CUDA (Compute Unified Device Architecture) acceleration-based magnetic resonance image rapid reconstruction method and magnetic resonance imaging system

Abstract

The invention discloses a CUDA (Compute Unified Device Architecture) acceleration-based magnetic resonance image rapid reconstruction method and a magnetic resonance imaging system. The method comprises the following steps: acquiring under-sampling k-space data and full-sampling self-calibration signal data; constructing an overdetermined linear equation set; a sparse random projection matrix is designed, and equation set dimension reduction is completed; using CUDA (Compute Unified Device Architecture) to accelerate to solve the linear equation set after dimension reduction, and obtaining a GRAPPA linear combination coefficient; based on the combination coefficient and the under-sampled k-space data, performing parallel synthesis on missing k-space data through CUDA (Compute Unified Device Architecture); and performing two-dimensional Fourier transform and post-processing on the complete k-space data, and outputting a quickly reconstructed 2D magnetic resonance image. According to the method, the dimension reduction advantage of random projection and the parallel computing capability of CUDA are fused, the technical bottlenecks that in traditional 2D GRAPPA reconstruction, the calculation complexity in the calibration stage is high, and the CPU serial processing speed is low are effectively solved, extra hardware transformation or channel compression dependence is avoided, high-quality 2D magnetic resonance images can be stably output, and the clinical rapid diagnosis requirement is accurately met.

Description

Technical Field

[0001] This invention belongs to the field of magnetic resonance imaging and medical image processing technology, specifically relating to a method for rapid reconstruction of magnetic resonance images based on CUDA acceleration and a magnetic resonance imaging system. Background Technology

[0002] Magnetic Resonance Imaging (MRI), with its unique advantages of no ionizing radiation and high soft tissue resolution, has become an indispensable imaging technique in clinical disease diagnosis. GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA), as the core reconstruction method of parallel MRI, acquires k-space data through a multi-channel phase array coil, estimates linear combination coefficients using autocalibration signals (ACS), and then synthesizes missing k-space data. This effectively shortens scan time, meets the needs of rapid clinical imaging, and is widely used, especially in 2D MRI (such as spin echo and gradient echo sequences).

[0003] However, traditional 2D GRAPPA reconstruction faces significant technical bottlenecks: On the one hand, the calibration stage requires solving an overdetermined linear system of equations based on ACS data to obtain combined coefficients. With the widespread use of multi-channel coils, the dimension of the equation system (number of rows m, number of columns n) increases dramatically, leading to a quadratic increase in computational complexity and a significant extension of reconstruction time. This is because solving the equation system involves large-scale matrix multiplication and inversion operations, and its computational load is positively correlated with the number of channels and the amount of ACS data. In clinical high-channel, high-speed-ratio scenarios, CPU serial processing is difficult to meet the real-time reconstruction requirements. On the other hand, existing solutions to this problem have obvious limitations: hardware-level channel reduction schemes require additional deployment of radio frequency signal synthesis equipment, which is costly and inflexible, and cannot be adapted to existing clinical MRI systems; software-level channel compression technologies (such as principal component analysis PCA) require channel correlation analysis first, which adds additional computational overhead, and are only suitable for scenarios with a large number of channels. The acceleration effect on conventional configurations such as 8 channels is limited, and it does not address the core computational bottleneck of solving the equation system during the calibration stage.

[0004] Furthermore, CUDA (Compute Unified Device Architecture), as a GPU parallel computing architecture, possesses the inherent advantage of multi-core parallel processing of large-scale matrix operations, and has already achieved efficiency improvements in multiple image processing fields. However, traditional 2D GRAPPA reconstruction largely relies on CPU serial execution, failing to fully utilize CUDA's parallel computing potential. This results in low computational efficiency for key steps such as matrix multiplication and equation solving, further exacerbating the problem of excessively long reconstruction times. Meanwhile, clinical practice demands increasingly higher efficiency from 2D MRI, requiring both ensuring image quality (such as spatial resolution and soft tissue contrast) to meet diagnostic needs and shortening reconstruction time to improve the efficiency of the diagnostic and treatment process. Traditional methods struggle to achieve a balance between these two aspects. Simply reducing the amount of ACS data to lower computational complexity leads to decreased accuracy in combined coefficient calibration, image artifacts, or a reduced signal-to-noise ratio. Conversely, maintaining the amount of ACS data to ensure image quality results in excessively long reconstruction times, impacting the clinical application experience.

