Magnetic resonance imaging method and apparatus, electronic device, storage medium, and program product

Abstract

A magnetic resonance imaging method and apparatus, an electronic device, a storage medium, and a program product. The method comprises: for a target part to be subjected to magnetic resonance imaging, acquiring k-space data of the target part, and reconstructing a preliminary magnetic resonance image on the basis of the k-space data (S110); acquiring a pre-constructed magnetic resonance image reconstruction network, wherein the magnetic resonance image reconstruction network at least comprises a spatial domain equivariant convolutional layer, constructed on the basis of group theory and having rotational equivariance in a spatial domain (S120); and inputting the preliminary magnetic resonance image into the magnetic resonance image reconstruction network, so as to perform image reconstruction by utilizing the rotational symmetry of the preliminary magnetic resonance image in the spatial domain by means of the spatial domain equivariant convolutional layer in the magnetic resonance image reconstruction network to obtain a target magnetic resonance image (S130).

Description

Magnetic resonance imaging method, device, electronic equipment, storage medium and program product

[0001] The present application claims priority to the Chinese patent application No. 202410713218.5, filed on June 4, 2024, to the Chinese Patent Office, the content of which is incorporated herein by reference in its entirety. TECHNICAL FIELD

[0002] Embodiments of the present application relate to the technical field of magnetic resonance imaging, for example, to a magnetic resonance imaging method, device, electronic equipment, storage medium and program product. BACKGROUND

[0003] Cardiac Cine Magnetic Resonance Imaging is a non-invasive medical imaging technique that can be used to observe and evaluate the structure and function of the heart.

[0004] In clinical practice, the scanning time of Cardiac Cine Magnetic Resonance Imaging is relatively long, which can cause discomfort to the patient and increase the risk of image artifacts due to patient movement, and due to the inherent physical limitations of magnetic resonance, it is difficult to achieve high spatial and temporal resolution in the reconstructed image. Therefore, fast imaging to improve the spatial and temporal resolution and shorten the scanning time is an urgent need for Cardiac Cine Magnetic Resonance Imaging.

[0005] Currently, the commonly used fast imaging techniques are parallel imaging and compressed sensing, but both have their own shortcomings. In recent years, related technologies using Convolutional Neural Network (CNN) have shown great potential in Cardiac Cine Magnetic Resonance Imaging. Compared with traditional parallel imaging or compressed sensing techniques, CNN can achieve better imaging quality and higher acceleration factor.

[0006] However, the image quality of the magnetic resonance image reconstructed by CNN, i.e., the imaging quality achieved, is still difficult to truly meet the clinical needs.

[0007] SUMMARY

[0008] Embodiments of the present application provide a magnetic resonance imaging method, device, electronic equipment, storage medium and program product to improve the reconstruction quality of the magnetic resonance image.

[0009] According to an aspect of the present application, a magnetic resonance imaging method is provided, which can include:

[0010] For a target site to be subjected to magnetic resonance imaging, k-space data of the target site is collected, and a preliminary magnetic resonance image is reconstructed based on the k-space data;

[0011] acquire a pre-built magnetic resonance image reconstruction network, wherein the magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolution layer constructed based on group theory and having rotational equivariance in a spatial domain;

[0012] input the preliminary magnetic resonance image into the magnetic resonance image reconstruction network to perform image reconstruction using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, and obtain a target magnetic resonance image.

[0013] According to another aspect of the present application, a magnetic resonance imaging device can include:

[0014] a preliminary magnetic resonance image reconstruction module configured to acquire k-space data of a target part to be subjected to magnetic resonance imaging, and reconstruct a preliminary magnetic resonance image based on the k-space data;

[0015] a magnetic resonance image reconstruction network acquisition module configured to acquire a pre-built magnetic resonance image reconstruction network, wherein the magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolution layer constructed based on group theory and having rotational equivariance in a spatial domain;

[0016] a target magnetic resonance image obtaining module configured to input the preliminary magnetic resonance image into the magnetic resonance image reconstruction network to perform image reconstruction using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, and obtain a target magnetic resonance image.

[0017] According to another aspect of the present application, an electronic device can include:

[0018] at least one processor; and

[0019] a memory communicatively connected to the at least one processor; wherein

[0020] the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to cause the at least one processor to implement the magnetic resonance imaging method provided by any of the embodiments of the present application.

[0021] According to another aspect of the present application, a computer readable storage medium having stored thereon computer instructions for causing a processor to implement the magnetic resonance imaging method provided by any of the embodiments of the present application when executed by the processor.

