Magnetic resonance image undersampling reconstruction method, system, medium, and electronic device

Abstract

The present invention provides a method, system, medium, and electronic device for undersampling reconstruction of magnetic resonance images, comprising the following steps: modeling an MRI image and a coil sensitivity image as continuous functions; predefining the spatial coordinates of pixel points of the MRI image and the coil sensitivity image; training the continuous function based on the spatial coordinates; inputting the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image into the trained continuous function to obtain an MRI image matrix and a coil sensitivity matrix; obtaining predicted k-space data of the MRI image based on the MRI image matrix and the coil sensitivity matrix according to an MRI forward physical model; and obtaining an MRI reconstructed image based on the actual k-space data and the predicted k-space data. The method, system, medium, and electronic device for undersampling reconstruction of magnetic resonance images of the present invention can perform MRI image reconstruction based on undersampled k-space data expressed by implicit neural networks, thereby further accelerating MRI image acquisition while ensuring the quality of the reconstructed image.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance imaging (MRI), and in particular to a method, system, medium, and electronic equipment for undersampling reconstruction of magnetic resonance images. Background Art

[0002] Magnetic resonance imaging (MRI) is a widely used imaging technique in clinical diagnosis and research due to its safety, lack of radiation, and excellent soft tissue contrast. However, the main disadvantage of MRI is its long acquisition time. To address this issue, researchers have proposed different acceleration strategies, the main purpose of which is to reconstruct artifact-free MRI images from undersampled K-space data to exceed the limitations of the Nyquist sampling theorem. Currently, almost all clinical MRI systems use parallel imaging technology to accelerate scanning by exploiting the information redundancy of multiple receiving coils.

[0003] The existing parallel imaging technologies are mainly divided into two categories: one is to model image reconstruction as an inverse problem in the spatial domain, which requires explicitly estimating the coil sensitivity image from the fully sampled auto calibration signal (ACS) region; the other is to interpolate the missing data in the K space, implicitly utilizing the coil sensitivity information contained in the ACS region. However, when faced with a high acceleration factor and less ACS data, parallel imaging technology will produce the problem of noise amplification, which reduces the quality of the reconstructed image, and limits the further improvement of the MRI acquisition speed. In addition, compressed sensing provides an alternative solution for MRI acceleration. According to the theory of compressed sensing, K-space data needs to be unevenly undersampled, and this requirement hinders its application in conventional two-dimensional Cartesian coordinate acquisition.

[0004] Currently, deep learning-based methods have shown promising results in the field of MRI reconstruction. For supervised deep learning methods, neural networks rely on large-scale training datasets to directly learn the mapping from undersampled data to fully sampled data. However, in most practical situations, fully sampled real data is often unavailable; and when the distribution of the test dataset differs from that of the training dataset, the trained neural network may suffer from generalization problems, significantly reducing reconstruction performance. To avoid using fully sampled data as training labels, some self-supervised deep learning methods have been developed. However, these methods still require a large amount of undersampled data as training sets. In addition, researchers have proposed another class of scan-specific methods, which use convolutional neural networks to learn k-space interpolation kernels from fully sampled calibration regions, similar to those used in traditional parallel imaging techniques, to interpolate the missing k-space data. Although these methods outperform traditional parallel imaging methods at high acceleration factors, they still rely on sufficient ACS data to effectively train the convolutional neural network.

[0005] On the other hand, most of the aforementioned methods involve precalculating coil sensitivities and then directly applying them to the MRI reconstruction model. However, accurately estimating coil sensitivity maps from small ACS regions is challenging. This limits further acceleration of k-space data acquisition, and errors in inaccurate coil sensitivity maps are further amplified in subsequent image reconstruction, resulting in visible artifacts on the reconstructed images. Summary of the Invention

[0006] In view of the shortcomings of the prior art described above, the object of the present invention is to provide a method, system, medium, and electronic device for undersampling reconstruction of magnetic resonance images, which can reconstruct MRI images based on undersampled k-space data expressed by implicit neural networks, thereby further accelerating the acquisition of MRI images while ensuring the quality of the reconstructed images.