[0005] Therefore, how to optimize the computational bottleneck in the 2DGRAPPA calibration stage without relying on additional hardware modifications or channel compression, and combine it with CUDA parallel computing capabilities to achieve the goal of no loss of image quality and a significant improvement in reconstruction speed, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a fast reconstruction method for magnetic resonance images based on CUDA acceleration.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a CUDA-accelerated rapid reconstruction method for magnetic resonance images, comprising the following steps: Step S1, acquiring undersampled k-space data and fully sampled self-calibration signal data for calibration from a 2D magnetic resonance imaging sequence using a multi-channel phase array coil; Step S2, constructing a 2D image based on the fully sampled self-calibration signal data in Step S1. The GRAPPA calibration stage involves the following steps: Step S3: Based on the overdetermined linear equations and their dimensions from Step S2, a sparse random projection matrix is ​​designed, satisfying the Johnson-Lindestrauss lemma; Step S4: Based on the CUDA parallel computing architecture, the sparse random projection matrix from Step S3 is multiplied in parallel with the equation matrix from Step S2 to obtain a dimension-reduced linear equation system; Step S5: CUDA is used to accelerate the solution of the dimension-reduced linear equation system from Step S4, employing the least squares method to perform matrix inversion and multiplication in parallel, quickly obtaining the GRAPPA linear combination coefficients; Step S6: Based on the GRAPPA linear combination coefficients from Step S5 and the undersampled k-space data acquired in Step S1, the missing k-space data is synthesized through CUDA parallel computing to restore the complete k-space data; Step S7: A two-dimensional Fourier transform is performed on the restored complete k-space data from Step S6 to convert the k-space data into image domain data, followed by square root summation to output the final 2D magnetic resonance reconstructed image.

[0008] In some implementations, the overdetermined linear equations in step S2 are formulated as follows: , where matrix A is composed of source k-space data from all channels, and its dimension m×n satisfies , , The number of positions fitted to the phase encoding direction. Number of frequency coding direction points, , The convolution dimensions of GRAPPA in the frequency coding and phase coding directions, respectively. For the number of channels, the matrix It consists of calibration data from the target channel, with dimensions m×l satisfying , Acceleration factor; matrix Let be the coefficients of the GRAPPA linear combination to be solved.

[0009] In some implementations, the sparse random projection matrix R in step S3 has a dimension of , Matrix R contains only one non-zero element in each row, and the non-zero element takes values ​​of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ... ,in This is a sparsity control parameter, with values ​​of 1, 1 / 3, or... The over-determined factor is defined as , The The value range is 2 to 4.

[0010] In some implementations, the equation system matrix is ​​used in step S4. , Parallel multiplication yields a system of linear equations with reduced dimensionality, as shown in the formula. .

[0011] In some implementations, the 2D magnetic resonance imaging sequence in step S1 is one of a spin echo sequence or a gradient echo sequence.

[0012] In some implementations, the overdetermined linear equations in step S2 are directly generated based on the source-target data mapping relationship of the fully sampled self-calibrated signal data.

[0013] In some implementations, the sparse random projection matrix R in step S3 is a sparse structure for reducing the dimension of the overdetermined system of equations by randomly selecting k rows of data from matrix A.

[0014] In some implementations, the synthesis of missing k-space data in step S6 is achieved by CUDA parallel traversal of the missing positions in the undersampled k-space and synchronously completing multi-position data synthesis based on GRAPPA linear combination coefficients.

[0015] In some implementations, the two-dimensional Fourier transform and square root summation post-processing in step S7 are both implemented in parallel using CUDA.

[0016] Another technical problem to be solved by the present invention is to provide a magnetic resonance imaging system.

[0017] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a magnetic resonance imaging system, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to realize the above-mentioned CUDA-accelerated rapid reconstruction method of magnetic resonance images for imaging.

[0018] The scope of this invention is not limited to technical solutions formed by specific combinations of the above-described technical features, but also includes other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in this application.