[0022] According to another aspect of the present application, a computer program product having stored thereon a computer program, which, when executed by a processor, can implement the magnetic resonance imaging method provided by any of the embodiments of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0023] FIG. 1 is a flowchart of a magnetic resonance imaging method according to an embodiment of the present application;

[0024] FIG. 2 is a schematic diagram of a compressed sensing and deep learning based cardiac cine magnetic resonance imaging network in a magnetic resonance imaging method according to an embodiment of the present application;

[0025] FIG. 3 is a schematic diagram of a spatio-temporal rotation equivariant convolution network in a magnetic resonance imaging method according to an embodiment of the present application;

[0026] FIG. 4 is a flowchart of another magnetic resonance imaging method according to an embodiment of the present application;

[0027] FIG. 5 is a schematic diagram of an example framework of an input equivariant layer, a temporal equivariant convolution layer and an intermediate equivariant layer in another magnetic resonance imaging method according to an embodiment of the present application;

[0028] FIG. 6 is a flowchart of yet another magnetic resonance imaging method according to an embodiment of the present application;

[0029] FIG. 7A is a schematic diagram of a comparison experiment result in yet another magnetic resonance imaging method according to an embodiment of the present application;

[0030] FIG. 7B is a comparison schematic diagram of a reconstructed target magnetic resonance image in yet another magnetic resonance imaging method according to an embodiment of the present application;

[0031] FIG. 8 is a structural block diagram of a magnetic resonance imaging apparatus according to an embodiment of the present application;

[0032] FIG. 9 is a structural schematic diagram of an electronic device implementing a magnetic resonance imaging method according to an embodiment of the present application. DETAILED DESCRIPTION

[0033] The embodiments of the present application will be described hereinafter with reference to the drawings. The embodiments described are some of the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of the present application.

[0034] It is to be noted that the terms "first", "second", and the like in the description and in the claims of the present application and the above-described drawings are intended to distinguish similar objects and are not necessarily intended to describe a particular sequential or chronological order. It is to be understood that the data thus designated can be interchanged, where appropriate, so that the embodiments of the present application described herein can be carried out in other than the order shown or described herein. The same applies to the cases of "target", "original", etc. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product, or apparatus that includes a series of steps or units does not have to be limited to the listed steps or units, but can include other steps or units that are not listed or inherent to these processes, methods, products, or apparatuses.

[0035] Before introducing the embodiments of the present application, the above-described compressed sensing and CNN are exemplarily described so as to understand the reason why the better imaging quality cannot be achieved.

[0036] Exemplarily, compressed sensing is to improve the imaging speed by reducing the k-space sampling points and utilizing the sparsity of the imaging object (for example, the heart). However, compressed sensing has a long reconstruction time due to iterative reconstruction, and it is difficult to select a sparse transform and reconstruction parameters.

[0037] In contrast, CNN can extract image features through multi-level convolution and pooling operations, learn the optimal parameters required for reconstruction from a large amount of training data, or directly learn the mapping relationship between the under-sampled k-space data and the fully-sampled image, thereby achieving better imaging quality and higher acceleration ratio.

[0038] It is emphasized that CNN, through parameter sharing and sliding window technology, not only improves the robustness of the model, but also successfully describes the translational symmetry, which is a ubiquitous image prior. However, in addition to translational symmetry, there is also rotational symmetry in the morphological structure of the heart, that is, rotational symmetry is ubiquitous in cardiac cine magnetic resonance images and can be used as an image prior to play a huge role in the process of magnetic resonance imaging. The rotational symmetry can be understood as the imaging object maintaining the same properties as the original morphology after a certain rotation operation. However, the currently applied CNN cannot describe the rotational symmetry, that is, it cannot utilize the effective image prior of rotational symmetry, thereby affecting the quality of magnetic resonance imaging.

[0039] In view of this, data augmentation is the most commonly used solution, which improves the ability of the model to handle global symmetry by performing overall rotation transformation on the image. However, for the symmetry change of local features, such as the diversity of the rotation direction of the local myocardial edge and the cardiovascular wall, data augmentation cannot be well described.

[0040] Therefore, in order to solve the problem of low magnetic resonance imaging quality caused by the inability of CNN to depict rotational symmetry in the magnetic resonance imaging process, the magnetic resonance imaging scheme described in the following embodiments is proposed.

[0041] FIG. 1 is a flowchart of a magnetic resonance imaging method provided by an embodiment of the present application. The present embodiment can be applied to the case of performing magnetic resonance imaging on a target part, for example, to the case of performing magnetic resonance imaging on a heart, and to the case of performing magnetic resonance imaging on a local feature of a heart. The method can be performed by a magnetic resonance imaging device provided by an embodiment of the present application, which can be implemented in software and / or hardware, and can be integrated on an electronic device, which can be various user terminals or a server.