[0007] In a first aspect, the present invention provides a method for undersampling reconstruction of magnetic resonance images, the method comprising the following steps: modeling an MRI image and a coil sensitivity image as continuous functions; the continuous function of the MRI image is used to output an MRI image matrix corresponding to the spatial coordinates of the pixel points of the MRI image, and the continuous function of the coil sensitivity image is used to output a coil sensitivity matrix corresponding to the spatial coordinates of the pixel points of the coil sensitivity image; pre-defining the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image; training the continuous function based on the spatial coordinates; inputting the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image into the trained continuous function to obtain the MRI image matrix and the coil sensitivity matrix; based on the MRI image matrix and the coil sensitivity matrix, obtaining predicted k-space data of the MRI image according to an MRI forward physical model; and obtaining an MRI reconstructed image based on the actual k-space data and the predicted k-space data.

[0008] In one implementation of the first aspect, modeling the MRI image and the coil sensitivity image as continuous functions of spatial coordinates includes the following steps:

[0009] The continuous function obtained by MRI image modeling uses two sinusoidal expression networks, which respectively express the real and imaginary parts of the MRI image. Each sinusoidal expression network consists of eight fully connected layers, with the first layer having two input channels for receiving spatial coordinates and the last layer having one output channel for generating the real or imaginary part of the MRI image corresponding to the spatial coordinates. The middle layer has 256 neurons, and a sinusoidal function is set as an activation function between two adjacent fully connected layers. The real and imaginary parts of the MRI image constitute the MRI image matrix.

[0010] The continuous function obtained by coil sensitivity image modeling adopts polynomial function Among them C j (x, y) represents the coil sensitivity value of the jth coil at (x, y), N is the order of the polynomial, are the polynomial coefficients to be solved, p is the degree of the coordinate x, and q is the degree of the coordinate y; the coil sensitivity values ​​constitute the coil sensitivity matrix.

[0011] In one implementation of the first aspect, predefining the spatial coordinates of pixel points of the to-be-reconstructed MRI image and coil sensitivity image includes the following steps:

[0012] dividing the MRI image and the coil sensitivity image into equal intervals;

[0013] The x and y coordinates of each pixel are uniformly mapped to the value range of [-1, 1] with the origin as the center.

[0014] In an implementation of the first aspect, training the continuous function based on the spatial coordinates includes the following steps:

[0015] Inputting the spatial coordinates into the continuous function, and designing a loss function based on an MRI forward physical model and a regularization term containing image prior information;

[0016] The loss function is minimized using a gradient back-propagation algorithm to obtain a trained continuous function.

[0017] In an implementation of the first aspect, the regularization term containing image prior information adopts the total variation of the image; the loss function is S j represents the actual k-space data of the j-th coil, I(θ) represents the MRI image matrix obtained based on the continuous function of the MRI image, θ represents the optimizable parameter in the continuous function of the MRI image, represents the coil sensitivity matrix obtained based on the continuous function of coil sensitivity, represents the optimizable parameter in the continuous function of coil sensitivity, ||·||1 represents the L1 norm of the matrix, c represents the total number of coils, G represents the gradient operator of the image, λ represents the weight of the regularization term, F is the Fourier transform matrix, and M is the undersampling mask matrix.

[0018] In an implementation of the first aspect, the MRI forward physical model is in, represents the predicted k-space data of the j-th coil, is the predicted MRI image matrix, C j represents the j-th coil sensitivity matrix, and F is the Fourier transform matrix.

[0019] In one implementation of the first aspect, acquiring an MRI reconstructed image based on actual k-space data and the predicted k-space data includes the following steps:

[0020] replacing corresponding data in the predicted K-space data with actual K-space data to obtain composite K-space data;

[0021] The composite K-space data is subjected to two-dimensional inverse Fourier transform coil by coil, and then different coil images are merged based on the coil sensitivity matrix to obtain the MRI reconstructed image.