[0019] Due to the application of the above technical solutions, this invention has the following advantages compared with the prior art: This invention provides a CUDA-accelerated method for rapid reconstruction of magnetic resonance images and a magnetic resonance imaging system. It reduces the dimension of the overdetermined equation system in the 2D GRAPPA calibration stage by using random projection technology, and accelerates the entire process of key steps such as matrix operations, equation solving, and Fourier transforms by combining the CUDA parallel computing architecture. This reduces the 2D magnetic resonance image reconstruction time by more than 3 times compared with the traditional GRAPPA, significantly improving real-time performance. The random projection matrix follows the Johnson-Lindestrauss lemma, ensuring that the quality of the reconstructed image is not significantly different from that of the traditional method, thus guaranteeing the accuracy of clinical diagnosis. No additional hardware modification or channel compression processing is required. It is compatible with multi-channel coils and various 2D imaging sequences, and can be directly integrated into existing magnetic resonance systems, resulting in low implementation costs. The algorithm adopts a sparse random projection matrix design and is combined with mature CUDA library calls, making engineering implementation difficult. It is also applicable to rapid clinical imaging scenarios for multiple parts such as the head and limbs, demonstrating outstanding practicality and promotional value. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall process of the fast reconstruction method for random projection GRAPPA magnetic resonance images based on CUDA acceleration of the present invention. Figure 2 This is a schematic diagram of the structure of the sparse random projection matrix R in this invention; Figure 3 This is a schematic diagram of thread partitioning and data processing in the CUDA parallel computing architecture of this invention; Figure 4 This is a schematic diagram comparing the dimensions of the 2D GRAPPA calibration equation system before and after dimensionality reduction in the invention. Figure 5 This is a comparison of the 2D magnetic resonance image reconstruction results of the method of the present invention and the traditional GRAPPA method (knee). Figure 6 This is a comparison image (head) of the 2D magnetic resonance image reconstruction results of the method of the present invention and the traditional GRAPPA method. Detailed Implementation

[0021] like Figure 1 The schematic diagram of the overall process of the present invention shown includes, in sequence, data acquisition, construction of calibration equations, design of random projection matrix, CUDA parallel dimensionality reduction, coefficient solving, synthesis of missing data, image reconstruction and output. Following this process, high-quality 2D magnetic resonance images can be efficiently acquired in a magnetic resonance imaging system.

[0022] The magnetic resonance imaging system utilizes random projection dimension reduction technology, CUDA parallel acceleration technology, and 2D GRAPPA reconstruction technology to quickly acquire and reconstruct 2D magnetic resonance images. It is suitable for rapid clinical imaging scenarios, including but not limited to 2D magnetic resonance examinations of the head, abdomen, and limbs.

[0023] A fast reconstruction method for stochastic projection GRAPPA magnetic resonance images based on CUDA acceleration includes the following steps: Step S1: Using a 2D magnetic resonance imaging sequence, undersampled k-space data under accelerated scanning and fully sampled self-calibration signal data for calibration are acquired through a multi-channel phase array coil. The 2D magnetic resonance imaging sequence can be selected according to clinical diagnostic needs, including but not limited to spin echo sequences and gradient echo sequences. Undersampled k-space data is obtained through accelerated scanning, acquiring only a portion of the k-space sampling points to shorten the scanning time. ACS data is fully sampled data, covering the central region of k-space, used to ensure the calibration accuracy of the GRAPPA linear combination coefficients and avoid reconstruction artifacts caused by insufficient data.

[0024] Step S2: Based on the ACS data acquired in step S1, construct the overdetermined linear equation system for the 2D GRAPPA calibration stage. The construction logic of matrix A is as follows: extract the source k-space data of all channels in the ACS data, that is, the adjacent k-space points actually acquired in the accelerated scanning, whose dimensions satisfy... , ,in This represents the number of fitted positions in the phase encoding direction, which is determined by the phase encoding range of the ACS data. This represents the number of points in the frequency coding direction, which is consistent with the frequency coding dimension of the imaging matrix. , These represent the convolution sizes of GRAPPA in the frequency coding and phase coding directions, respectively. The number of channels in a multi-channel coil; matrix The construction logic is as follows: extract the target k-space data from the ACS data, that is, the k-space points that were skipped in the accelerated scan but were acquired for calibration purposes, whose dimensions satisfy... ,in The acceleration factor for 2D GRAPPA; matrix The GRAPPA linear combination coefficients to be solved reflect the linear mapping relationship between the source k-space data and the target k-space data. Their values ​​are determined by factors such as coil sensitivity and k-space position, and need to be solved through the calibration process.