[0042] Referring to FIG. 1, the method of the present embodiment includes the following steps:

[0043] S110, for a target part to be subjected to magnetic resonance imaging, k-space data of the target part is collected, and a preliminary magnetic resonance image is reconstructed based on the k-space data.

[0044] The target part can be understood as a part to be subjected to magnetic resonance imaging, for example, a heart, a head, a neck, or a waist, etc., which is related to the actual situation. In an embodiment, when the target part is a heart, the above magnetic resonance imaging can be referred to as cardiac cine magnetic resonance imaging.

[0045] The k-space data applied in the magnetic resonance imaging process of the target part can be undersampled or fully sampled k-space data, which can be set according to actual needs.

[0046] Further, a preliminary magnetic resonance image of the target part is reconstructed based on the k-space data, which can be a magnetic resonance image with artifacts, i.e., a low-quality magnetic resonance image.

[0047] S120, a pre-built magnetic resonance image reconstruction network is obtained;

[0048] The magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolutional layer constructed based on group theory and having rotational equivariance in the spatial domain.

[0049] In some embodiments, the magnetic resonance image reconstruction network can be understood as a CNN built to solve the above problems for reconstructing a magnetic resonance image. The magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolutional layer, which is built based on group theory, thereby having rotational equivariance in the spatial domain, i.e., the spatial domain equivariant convolutional layer can depict the rotational symmetry of the target site located in the spatial domain by using group theory, which can be reflected in the global features and local features of the target site, so that the network has equivariance for the rotational transformation of the global features and local features, and thus the rotational symmetry, an effective image prior, can be used for image reconstruction in the magnetic resonance imaging process to improve the imaging quality.

[0050] In combination with the application scenarios that can be involved in the embodiments of the present application, in some embodiments, the types of the spatial domain equivariant convolutional layer can include at least one of an input equivariant layer, an intermediate equivariant layer, and an output equivariant layer, etc. In some embodiments, the number of the intermediate equivariant layers can be one, two, or more, which can be set according to actual needs.

[0051] In some embodiments, the magnetic resonance image reconstruction network can be understood as a CNN built to solve the above problems for reconstructing a magnetic resonance image. The magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolutional layer, which is built based on group theory, thereby having rotational equivariance in the spatial domain, i.e., the spatial domain equivariant convolutional layer can depict the rotational symmetry of the target site located in the spatial domain by using group theory, which can be reflected in the global features and local features of the target site, so that the network has equivariance for the rotational transformation of the global features and local features, and thus the rotational symmetry, an effective image prior, can be used for image reconstruction in the magnetic resonance imaging process to improve the imaging quality.

[0052] In some embodiments, the magnetic resonance image reconstruction network can be understood as a CNN built to solve the above problems for reconstructing a magnetic resonance image. The magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolutional layer, which is built based on group theory, thereby having rotational equivariance in the spatial domain, i.e., the spatial domain equivariant convolutional layer can depict the rotational symmetry of the target site located in the spatial domain by using group theory, which can be reflected in the global features and local features of the target site, so that the network has equivariance for the rotational transformation of the global features and local features, and thus the rotational symmetry, an effective image prior, can be used for image reconstruction in the magnetic resonance imaging process to improve the imaging quality.

[0053] In some embodiments, the magnetic resonance image reconstruction network can be understood as a CNN built to solve the above problems for reconstructing a magnetic resonance image. The magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolutional layer, which is built based on group theory, thereby having rotational equivariance in the spatial domain, i.e., the spatial domain equivariant convolutional layer can depict the rotational symmetry of the target site located in the spatial domain by using group theory, which can be reflected in the global features and local features of the target site, so that the network has equivariance for the rotational transformation of the global features and local features, and thus the rotational symmetry, an effective image prior, can be used for image reconstruction in the magnetic resonance imaging process to improve the imaging quality.

[0054] On this basis, it should be noted that the cardiac cine magnetic resonance image exists in the form of a video-like two-dimensional (2D) image space + time domain (t). The rotational symmetry exists not only in a single two-dimensional image, but also widely exists between different frames of images. For example, for a cardiac structure that changes little or does not change along the time direction, the rotational symmetry appears more frequently.

[0055] Therefore, to improve the imaging quality, the following optional embodiment is proposed, the magnetic resonance image reconstruction network further includes a time domain equivariant convolution layer having rotational equivariance in the time domain;

[0056] Through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, the rotational symmetry of the preliminary magnetic resonance image in the spatial domain is utilized for image reconstruction to obtain a target magnetic resonance image, including:

[0057] For the spatial domain equivariant convolution layer and the time domain equivariant convolution layer in the magnetic resonance image reconstruction network, through the spatial domain equivariant convolution layer, the rotational symmetry of the preliminary magnetic resonance image in the spatial domain is utilized, and through the time domain equivariant convolution layer, the rotational symmetry of the preliminary magnetic resonance image in the time domain is utilized, to perform image reconstruction to obtain a target magnetic resonance image.

