, and PE represents the position of the vertical coordinate.

[0088] (1)

[0089] The interpolation module 102 is based on the grid interpolation of the kernel function, and uses the Gaussian kernel function to weight each non-uniform sampling point so that it is smoothly distributed to the nearby grid points to ensure that the K space coverage is complete, such as Figure 3 For each regular grid point, the weights of adjacent sampling points are accumulated to achieve complete K-space coverage and high-precision reconstruction, as shown in (a). Figure 3 As shown in (b).

[0090] The reconstruction module 103 is used to reconstruct images based on prior image constraints. Specifically, these prior constraints can effectively separate image structural information from noise characteristics, achieving clearer image restoration. By using appropriate prior information to adjust the reconstruction model, it adapts to data collected from different angles and requirements, thereby improving the algorithm's versatility and reconstruction quality.

[0091] The reconstruction module 103 utilizes the low-rank structure and sparse prior information of the image to perform reconstruction to improve the image's noise resistance and detail restoration effect. The low-rank components are used to capture the image's stable background information, while the sparse components extract dynamic features. Specifically:

[0092] The reconstruction module 103 establishes an optimization problem. During the reconstruction process, the K-space data is decomposed into low-rank and sparse components by solving a convex optimization problem with image prior constraints to minimize the reconstruction error. The optimization formula is as follows:

[0093] (2)

[0094] in, is the nuclear norm of the low-rank component, is the L1 norm of the sparse component, and are the weight parameters of low-rank and sparse terms respectively, is the sampling operator, is the K-space data obtained after interpolation by the interpolation module 102. By using this prior constraint model, the image restoration capability in a low-field imaging environment is effectively enhanced.

[0095] The reconstruction module 103 performs iterative optimization. It uses the low-rank characteristics and sparse priors of the image to perform iterative optimization to gradually adjust the weight parameters of the low-rank and sparse components. and , in order to achieve the best reconstruction effect.

[0096] The optimization module 104 is used to tune parameters using the Whale Optimization Algorithm (WOA). WOA uses a hybrid kernel function to gradually optimize the parameters of low-rank and sparse components, and incorporates the image's low-rank characteristics and sparse prior information to impose constraints to enhance image reconstruction. This significantly improves the reconstructed image's noise immunity and detail restoration, resulting in a final image with higher clarity and diagnostic value. This optimization strategy achieves optimal reconstruction quality in various imaging scenarios, further enhancing the clinical value of the images.

[0097] Based on the prior information of the image, the optimization module 104 uses the Whale Optimization Algorithm (WOA) to further optimize the low-rank structure and coefficient components. The details are as follows:

[0098] The optimization module 104 defines a hybrid kernel function, using an improved Gaussian-polynomial hybrid kernel function, and directly introduces the prior coefficients L and S into the WOA. During the optimization process, the balance between the two is gradually adjusted to achieve the best reconstruction quality. The specific formula is as follows:

[0099] (3)

[0100] The optimization module 104 performs an iterative solution, gradually adjusting the kernel function parameters through WOA to achieve an optimal balance between low-rank and sparse components, thereby significantly improving image clarity and effectively suppressing artifacts. The reconstruction error is gradually reduced over multiple iterations, resulting in high-quality image reconstruction.

[0101] In other embodiments, for high motion artifacts or low signal-to-noise ratio environments, Total Variation (TV) regularization or deep learning-based reconstruction techniques may be more suitable, and the above methods can provide better detail enhancement and artifact suppression effects. In high-field or ultra-high-field magnetic resonance systems, the sampling density and reconstruction strategy can be further adjusted, such as reducing repeated sampling of low-frequency areas in high-field systems to optimize sampling efficiency. In addition, the resolution and accuracy of diffusion-weighted imaging can be further improved by utilizing the higher gradient intensity and larger b-value provided by the high-field system. The present application can also be applied to magnetic resonance angiography (MRA) or functional magnetic resonance imaging (fMRI). In particular, for imaging sequences that are sensitive to motion artifacts, increasing repeated sampling in low-frequency areas can help improve image consistency and enhance motion artifact suppression, thereby enhancing its application potential in cardiovascular or neuroimaging.

[0102] The present invention comprehensively solves the problems of low signal-to-noise ratio, multiple motion artifacts, and long sampling time in low-field MRI systems through innovative bidirectional radial sampling sequence design, Gaussian kernel-based grid interpolation K-space completion method, image reconstruction based on image prior information, and the application of whale optimization algorithm, thereby improving the overall image quality of low-field diffusion imaging.

[0103] This application uses a radial sampling pattern that crosses the center of K-space multiple times, increasing acquisition speed and density for low-frequency information. It also fine-tunes image prior constraints using the Whale Optimization Algorithm (WOA), ultimately effectively improving image clarity and artifact suppression. This application enables diffusion imaging in low-field MRI systems, enhancing their practicality and reliability in clinical and scientific research applications.