[0025] The overdetermined linear equations are generated directly from the source-target data mapping relationship of ACS data, without involving channel compression processing. They are suitable for 2D imaging scenarios with different numbers of channels and do not require additional channel correlation analysis.

[0026] Step S3, Design A sparse random projection matrix R, such as Figure 2 As shown, this ensures that key information of the data is not lost after dimensionality reduction; the core constraints of matrix R satisfy the Johnson-Lindenstrauss lemma, that is, for any two data points u, v ∈ row vectors of matrix A, there exists a mapping relationship. , making ,in To ensure error tolerance, the relative distances of the data are preserved after dimensionality reduction, thereby ensuring the accuracy of the combined coefficients; matrix The structural design employs a sparse construction, where each row contains only one non-zero element, and the non-zero element takes values ​​of 10 ... , This is a sparsity control parameter, which can be selected as 1, 1 / 3, or... In this embodiment, the non-zero element takes the value of That is, P=1, to ensure matrix sparsity and reduce computational cost.

[0027] The random projection matrix R has a sparse structure. The dimension reduction of the overdetermined system of equations is achieved by randomly selecting k rows of data from matrix A. The sparse design can minimize the computational cost of projection and satisfy the Johnson-Lindestrauss lemma, ensuring that the solution of the system of equations after dimension reduction is consistent with the accuracy of the solution of the original system of equations.

[0028] Sparse structures can minimize the cost of projection calculations and avoid introducing significant additional computational overhead; the dimensionality reduction dimension k is achieved by defining an overdetermined factor. Sure, The value range is 2~4, when When the dimensionality reduction is insufficient, the overdeterminism of the equation system is insufficient, and the stability of the solution decreases; when At this time, the reduction in computational complexity is not significant and may introduce redundant computations; at the same time, it is necessary to satisfy ,conventional for Use 1 / 5 to 1 / 10 of the dimensionality to ensure the effectiveness of dimensionality reduction.

[0029] Step S4: Based on the CUDA parallel computing architecture, parallel dimensionality reduction of the random projection matrix and calibration equations is achieved. The CUDA parallel computing architecture achieves parallel execution of matrix multiplication through reasonable division of thread blocks and threads, avoiding the bottleneck of CPU serial computing and greatly improving the computational efficiency of projection dimensionality reduction; the parallel multiplication operation supports efficient processing of large-scale matrices.

[0030] In this embodiment, based on the NVIDIA RTX A2000 GPU and CUDA 12.1 architecture, parallel multiplication of the random projection matrix and the calibration equations is implemented. Matrices A and b, and the random projection matrix R are divided according to CUDA's block and thread dimensions. Each thread is responsible for processing one or more element multiplications in the matrix, and shared memory is used within the thread block to reduce data access latency. Figure 3 As shown, Figure 3 A schematic diagram of thread partitioning in the CUDA parallel computing architecture is provided. Matrices A, b, and R are divided into 16×16 thread blocks and thread dimensions. Each thread is responsible for processing multiplication operations of one element. Frequently accessed matrix elements are cached in shared memory within the thread block to reduce global memory access latency. Furthermore, matrix multiplication is performed through CUDA kernel functions. and Generate a system of linear equations after dimensionality reduction. This step significantly reduces computation time compared to CPU serial multiplication. CUDA's multi-core parallel processing greatly improves matrix multiplication efficiency, especially for large-scale matrix operations. CUDA optimization strategies include batch processing to reduce data transfer overhead, shared memory caching of frequently accessed elements, and parallel LU decomposition to accelerate matrix inversion.