[0022] In a second aspect, the present invention provides a magnetic resonance image undersampling reconstruction system, the system comprising a modeling module, a coordinate definition module, a training module, an acquisition module, a prediction module, and a reconstruction module;

[0023] The modeling module is used to model the MRI image and the coil sensitivity image as continuous functions; the continuous function of the MRI image is used to output the MRI image matrix corresponding to the spatial coordinates of the pixel points of the MRI image, and the continuous function of the coil sensitivity image is used to output the coil sensitivity matrix corresponding to the spatial coordinates of the pixel points of the coil sensitivity image;

[0024] The coordinate definition module is used to predefine the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image;

[0025] The training module is used to train the continuous function based on the spatial coordinates;

[0026] The acquisition module is used to input the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image into a trained continuous function to obtain the MRI image matrix and the coil sensitivity matrix;

[0027] The prediction module is used to obtain predicted k-space data of the MRI image based on the MRI image matrix and the coil sensitivity matrix according to the MRI forward physical model;

[0028] The reconstruction module is used to obtain an MRI reconstructed image based on actual k-space data and the predicted k-space data.

[0029] In a third aspect, the present invention provides a storage medium having a computer program stored thereon, which implements the above-mentioned magnetic resonance image undersampling reconstruction method when executed by a processor.

[0030] In a fourth aspect, the present invention provides an electronic device, comprising: a processor and a memory;

[0031] The memory is used to store computer programs;

[0032] The processor is configured to execute the computer program stored in the memory, so as to enable the electronic device to perform the above-mentioned magnetic resonance image undersampling reconstruction method.

[0033] As described above, the magnetic resonance image undersampling reconstruction method, system, medium, and electronic device of the present invention have the following beneficial effects:

[0034] (1) MRI image reconstruction based on undersampled k-space data of implicit neural expression, the quality of the reconstructed image is superior to that of similar methods in both qualitative and quantitative evaluation;

[0035] (2) It does not require any training data other than the reconstruction data itself and can be generalized to different imaging modalities, acceleration factors, tissues and organs, etc.

[0036] (3) It can jointly estimate coil sensitivity and MRI images, preventing the propagation of coil sensitivity errors and making it more robust to the size of the ACS region;

[0037] (4) It is easy to combine with other explicit regularization terms containing image priors to further improve the quality of the reconstructed image. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Shown is a flow chart of an embodiment of a magnetic resonance image undersampling reconstruction method according to the present invention;

[0039] Figure 2 Shown is a schematic diagram of a framework of a magnetic resonance image undersampling reconstruction method according to an embodiment of the present invention;

[0040] Figure 3 Schematic diagram showing a comparison between the magnetic resonance image undersampling reconstruction method of the present invention and other image reconstruction methods in one embodiment;

[0041] Figure 4 Schematic diagram showing a comparison between the magnetic resonance image undersampling reconstruction method of the present invention and other image reconstruction methods in another embodiment;

[0042] Figure 5 FIG2 is a schematic structural diagram of a magnetic resonance image undersampling reconstruction system according to an embodiment of the present invention;

[0043] Figure 6 FIG. 1 is a schematic structural diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The following describes the embodiments of the present invention through specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other unless they conflict.

[0045] It should be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. Therefore, the illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0046] The magnetic resonance image undersampling reconstruction method, system, medium, and electronic device of the present invention are based on the concept of implicit expression. They use the MRI physical model to learn continuous functions for expressing MRI images and coil sensitivity images from the undersampled K-space data itself, further improving the quality of reconstructed images without relying on other data, and are extremely practical.

[0047] The technical solutions in the embodiments of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0048] like Figure 1 and Figure 2 As shown, in one embodiment, the magnetic resonance image undersampling reconstruction method of the present invention includes the following steps:

[0049] Step S1: Model the MRI image and the coil sensitivity image as continuous functions; the continuous function of the MRI image is used to output the MRI image matrix corresponding to the spatial coordinates of the pixel points of the MRI image, and the continuous function of the coil sensitivity image is used to output the coil sensitivity matrix corresponding to the spatial coordinates of the pixel points of the coil sensitivity image.