[0058] The time domain equivariant convolution layer can be understood as a convolution layer having rotational equivariance in the time domain (i.e., the time domain) in the magnetic resonance image reconstruction network. In the embodiments of the present application, the time domain equivariant convolution layer can be connected to adjacent spatial domain equivariant convolution layers by utilizing the transformation between convolution channels, so that the network can utilize the rotational symmetry along the time domain, thereby improving the use degree of the network for the rotational symmetry.

[0059] In this way, not only the rotational symmetry of the preliminary magnetic resonance image in the spatial domain can be utilized through the spatial domain equivariant convolution layer, but also the rotational symmetry of the preliminary magnetic resonance image in the time domain can be utilized through the time domain equivariant convolution layer. The two are coordinated to improve the use degree of the network for the rotational symmetry, thereby improving the magnetic resonance imaging quality.

[0060] In some embodiments, the k-space data is undersampled k-space data, and the preliminary magnetic resonance image is reconstructed based on the k-space data, including:

[0061] Based on the undersampled k-space data, a coil sensitivity map is obtained;

[0062] Based on the coil sensitivity map, initial zero padding reconstruction is performed in combination with the undersampled k-space data to obtain a preliminary magnetic resonance image;

[0063] input the preliminary magnetic resonance image into the magnetic resonance image reconstruction network to perform image reconstruction by using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain through a spatial domain equivariant convolutional layer in the magnetic resonance image reconstruction network, to obtain the target magnetic resonance image, comprising:

[0064] input the preliminary magnetic resonance image and the coil sensitivity map into the magnetic resonance image reconstruction network to perform image reconstruction by using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain through a spatial domain equivariant convolutional layer in the magnetic resonance image reconstruction network, and to perform data consistency updates of the coil sensitivity map through the magnetic resonance image reconstruction network, to reconstruct the target magnetic resonance image.

[0065] The above embodiment improves the magnetic resonance imaging speed and the magnetic resonance imaging quality by combining the compressed sensing technology on the basis of deep learning.

[0066] On this basis, in order to more intuitively understand the above embodiment, an example is used for illustrative description. The example is based on a compressed sensing and deep learning based cardiac cine magnetic resonance imaging network, specifically a compressed sensing image reconstruction network (Recon-net) based on CNN. The spatial domain equivariant convolutional layer and the time domain equivariant convolutional layer are introduced into the Recon-net to obtain the magnetic resonance image reconstruction network.

[0067] Illustratively, referring to FIG. 2, the undersampled k-space data is first subjected to initial zero-padding reconstruction based on coil sensitivity map (ESPIRiT maps) calibration to obtain a preliminary magnetic resonance image. The preliminary magnetic resonance image and the coil sensitivity map are used as inputs of the iterative updated Recon-net. In the Recon-net, two iterative update steps, data consistency updates and three dimensional (3D) CNN, are alternately performed. On this basis, referring to FIG. 3, a spatiotemporal rotation equivariant convolutional neural network (SRE-CNN) is built in the example, and the SRE-CNN is used to replace the 3D CNN in the Recon-net to obtain the magnetic resonance image reconstruction network. The magnetic resonance image reconstruction network can effectively use the rotational symmetry in the preliminary magnetic resonance image to improve the reconstruction quality of the magnetic resonance image.

[0068] First, the Recon-net and its related content will be introduced. Image reconstruction from undersampled k-space data is an ill-posed inverse problem, which cannot obtain a specific solution. Among numerous potential solutions, compressive sensing technology seeks the sparsest solution, i.e., in the imaging network of compressive sensing technology, in addition to the data fidelity term, there is also a sparse term, and the objective function can be written as follows:

[0069] wherein, is the reconstructed target magnetic resonance image; A represents an encoding matrix, generally an undersampled Fourier operator; x represents a fully sampled true value magnetic resonance image, which can be used as a label in network training; y is the acquired undersampled k-space data; R(·) represents a sparse transform, such as wavelet transform and total variation; and λ is a coefficient.

[0070] Exemplarily, continuing to refer to FIG. 2, the left white background box part shows the initial reconstruction step based on the coil sensitivity map (including three white background boxes of “time average calculation”, “coil sensitivity calibration” and “initial zero padding reconstruction” in the figure). The format of the undersampled k-space data is [k x ,k y ,T,C], wherein k x ,k y is the size of the data; T is the time domain, i.e., how many frames of images the data contains; and C is the number of channels of the data.