[0031] Step S5: CUDA is used to accelerate the solution of the dimensionality-reduced linear equation system. Parallel matrix inversion and batch multiplication optimization are employed to obtain the GRAPPA linear combination coefficients x. The least squares method is then used to solve... Obtain the combination coefficients x; invert the matrix. A parallelized LU decomposition algorithm is employed, distributing the matrix decomposition task across multiple thread blocks for synchronous execution. In this embodiment, it is distributed across eight thread blocks for synchronous execution. For matrix multiplication... Batch processing optimization is employed, processing 16 columns of data at a time to improve data access efficiency and reduce the overhead of data transfer between GPU global memory and registers; the dimension of the equation system after dimensionality reduction is... , Combined with CUDA parallel solution, Figure 4 The paper presents a comparison of the dimensions of the equation system before and after dimensionality reduction. After dimensionality reduction, the solution time of the equation system is shortened from 2.1s in CPU serial mode to 0.31s in GPU parallel mode, and the linear combination coefficients x are finally obtained.

[0032] Step S6: Based on the combination coefficient x and the undersampled k-space data, the missing data is synthesized in parallel using CUDA. The missing positions of the undersampled k-space are traversed by thread blocks, with each thread responsible for the synthesis calculation of one missing point. According to the linear combination formula of 2D GRAPPA, the calculation is completed synchronously using the source data and the combination coefficient x, and finally the complete k-space data is obtained.

[0033] The synthesis process of missing k-space data uses CUDA to traverse the missing locations of the undersampled k-space in parallel, and synchronously completes the synthesis of multi-location data based on the combination coefficient x, further shortening the data recovery time.

[0034] Step S7: Perform parallel two-dimensional Fourier transform on the complete k-space data using CUDA's cuFFT library to convert the k-space data into image domain data. In this embodiment, perform square root summation post-processing on the image domain data of 8 channels to eliminate multi-channel phase interference and output the final 2D magnetic resonance image.

[0035] Both the two-dimensional Fourier transform and the square root summation post-processing are implemented in parallel using CUDA, ensuring acceleration of the entire process from k-space data to image output.

[0036] like Figure 5 and Figure 6 As shown, the reconstruction effects of the method of the present invention and the traditional GRAPPA method are compared at different locations. Figure 5 For the knee area, the reconstruction time of traditional GRAPPA is 2.60s, while the reconstruction time of the method of this invention is 0.51s. There is no significant difference in spatial resolution and soft tissue contrast between the two reconstructed images. The difference in the difference image is 4.4% ≤5%, with only a slight difference in grayscale, which meets the requirements for clinical diagnosis.

[0037] Figure 6 Representing the head region, the reconstruction time of traditional GRAPPA is 3.10s, while the reconstruction time of the method of this invention is 0.75s; there is no significant difference in spatial resolution and soft tissue contrast between the two reconstructed images, and the difference in the difference image is only 0.6%, ≤5%, which meets the requirements for clinical diagnosis.

[0038] This invention discloses a CUDA-accelerated method for rapid reconstruction of random projection GRAPPA magnetic resonance images and a magnetic resonance imaging system applying it. The method includes: using a 2D magnetic resonance imaging sequence (spin echo, gradient echo, etc.), acquiring undersampled k-space data and fully sampled self-calibration signal (ACS) data through a multi-channel phase array coil; constructing an overdetermined linear equation system for the 2D GRAPPA calibration stage based on the ACS data; designing a sparse random projection matrix satisfying the Johnson-Lindestrauss lemma, and performing parallel multiplication of the projection matrix and the equation system using a CUDA parallel computing architecture to reduce the dimensionality of the equation system; using CUDA to accelerate the solution of the dimensionality-reduced linear equation system to obtain GRAPPA linear combination coefficients; synthesizing the missing k-space data in parallel using CUDA based on the combination coefficients and the undersampled k-space data; performing a two-dimensional Fourier transform and post-processing on the complete k-space data to output a rapidly reconstructed 2D magnetic resonance image. Applying this method to clinical 2D magnetic resonance imaging scenarios can significantly shorten the reconstruction time while ensuring image quality. This invention also provides a magnetic resonance imaging system that uses this method to achieve rapid reconstruction of 2D magnetic resonance images. Because this invention combines the dimensionality reduction advantage of random projection with the parallel computing capabilities of CUDA, it effectively solves the technical bottlenecks of high computational complexity and slow CPU serial processing speed in the calibration stage of traditional 2D GRAPPA reconstruction. It avoids additional hardware modifications or channel compression dependencies, and can stably output high-quality 2D magnetic resonance images, accurately meeting the needs of rapid clinical diagnosis. At the same time, the provided magnetic resonance imaging system can be directly integrated into existing equipment and is suitable for magnetic resonance examinations of multiple parts such as the head and limbs, with outstanding clinical application value and promotion prospects.