[0050] Specifically, the continuous function obtained by MRI image modeling uses two sinusoidal representation networks (SIRENs). The two sinusoidal representation networks respectively express the real and imaginary parts of the MRI image; each sinusoidal representation network consists of eight fully connected layers. The first layer has two input channels for receiving spatial coordinates, and the last layer has one output channel for generating the real or imaginary part of the MRI image corresponding to the spatial coordinates. The middle layer has 256 neurons, and a sine function is set as the activation function between two adjacent fully connected layers.

[0051] The continuous function obtained by coil sensitivity image modeling adopts polynomial function Among them C j (x, y) represents the coil sensitivity value of the jth coil at (x, y), N is the order of the polynomial, are the coefficients of the polynomial to be solved, p is the degree of the coordinate x, and q is the degree of the coordinate y. Preferably, N is 15.

[0052] Step S2: pre-define the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image.

[0053] Specifically, the MRI image and the coil sensitivity image are divided into equal intervals; and the x and y coordinates of each pixel point are evenly mapped within a numerical range of [-1, 1] with the origin as the center.

[0054] Step S3: training the continuous function based on the spatial coordinates.

[0055] Specifically, the spatial coordinates of the pixels of the MRI image are input into a corresponding continuous function, and the real and imaginary parts of the MRI image are output. The real and imaginary parts of the MRI image are constructed into an MRI image matrix. The spatial coordinates of the pixels of the coil sensitivity image are input into a corresponding continuous function to obtain coil sensitivity values. The coil sensitivity values ​​are constructed into a coil sensitivity matrix.

[0056] When training the continuous function, a loss function is designed based on the MRI forward physical model and a regularization term containing image prior information, and the gradient backpropagation algorithm is used to minimize the loss function to obtain a trained continuous function. The MRI image matrix and the coil sensitivity matrix are input into the MRI forward physical model to obtain predicted k-space data of the MRI image. The predicted k-space data is compared with the actual k-space data collected. The parameters of the continuous function are reversely adjusted based on the comparison results to achieve training of the continuous function. Preferably, the parameters of the continuous function include weights in the sinusoidal expression network and coefficients in the polynomial function, which are optimized simultaneously using two different Adam optimizers. For the sinusoidal expression network, the initial learning rate is 0.0001, which is reduced to the original 0.8 every 500 iterations; for the coefficients in the polynomial, the initial learning rate is 0.1, which is reduced to the original 0.5 every 500 iterations. The number of iterations of the continuous function is 1500.

[0057] Preferably, the present invention builds a network model based on PyTorch 1.10.2 and Python 3.9, and uses NVIDIA GeForce RTX 3090 GPU for training.

[0058] In one embodiment, the regularization term containing image prior information adopts the total variation of the image. The loss function is S j represents the actual k-space data of the j-th coil, I(θ) represents the MRI image matrix obtained based on the continuous function of the MRI image, θ represents the optimizable parameter in the continuous function of the MRI image, represents the coil sensitivity matrix obtained based on the continuous function of coil sensitivity, represents the optimizable parameter in the continuous function of coil sensitivity, ||·||1 represents the L1 norm of the matrix, c represents the total number of coils, G represents the gradient operator of the image, λ represents the weight of the regularization term, F is the Fourier transform matrix, and M is the undersampling mask matrix.

[0059] The MRI forward physical model is in, represents the predicted k-space data of the j-th coil, is the predicted MRI image matrix, C j represents the j-th coil sensitivity matrix, and F is the Fourier transform matrix.

[0060] Step S4: Inputting the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image into a trained continuous function to obtain the MRI image matrix and the coil sensitivity matrix.

[0061] Specifically, after the continuous function training is completed, the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image are input into the trained continuous function to obtain the MRI image matrix and the coil sensitivity matrix.

[0062] Step S5: Based on the MRI image matrix and the coil sensitivity matrix, obtain predicted k-space data of the MRI image according to the MRI forward physical model.