[0071] First, a fully sampled calibration region (i.e., coil sensitivity calibration) is extracted from the time-averaged undersampled k-space data, and is used to calculate the coil sensitivity map in the format of [X, Y, C, M]. The coil sensitivity map can utilize the correlation between multi-channel magnetic resonance data to flexibly represent the overlapping anatomy structure with reduced field of view acquisition. Generally, two sets of coil sensitivity maps are sufficient to achieve high-fidelity reconstruction of magnetic resonance images with anatomical overlap, which are represented by set 1 and set 2 in FIG. 2. Then, the coil sensitivity maps are used to calculate the initial zero padding reconstruction from the undersampled k-space data, to obtain a low-quality preliminary magnetic resonance image.

[0072] The preliminary magnetic resonance image is inputted into the Recon-net together with the coil sensitivity map. In the Recon-net, the reconstruction can be divided into three main steps: 1) unfolding the compressed sensing algorithm to a fixed number of iterations; 2) in each iteration, two iterative update steps: data consistency update and 3D CNN are alternately performed, and the prior information in each iteration is enforced by the 3D CNN; 3) training the unfolded compressed sensing algorithm in a supervised manner so that the target magnetic resonance image output by the Recon-net gradually approximates the full-sampled true value magnetic resonance image. Finally, the input preliminary magnetic resonance image can obtain a low-artifact, i.e. high-quality target magnetic resonance image through the trained Recon-net.

[0073] Next, the SRE-CNN proposed above is described. For example, the SRE-CNN is used to replace the 3D CNN in each iteration. In each iteration, the SRE-CNN is constructed as shown in FIG. 3, and four 3D convolution layers are connected in turn. Each 3D convolution layer is in the form of a 2D convolution layer + a 1D convolution layer (i.e. 2D+1D in the figure), so as to improve the use efficiency of network parameters. There is a nonlinear activation layer between each convolution layer, which is used to enable the network to process and represent complex nonlinear relationships. The first (2D+1D) convolution layer is composed of a 2D input equivariant layer and a 1D time domain equivariant convolution layer, the second (2D+1D) convolution layer is composed of a 2D intermediate equivariant layer and a 1D time domain equivariant convolution layer, the third (2D+1D) convolution layer has the same structure as the second layer, and the fourth (2D+1D) convolution layer is composed of a 2D output equivariant layer and a 1D traditional convolution layer.

[0074] As can be seen from the above, in the SRE-CNN, group theory is introduced to construct a spatial domain equivariant convolution layer using the symmetry of the group. The spatial domain equivariant convolution layer has three types, namely an input equivariant layer, an intermediate equivariant layer and an output equivariant layer. By reasonably combining the above three types of spatial domain equivariant convolution layers, the SRE-CNN constructed based thereon has rotational equivariance in the spatial domain, and the magnetic resonance image reconstruction network constructed based on the SRE-CNN also has rotational equivariance in the spatial domain.

[0075] On the basis of the spatial domain equivariant convolution layer, a time domain equivariant convolution layer is also constructed in the SRE-CNN, which uses the transformation between convolution channels to connect adjacent spatial domain equivariant convolution layers, so that the network can use the rotational symmetry along the time domain, thereby improving the use degree of the SRE-CNN for rotational symmetry.

[0076] FIG. 4 is a flowchart of another magnetic resonance imaging method provided in the embodiments of the present application. The present embodiment is adjusted based on the above-mentioned embodiments. In the present embodiment, the spatial domain equivariant convolution layer can optionally include at least an input equivariant layer, and the input convolution kernel of the input equivariant layer is obtained by rotating a preset convolution kernel using a first rotation subgroup of a preset rotation transformation group to expand the number of convolution kernels of the preset convolution kernel to obtain the input convolution kernel. The target magnetic resonance image is obtained by using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain to perform image reconstruction through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, including: using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain to perform feature extraction on the preliminary magnetic resonance image through the input convolution kernel of the input equivariant layer in the magnetic resonance image reconstruction network to obtain a first layer feature map defined on the rotation transformation group, and performing image reconstruction based on the first layer feature map to obtain the target magnetic resonance image. The explanations of the same or corresponding terms as in the above-mentioned embodiments are not repeated here.

[0077] Referring to FIG. 4, the method of the present embodiment can include the following steps:

[0078] S210, acquiring k-space data of a target site to be subjected to magnetic resonance imaging, and reconstructing a preliminary magnetic resonance image based on the k-space data.

[0079] S220, obtaining a magnetic resonance image reconstruction network built in advance;

[0080] The magnetic resonance image reconstruction network includes at least a spatial domain equivariant convolution layer having rotational equivariance in the spatial domain constructed based on group theory, and the spatial domain equivariant convolution layer includes at least an input equivariant layer.