[0039] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A fast reconstruction method for magnetic resonance images based on CUDA acceleration, characterized in that: Includes the following steps: Step S1: Acquire undersampled k-space data and fully sampled self-calibration signal data for calibration from the 2D magnetic resonance imaging sequence using a multi-channel phase array coil; Step S2: Construct an overdetermined linear equation system for the 2D GRAPPA calibration stage based on the fully sampled self-calibration signal data from step S1. Step S3: Design a sparse random projection matrix based on the overdetermined linear equations and their dimensions in step S2. The sparse random projection matrix satisfies the Johnson-Lindestrauss lemma. Step S4: Based on the CUDA parallel computing architecture, the sparse random projection matrix in step S3 and the equation system matrix in step S2 are multiplied in parallel to obtain the dimension-reduced linear equation system. Step S5: Use CUDA to accelerate the solution of the reduced-dimensional linear equation system in step S4. Use the least squares method to perform matrix inversion and multiplication operations in parallel to quickly obtain the GRAPPA linear combination coefficients. Step S6: Based on the GRAPPA linear combination coefficients from step S5 and the undersampled k-space data collected in step S1, the missing k-space data is synthesized through parallel computation using CUDA to restore the complete k-space data. Step S7: Perform a two-dimensional Fourier transform on the complete k-space data recovered in step S6 to convert the k-space data into image domain data. After square root summation, output the final 2D magnetic resonance reconstructed image.

2. The method for fast reconstruction of magnetic resonance images based on CUDA acceleration according to claim 1, characterized in that: The formula for the overdetermined linear equation system in step S2 is as follows: , where matrix A is composed of source k-space data from all channels, and its dimension m×n satisfies , , The number of positions fitted to the phase encoding direction. Number of frequency coding direction points, , The convolution dimensions of GRAPPA in the frequency coding and phase coding directions, respectively. For the number of channels, the matrix It consists of calibration data from the target channel, with dimensions m×l satisfying , Acceleration factor; matrix denoted as the coefficients of the GRAPPA linear combination to be solved.

3. The method for fast reconstruction of magnetic resonance images based on CUDA acceleration according to claim 2, characterized in that: The sparse random projection matrix R in step S3 has dimensions of , Matrix R contains only one non-zero element in each row, and the non-zero element takes values ​​of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ... ,in This is a sparsity control parameter, with values ​​of 1, 1 / 3, or... The over-determined factor is defined as , The The value range is 2 to 4.

4. The method for fast reconstruction of magnetic resonance images based on CUDA acceleration according to claim 3, characterized in that: In step S4, the system of equations matrix , Parallel multiplication yields a system of linear equations with reduced dimensionality, as shown in the formula. .

5. The method for fast reconstruction of magnetic resonance images based on CUDA acceleration according to claim 1, characterized in that: The 2D magnetic resonance imaging sequence in step S1 is either a spin echo sequence or a gradient echo sequence.

6. The method for fast reconstruction of magnetic resonance images based on CUDA acceleration according to claim 1, characterized in that: The overdetermined linear equations in step S2 are directly generated based on the source-target data mapping relationship of the fully sampled self-calibrated signal data.

7. The method for fast reconstruction of magnetic resonance images based on CUDA acceleration according to claim 1, characterized in that: The sparse random projection matrix R in step S3 is a sparse structure for reducing the dimension of the overdetermined system of equations by randomly selecting k rows of data from matrix A.

8. The method for fast reconstruction of magnetic resonance images based on CUDA acceleration according to claim 1, characterized in that: The synthesis of missing k-space data in step S6 is achieved by traversing the missing positions of the undersampled k-space in parallel using CUDA, and simultaneously synthesizing multi-position data based on the linear combination coefficients of GRAPPA.

9. The method for fast reconstruction of magnetic resonance images based on CUDA acceleration according to claim 1, characterized in that: In step S7, the two-dimensional Fourier transform and the square root summation post-processing are both implemented in parallel using CUDA.

10. A magnetic resonance imaging system, characterized in that: It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the CUDA-accelerated rapid reconstruction method for magnetic resonance images as described in any one of claims 1 to 9.

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