[0063] Specifically, the MRI image matrix and the coil sensitivity matrix are input into the MRI forward physical model to obtain the predicted k-space data of the MRI image.

[0064] Step S6: Acquire an MRI reconstructed image based on the actual k-space data and the predicted k-space data.

[0065] Specifically, acquiring an MRI reconstructed image based on actual k-space data and the predicted k-space data includes the following steps:

[0066] 61) Substituting the corresponding data in the predicted K-space data with the undersampled actual K-space data to obtain composite K-space data.

[0067] 62) Performing a two-dimensional inverse Fourier transform on the composite K-space data coil by coil, and then merging different coil images based on the coil sensitivity matrix to obtain the MRI reconstructed image. The specific merging process of different coil images is as follows: in is the final coil merged image, C j represents the j-th coil sensitivity matrix, represents the MRI image matrix of the j-th coil, and conj(·) represents taking the complex conjugate.

[0068] The magnetic resonance image undersampling reconstruction method of the present invention is further verified by using specific examples below.

[0069] Example 1

[0070] The validation was performed on the open source dataset FastMRI. This dataset consists of 15 channels of fully sampled k-space knee joint data. First, the k-space was retrospectively undersampled, the acceleration factor R was set to 4 and 5, respectively, and 24 fully sampled ACS lines were retained in the center of the k-space. Then, the undersampled k-space data were reconstructed using the traditional GRAPPA algorithm, RAKI, Residual-RAKI, and the magnetic resonance image undersampling reconstruction method of the present invention. Finally, the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) between the results obtained by these methods and the fully sampled reconstructed image were calculated. The higher the values ​​of PSNR and SSIM, the smaller the error of the reconstructed image by the corresponding method.

[0071] like Figure 3 As shown in the figure, columns 1 to 5 show the reconstruction results of the fully sampled image, GRAPPA, RAKI, Residual-RAKI, and the method of the present invention at acceleration factors of R=4 and R=5, respectively, and an ACS of 24. The enlarged image shows that the reconstruction method of the present invention effectively suppresses noise and artifacts, and the resulting image has minimal error compared to the fully sampled image. Quantitative evaluation metrics also show that the method of the present invention achieves the highest PSNR and SSIM values.

[0072] Example 2

[0073] In this example, the method of the present invention was tested using open-source, 32-channel, fully sampled k-space human brain data. First, the k-space was retrospectively undersampled, with the acceleration factor R set to 5 and 6, respectively, and only eight fully sampled ACS lines were retained at the center of the k-space. The undersampled k-space data were reconstructed using the conventional GRAPPA algorithm, RAKI, Residual-RAKI, and the method of the present invention, and quantitatively evaluated by calculating PSNR and SSIM.

[0074] like Figure 4 As shown in the figure, the first to fifth columns are the reconstruction results of the full-sampled image, GRAPPA, RAKI, Residual-RAKI, and the method of the present invention, respectively, when the acceleration factors R are 4 and 5, respectively, and the ACS is only 8. It can be seen that compared with other comparison methods, the method of the present invention can still reconstruct high-quality images even with a very small ACS, indicating that it is more robust to the number of ACS.

[0075] The protection scope of the magnetic resonance image undersampling reconstruction method described in the embodiment of the present invention is not limited to the execution order of the steps listed in this embodiment. All solutions implemented by adding, reducing, or replacing steps in the prior art based on the principles of the present invention are included in the protection scope of the present invention.

[0076] An embodiment of the present invention further provides a magnetic resonance image undersampling reconstruction system, which can implement the magnetic resonance image undersampling reconstruction method described in the present invention. However, the implementation device of the magnetic resonance image undersampling reconstruction system described in the present invention includes but is not limited to the structure of the magnetic resonance image undersampling reconstruction system listed in this embodiment. All structural variations and replacements of the prior art made according to the principles of the present invention are included in the protection scope of the present invention.