[0081] The input convolution kernel of the input equivariant layer is obtained by rotating a preset convolution kernel using a first rotation subgroup of a preset rotation transformation group to expand the number of convolution kernels of the preset convolution kernel.

[0082] The input equivariant layer can be understood as the first spatial domain equivariant convolution layer for performing feature extraction on the preliminary magnetic resonance image.

[0083] In the embodiments of the present application, the input convolution kernel of the input equivariant layer can be obtained by rotating a preset convolution kernel using a first rotation subgroup of a preset rotation transformation group to expand the number of convolution kernels of the preset convolution kernel to obtain the input convolution kernel.

[0084] wherein the input convolution kernel is a convolution kernel of the input equivariant layer. The rotation transformation group S can be understood as a pre-set group with s elements for implementing rotation transformation (i.e. rotation operation). The first rotation operation subgroup A is a subgroup of S, i.e. A∈S, for rotating the pre-set convolution kernel, an example of which can be expressed as For any A, the rotation equivariant convolution of the input equivariant layer can be mapped as:

[0085] wherein I is the input preliminary magnetic resonance image, is a pre-set convolution kernel, see Fig. 5, which shows an example, p x p represents the size of the dimension, since it is a 2D convolution layer in the 2D+1D convolution layer, only one unit is needed in the third dimension (i.e. the time domain dimension), which is represented by 1. s represents the extension of the first rotation operation subgroup. * represents the conventional discrete convolution operation. ★ represents the group convolution operation.

[0086] Exemplarily, in the input equivariant layer, the number of convolution kernels of the pre-set convolution kernel is extended, and the input convolution kernel obtained after the extension is subjected to group transformation. In other words, the rotation equivariant convolution of the input equivariant layer maps the preliminary magnetic resonance image defined on to the first layer feature map defined on S.

[0087] S230, inputting the preliminary magnetic resonance image into the magnetic resonance image reconstruction network, so as to extract features of the preliminary magnetic resonance image by using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the input convolution kernel of the input equivariant layer in the magnetic resonance image reconstruction network, to obtain the first layer feature map defined on the rotation transformation group, so as to perform image reconstruction based on the first layer feature map to obtain the target magnetic resonance image.

[0088] wherein the preliminary magnetic resonance image is input into the magnetic resonance image reconstruction network, so that features of the preliminary magnetic resonance image can be extracted through the input convolution kernel of the input equivariant layer therein, to obtain the first layer feature map, so as to subsequently perform image reconstruction based on the first layer feature map to obtain the target magnetic resonance image.

[0089] Exemplarily, continuing to refer to Fig. 5, after the input equivariant layer, the first layer feature map F (1) There are three types of line cubes shown: solid line cube (A1), dashed line cube (A2) and dotted line cube (A3), which represent the three elements of A, i.e. three rotation angles, of which 0 degrees, 120 degrees and 240 degrees are exemplarily shown in Fig. 5.

[0090] The embodiment of the present application can expand the number of preset convolution kernels by rotating the preset convolution kernels by using a first rotation operation subgroup in a rotation transformation group, so as to obtain an input convolution kernel. The input convolution kernel can be understood as a convolution kernel prepared for a preliminary magnetic resonance image under different rotation angles, and the feature extraction of the preliminary magnetic resonance image can be performed by using the input convolution kernel, so that the rotation symmetry of the preliminary magnetic resonance image in the spatial domain can be effectively utilized, and the image reconstruction quality is improved.

[0091] FIG. 6 is a flowchart of another magnetic resonance imaging method provided in the embodiment of the present application. The present embodiment is adjusted on the basis of the above-mentioned embodiments. In the present embodiment, the magnetic resonance image reconstruction network further includes at least one time domain isomorphism convolution layer having rotation isomorphism in the time domain; and the image reconstruction based on the first layer feature map to obtain the target magnetic resonance image includes: for the time domain convolution kernel of the time domain isomorphism convolution layer adjacent to the input isomorphism layer in the at least one time domain isomorphism convolution layer, in the case that it is determined that each channel of the time domain convolution kernel needs to be shifted according to the rotation condition of the preliminary magnetic resonance image, shifting each channel of the time domain convolution kernel according to the rotation condition and by using a preset non-rotation transformation subgroup; and performing convolution operation on the first layer feature map by using the shifted time domain convolution kernel to obtain the second layer feature map, so as to perform image reconstruction based on the second layer feature map to obtain the target magnetic resonance image. The explanations of the same or corresponding terms as those in the above-mentioned embodiments are not repeated here.

[0092] Referring to FIG. 6, the method of the present embodiment can include the following steps:

[0093] S310, acquiring k-space data of a target part to be subjected to magnetic resonance imaging, and reconstructing a preliminary magnetic resonance image based on the k-space data.