[0104] Although the present invention has been described with reference to the current preferred embodiments, those skilled in the art should understand that the above-mentioned preferred embodiments are only used to illustrate the present invention and are not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A low-field magnetic resonance diffusion imaging reconstruction method, characterized in that: The method comprises the following steps: S1, acquisition of K-space data of low-field magnetic resonance imaging; S2 uses the Gaussian kernel grid interpolation method to map the collected K-space data into a standard Cartesian coordinate system. Each radial sampling point is weighted by the Gaussian kernel function to ensure that the data is smoothly distributed on the standard grid. S3, using the interpolated K-space data to reconstruct an image based on image prior constraints, wherein the image prior constraints include: a low-rank structure and sparse prior information of the image; S4, by using a hybrid kernel function to gradually optimize the parameters of low-rank and sparse components, and combining the low-rank structure and sparse prior information of the image to constrain, improves the image reconstruction effect; The step S1 includes: Step S11: establishing an adaptive K-space sampling model under low field strength conditions; Step S12, designing a low-field diffusion imaging sequence; Step S13: Acquire K-space data according to the designed sampling trajectory and time sequence; The step S11 includes: The signal acquisition trajectory is determined to be bidirectional radial, so that the central area of ​​the K-space can be repeatedly and densely sampled, while the edges ensure sparseness to reduce acquisition time, and the final K-space sampling model is obtained; The step S12 includes: First, a 90-degree excitation pulse is applied, while slice selection is achieved using gradient G1. Phase errors caused by the slice selection gradient are compensated using phase compensation gradient G2. Gradients G3 and G13 then control the acquisition direction, allowing for continuous radial sampling at different angles. These gradients, after passing through the center of K-space, continue to extend outward, achieving bidirectional acquisition. After the 180-degree focusing pulse, readout gradients G5 and G15 are responsible for data acquisition to ensure signal coverage in the entire K-space. Simultaneously, a diffusion gradient is applied before G3 and G13 to directionally compensate for magnetic field inhomogeneities, capture anisotropic water molecule diffusion information, and ensure reliable diffusion-weighted imaging signals at low fields. Gradient G4 was set after the 180-degree pulse to eliminate unwanted echoes and enhance stability, while destruction gradients G6, G7, and G8 were used to suppress secondary echoes, flow signals, and residual spin effects.

2. The method according to claim 1, wherein The step S2 includes: Step S21: Project the collected radial K-space data onto a standard Cartesian grid using the polar coordinate to Cartesian coordinate conversion formula (1), where: is the distance from the sampling point to the center of K space, n represents the nth piece of projection data collected, θ is the step size of the projection angle change for each data collection, FE represents the position of the abscissa in the standard Cartesian coordinate system with the center of K space as the origin, and PE represents the position of the ordinate; （1）； Step S22: Kernel function-based grid interpolation uses a Gaussian kernel function to weight each non-uniform sampling point so that it is smoothly distributed to nearby grid points to ensure complete K-space coverage.

3. The method according to claim 2, wherein The step S3 includes: Step S31, establishing an optimization problem: during the reconstruction process, the K-space data is decomposed into low-rank and sparse components by solving a convex optimization problem with image prior constraints; Step S32, iterative optimization: utilizing the low-rank characteristics and sparse prior of the image, iterative optimization is performed to gradually adjust the weight parameters of the low-rank and sparse components to achieve the best reconstruction effect.

4. The method according to claim 3, wherein The step S4 includes: Step S41: define a hybrid kernel function, use an improved Gaussian-polynomial hybrid kernel function, directly introduce the prior coefficients into the whale optimization algorithm, and gradually adjust the balance between the two during the optimization process to achieve the best reconstruction quality; Step S42: Iterative solution, using the whale optimization algorithm to gradually and iteratively adjust the kernel function parameters so that the low-rank and sparse components reach the optimal balance, thereby significantly improving the image clarity and effectively suppressing artifacts.

5. A low-field magnetic resonance diffusion imaging reconstruction system using the low-field magnetic resonance diffusion imaging reconstruction method according to claim 1, characterized in that: The system includes an acquisition module, an interpolation module, a reconstruction module, and an optimization module, wherein: The acquisition module is used to acquire K-space data of low-field magnetic resonance imaging; The interpolation module is used to map the collected K-space data into a standard Cartesian coordinate system using a Gaussian kernel grid interpolation method, and weight each radial sampling point using a Gaussian kernel function to ensure that the data is smoothly distributed on the standard grid; The reconstruction module is used to use the interpolated K-space data to reconstruct the image based on the image prior constraints, wherein the image prior constraints include: low-rank structure and sparse prior information of the image; The optimization module is used to gradually optimize the parameters of low-rank and sparse components by using a hybrid kernel function, and to perform constraints in combination with the low-rank structure and sparse prior information of the image to improve the effect of image reconstruction.

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