[0077] like Figure 5 As shown, in one embodiment, the magnetic resonance image undersampling reconstruction system of the present invention includes a modeling module 51 , a coordinate definition module 52 , a training module 53 , an acquisition module 54 , a prediction module 55 and a reconstruction module 56 .

[0078] The modeling module 51 is used to model the MRI image and the coil sensitivity image as continuous functions; the continuous function of the MRI image is used to output the MRI image matrix corresponding to the spatial coordinates of the pixel points of the MRI image, and the continuous function of the coil sensitivity image is used to output the coil sensitivity matrix corresponding to the spatial coordinates of the pixel points of the coil sensitivity image.

[0079] The coordinate definition module 52 is used to predefine the spatial coordinates of the pixels of the MRI image and the coil sensitivity image.

[0080] The training module 53 is connected to the modeling module 51 and the coordinate definition module 52, and is used to train the continuous function based on the spatial coordinates.

[0081] The acquisition module 54 is connected to the training module 53 and is used to input the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image into a trained continuous function to obtain the MRI image matrix and the coil sensitivity matrix.

[0082] The prediction module 55 is connected to the acquisition module 54 and is configured to acquire predicted k-space data of the MRI image based on the MRI image matrix and the coil sensitivity matrix according to the MRI forward physical model.

[0083] The reconstruction module 56 is connected to the prediction module 55 and is configured to acquire an MRI reconstructed image based on the actual k-space data and the predicted k-space data.

[0084] Among them, the structures and principles of the modeling module 51, the coordinate definition module 52, the training module 53, the acquisition module 54, the prediction module 55 and the reconstruction module 56 correspond one to one with the steps in the above-mentioned magnetic resonance image undersampling reconstruction method, so they are not repeated here.

[0085] In the several embodiments provided by the present invention, it should be understood that the disclosed systems, devices or methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of modules / units is only a logical function division. There may be other division methods in actual implementation. For example, multiple modules or units can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules or units, which can be electrical, mechanical or other forms.

[0086] Modules / units described as separate components may or may not be physically separate, and components displayed as modules / units may or may not be physical modules, that is, they may be located in one place or distributed across multiple network elements. Some or all of the modules / units may be selected based on actual needs to achieve the objectives of the embodiments of the present invention. For example, the functional modules / units in various embodiments of the present invention may be integrated into a single processing module, each module / unit may exist physically separately, or two or more modules / units may be integrated into a single module / unit.

[0087] Those skilled in the art should further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the composition and steps of each example according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0088] The present invention also provides a computer-readable storage medium. A person skilled in the art will appreciate that all or part of the steps in the magnetic resonance image undersampling reconstruction method of the above embodiment can be performed by instructing a processor through a program. The program can be stored in a computer-readable storage medium, which is a non-transitory medium, such as a random access memory, a read-only memory, a flash memory, a hard disk, a solid-state drive, a magnetic tape, a floppy disk, an optical disc, or any combination thereof. The storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a magnetic tape), an optical medium (e.g., a digital video disc (DVD)), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0089] An embodiment of the present invention further provides an electronic device comprising a processor and a memory.

[0090] The memory is used to store computer programs.

[0091] The memory includes various media that can store program codes, such as ROM, RAM, magnetic disk, USB flash drive, memory card or optical disk.

[0092] The processor is connected to the memory and is used to execute the computer program stored in the memory, so that the electronic device performs the above-mentioned magnetic resonance image undersampling reconstruction method.

[0093] Preferably, the processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0094] like Figure 6As shown, the electronic device of the present invention is in the form of a general-purpose computing device. Components of the electronic device may include, but are not limited to: one or more processors or processing units 61, memory 62, and a bus 63 connecting different system components (including memory 62 and processing unit 61).

[0095] Bus 63 represents one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor, or a local bus using any of a variety of bus architectures. Examples of these architectures include, but are not limited to, an Industry Standard Architecture (ISA) bus, a Micro Channel Architecture (MAC) bus, an Enhanced ISA bus, a Video Electronics Standards Association (VESA) local bus, and a Peripheral Component Interconnect (PCI) bus.