[0094] S320, obtaining a magnetic resonance image reconstruction network built in advance;

[0095] In some embodiments, the magnetic resonance image reconstruction network includes at least one time domain isomorphism convolution layer having rotation isomorphism in the time domain and a spatial domain isomorphism convolution layer having rotation isomorphism in the spatial domain constructed based on group theory, and the spatial domain isomorphism convolution layer at least includes an input isomorphism layer.

[0096] The input convolution kernel of the input isomorphism layer is obtained by rotating a preset convolution kernel by using a first rotation operation subgroup in a preset rotation transformation group to expand the number of the preset convolution kernel.

[0097] As described above, the time domain isomorphism convolution layer is essentially a 1D convolution layer for extracting the variation of the preliminary magnetic resonance image in the time domain.

[0098] In the embodiments of the present application, the number of the time domain equivariant convolution layers can be one or more, which is related to the actual situation. For example, the one or more time domain equivariant convolution layers can be a time domain equivariant convolution layer connected between adjacent input equivariant layers and intermediate equivariant layers, a time domain equivariant convolution layer connected between two adjacent intermediate equivariant layers, or a time domain equivariant convolution layer connected between adjacent intermediate equivariant layers and output equivariant layers, etc.

[0099] S330, inputting the preliminary magnetic resonance image to the magnetic resonance image reconstruction network to perform S340-S360.

[0100] S340, performing feature extraction on the preliminary magnetic resonance image by using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the input convolution kernel of the input equivariant layer in the magnetic resonance image reconstruction network to obtain a first layer feature map defined in a rotational transformation group.

[0101] S350, for the time domain convolution kernel of the time domain equivariant layer adjacent to the input equivariant layer in the at least one time domain equivariant layer, in a case where it is determined according to the rotation condition of the preliminary magnetic resonance image that each channel of the time domain convolution kernel needs to be shifted, shifting each channel of the time domain convolution kernel according to the rotation condition and using a preset non-rotational transformation subgroup.

[0102] Wherein, the time domain convolution kernel can be understood as the convolution kernel of the time domain equivariant layer X adjacent to the input equivariant layer in each time domain equivariant layer.

[0103] According to the above description, in the previous input equivariant layer, the channels of the input convolution kernel have been expanded by A, and there is a specific arrangement rule between the channels. Therefore, here the channels of the time domain convolution kernel can be matched with the channels of the first layer feature map expanded by A by circularly shifting the channels of the time domain convolution kernel, so as to maintain the equivariance between the two spatial domain equivariant layers connected by the time domain equivariant layer X.

[0104] In form, the rotational equivariant convolution mapping of the time domain equivariant convolution layer X can be expressed as:

[0105] Wherein, The time domain convolution kernel of the time domain equivariant convolution layer X is expressed as 1×1×p in size in an example shown in FIG. 5. B is another subgroup S of S, i.e., a second rotational operation subgroup, used to rotate the time domain convolution kernel. T is a 1D non-rotational transformation subgroup with s elements, used for channel transformation of the time domain convolution kernel, which does not operate on the time domain convolution kernel in 2D. T1, T2 and T3 in FIG. 5 are three elements in T.

[0106] The rotation condition can represent whether the preliminary magnetic resonance image is rotated, and can also represent a rotation angle in the case of rotation. Therefore, in the case of determining that each channel of the time domain convolution kernel needs to be shifted according to the rotation condition, each channel is shifted according to the rotation condition and using a preset non-rotation transformation subgroup T. For example, in the case of representing that the preliminary magnetic resonance image is rotated according to the rotation condition, it is determined that each channel needs to be shifted, and on this basis, each channel can be shifted using T according to the rotation angle represented by the rotation condition.

[0107] S360, performing convolution operation on the first layer feature map by the shifted time domain convolution kernel to obtain a second layer feature map, so as to perform image reconstruction based on the second layer feature map to obtain a target magnetic resonance image.

[0108] Wherein, since the channels of the shifted time domain convolution kernel match the channels of the first layer feature map, the first layer feature map can be convolved by using the shifted time domain convolution kernel, that is, feature extraction is performed to obtain the second layer feature map, so that subsequent image reconstruction can be performed based on the second layer feature map to obtain the target magnetic resonance image.

[0109] In the embodiments of the present application, a time domain equivariant convolution layer X connected with an input equivariant layer is built, so that each channel of the time domain convolution kernel of the time domain equivariant convolution layer X can be shifted to match the channels of the first layer feature map output by the input equivariant layer, so as to maintain the equivariance between the two spatial domain equivariant convolution layers connected by the time domain equivariant convolution layer X, and further enable the network to use the rotational symmetry along the time domain, thereby improving the use degree of the network for the rotational symmetry.