[0096] Electronic devices typically include a variety of computer system readable media. These media can be any available media that can be accessed by the electronic device, including volatile and non-volatile media, removable and non-removable media.

[0097] The memory 62 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 621 and / or cache memory 622. The electronic device may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the storage system 623 may be used to read and write non-removable, non-volatile magnetic media ( Figure 6 Not shown, often called a "hard drive"). Although Figure 6 Not shown, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk"), and an optical drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 63 via one or more data medium interfaces. Memory 62 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of various embodiments of the present invention.

[0098] A program / utility 624 having a set (at least one) of program modules 6241 may be stored, for example, in memory 62. Such program modules 6241 include, but are not limited to, an operating system, one or more application programs, other program modules, and program data, each of which, or some combination thereof, may include an implementation of a network environment. Program modules 6241 generally implement the functions and / or methods of the embodiments described herein.

[0099] The electronic device may also communicate with one or more external devices (e.g., keyboards, pointing devices, displays, etc.), one or more devices that enable a user to interact with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (e.g., network cards, modems, etc.). Such communication may be performed via input / output (I / O) interface 64. Furthermore, the electronic device may also communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via network adapter 65. Figure 6 As shown, the network adapter 65 communicates with other modules of the electronic device via the bus 63. It should be understood that, although not shown in the figures, other hardware and / or software modules may be used in conjunction with the electronic device, including but not limited to microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0100] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Anyone skilled in the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by one of ordinary skill in the art without departing from the spirit and technical principles disclosed herein are intended to be covered by the claims of the present invention.

Claims

1. A magnetic resonance image undersampling reconstruction method, characterized by: The method comprises the following steps: The MRI image and the coil sensitivity image are modeled as continuous functions; the continuous function of the MRI image is used to output an MRI image matrix corresponding to the spatial coordinates of the pixel points of the MRI image, and the continuous function of the coil sensitivity image is used to output a coil sensitivity matrix corresponding to the spatial coordinates of the pixel points of the coil sensitivity image; Predefine the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image; training the continuous function based on the spatial coordinates; Inputting the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image into a trained continuous function to obtain the MRI image matrix and the coil sensitivity matrix; Based on the MRI image matrix and the coil sensitivity matrix, obtaining predicted k-space data of the MRI image according to an MRI forward physical model; Acquire an MRI reconstructed image based on the actual k-space data and the predicted k-space data; Modeling the MRI image and coil sensitivity image as continuous functions of spatial coordinates includes the following steps: The continuous function obtained by MRI image modeling uses two sinusoidal expression networks, which respectively express the real and imaginary parts of the MRI image. Each sinusoidal expression network consists of eight fully connected layers, with the first layer having two input channels for receiving spatial coordinates and the last layer having one output channel for generating the real or imaginary part of the MRI image corresponding to the spatial coordinates. The middle layer has 256 neurons, and a sinusoidal function is set as an activation function between two adjacent fully connected layers. The real and imaginary parts of the MRI image constitute the MRI image matrix. The continuous function obtained by coil sensitivity image modeling adopts polynomial function Among them C j (x,y) represents the coil sensitivity value of the jth coil at (x,y), N is the order of the polynomial, are the polynomial coefficients to be solved, p is the degree of the coordinate x, and q is the degree of the coordinate y; the coil sensitivity values ​​constitute the coil sensitivity matrix.

2. The magnetic resonance image undersampling reconstruction method according to claim 1, wherein: Predefining the spatial coordinates of the pixel points of the MRI image and coil sensitivity image to be reconstructed includes the following steps: dividing the MRI image and the coil sensitivity image into equal intervals; The x and y coordinates of each pixel are uniformly mapped to the numerical range of [-1, 1] with the origin as the center.

3. The magnetic resonance image undersampling reconstruction method according to claim 1, wherein: Training the continuous function based on the spatial coordinates comprises the following steps: Inputting the spatial coordinates into the continuous function, and designing a loss function based on an MRI forward physical model and a regularization term containing image prior information; The loss function is minimized using a gradient back-propagation algorithm to obtain a trained continuous function.

4. The magnetic resonance image undersampling reconstruction method according to claim 3, wherein: The regularization term containing image prior information adopts the total variation of the image; the loss function is S j represents the actual k-space data of the j-th coil, I(θ) represents the MRI image matrix acquired based on the continuous function of the MRI image, θ represents the optimizable parameter in the continuous function of the MRI image, represents the coil sensitivity matrix obtained based on the continuous function of coil sensitivity, represents the optimizable parameter in the continuous function of coil sensitivity, ||·||1 represents the L1 norm of the matrix, c represents the total number of coils, G represents the gradient operator of the image, λ represents the weight of the regularization term, F is the Fourier transform matrix, and M is the undersampling mask matrix.

5. The magnetic resonance image undersampling reconstruction method according to claim 1, wherein: The MRI forward physical model is in, represents the predicted k-space data of the j-th coil, is the predicted MRI image matrix, C j represents the j-th coil sensitivity matrix, and F is the Fourier transform matrix.

6. The magnetic resonance image undersampling reconstruction method according to claim 1, wherein: Acquiring an MRI reconstructed image based on the actual k-space data and the predicted k-space data comprises the following steps: replacing corresponding data in the predicted K-space data with actual K-space data to obtain composite K-space data; The composite K-space data is subjected to two-dimensional inverse Fourier transform coil by coil, and then different coil images are merged based on the coil sensitivity matrix to obtain the MRI reconstructed image.

7. A magnetic resonance image undersampling reconstruction system, characterized by: The system includes a modeling module, a coordinate definition module, a training module, an acquisition module, a prediction module and a reconstruction module; The modeling module is used to model the MRI image and the coil sensitivity image as continuous functions; the continuous function of the MRI image is used to output the MRI image matrix corresponding to the spatial coordinates of the pixel points of the MRI image, and the continuous function of the coil sensitivity image is used to output the coil sensitivity matrix corresponding to the spatial coordinates of the pixel points of the coil sensitivity image; The coordinate definition module is used to predefine the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image; The training module is used to train the continuous function based on the spatial coordinates; The acquisition module is used to input the spatial coordinates of the pixel points of the MRI image and the coil sensitivity image into a trained continuous function to obtain the MRI image matrix and the coil sensitivity matrix; The prediction module is used to obtain predicted k-space data of the MRI image based on the MRI image matrix and the coil sensitivity matrix according to the MRI forward physical model; The reconstruction module is used to obtain an MRI reconstructed image based on the actual k-space data and the predicted k-space data; Modeling the MRI image and coil sensitivity image as continuous functions of spatial coordinates includes the following steps: The continuous function obtained by MRI image modeling uses two sinusoidal expression networks, which respectively express the real and imaginary parts of the MRI image. Each sinusoidal expression network consists of eight fully connected layers, with the first layer having two input channels for receiving spatial coordinates and the last layer having one output channel for generating the real or imaginary part of the MRI image corresponding to the spatial coordinates. The middle layer has 256 neurons, and a sinusoidal function is set as an activation function between two adjacent fully connected layers. The real and imaginary parts of the MRI image constitute the MRI image matrix. The continuous function obtained by coil sensitivity image modeling adopts polynomial function Among them C j (x,y) represents the coil sensitivity value of the jth coil at (x,y), N is the order of the polynomial, are the polynomial coefficients to be solved, p is the degree of the coordinate x, and q is the degree of the coordinate y; the coil sensitivity values ​​constitute the coil sensitivity matrix.

8. A storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the magnetic resonance image undersampling reconstruction method according to any one of claims 1 to 6 is implemented.

9. An electronic device, characterized in that: include: processor and memory; The memory is used to store computer programs; The processor is configured to execute the computer program stored in the memory, so as to enable the electronic device to perform the magnetic resonance image undersampling reconstruction method according to any one of claims 1 to 6.

Images