[0110] On this basis, in order to understand the working process of the input equivariant layer and the time domain equivariant convolution layer as a whole, the following will be illustrated in combination with FIG. 5.

[0111] For example, in the time domain equivariant convolution layer X, the time domain convolution kernel wrapped by three different line types of boxes (including solid line box, dashed line box and dotted line box) is shown in FIG. 5, one box represents one time domain convolution kernel, which is essentially a 1x1x3 3D convolution kernel, but since it only has a time dimension (i.e. the third dimension) valid (i.e. greater than 1), it is generally called a 1D convolution kernel. The channels C A1 , C A2 and C A3 are given above the box, which means that each time domain convolution kernel has 3 channels extended by the rotation transformation group. The extension is because it needs to correspond to the extension of the previous input equivariant layer. When the input preliminary magnetic resonance image (which can be simply referred to as input image in this example) passes through the input equivariant layer, the first layer feature map F (1) is obtained, and then F (1)The convolution operation with the time domain equivariant convolution layer X needs to be performed, and the process is as follows:

[0112] When F (1) When the convolution is performed with the different time domain convolution kernels in the solid line box in the time domain equivariant convolution layer X, the convolution relationship is as follows:

[0113] F (1) The solid line feature map in F is convolved with the first convolution kernel in the solid line box in the time domain equivariant convolution layer X;

[0114] F (1) The dotted line feature map in F is convolved with the second convolution kernel in the solid line box in the time domain equivariant convolution layer X;

[0115] F (1) The dot line feature map in F is convolved with the third convolution kernel in the solid line box in the time domain equivariant convolution layer X.

[0116] Referring to FIG. 5, in the solid line box in the time domain equivariant convolution layer X, there are three different block combinations from left to right, which are called the first convolution kernel (no shading), the second convolution kernel (dot-like shading), and the third convolution kernel (broken line-like shading) in sequence.

[0117] When F (1) When the convolution is performed with the time domain convolution kernels in the dashed line or dot line box in the time domain equivariant convolution layer X, a cyclic shift needs to be performed on the channel. This is because the extension of the rotation transformation group is actually prepared for input images under different rotation angles, for example:

[0118] Suppose that when the initial direction of the input image I is 0 degrees, that is, the direction of the positive direction, it can be defined as I_0. The angles of the input convolution kernels of the input equivariant layer are as follows: solid line—0 degrees, that is, the positive direction; dashed line—120 degrees; dot line—240 degrees, then the solid line convolution kernel (that is, the input convolution kernel corresponding to the solid line block ) in the input equivariant layer (that is, the “2D input equivariant layer” in FIG. 5) and I_0 obtain a feature f_0 with a relative direction angle of 0 degrees, the dashed line convolution kernel and I_0 obtain a feature f_120 with a relative direction angle of 120 degrees, and the dot line convolution kernel and I_0 obtain a feature f_240 with a relative direction angle of 240 degrees.

[0119] When the input image I is rotated 120 degrees clockwise, I_0 becomes I_120, and the features obtained by the input convolution kernel of the three different line types in the input equivariant layer change because the features extracted are different when the relative direction of the input image I and the input convolution kernel is different. However, the parameters of the input convolution kernel in the trained input equivariant layer are fixed, so when the input image I is rotated or the similar features in the input image I exist in different rotation angles, the features obtained in F(1) are different. For example, the feature obtained by the solid line convolution kernel is no longer f_0 with a relative direction angle of 0 degrees, but f_120 because the relative direction angle of I_120 and the solid line convolution kernel changes from 0 degrees to 120 degrees. At this time, the relative direction angle of I_120 and the dashed line convolution kernel in the input equivariant layer changes to 0 degrees, and the convolution of the two obtains f_0. Therefore, when the input image I changes from I_0 to I_120, the solid line feature map (1) in F now appears in the dashed line feature map Therefore, in order to extract f_0 using the same time domain convolution kernel to ensure that the same feature can be extracted in the subsequent spatial domain equivariant convolution layer, the first convolution kernel in the time domain equivariant convolution layer X needs to be moved one position backward in the channel dimension to match f_0. It can be inferred in turn that other convolution kernels also need the same operation to match their corresponding features, so the shift on the channel is cyclic.

[0120] That is, the solid line, the dashed line, and the dotted line actually correspond to different rotation angles (directions) of the input image I. The solid line convolution kernel and the time domain convolution kernel in the solid line box are used to extract the features of the input image I in the positive direction, that is, the initial direction; the dashed line convolution kernel and the time domain convolution kernel in the dashed line box are used to extract the features of the input image I at 120 degrees; and the dotted line convolution kernel and the time domain convolution kernel in the dotted line box are used to extract the features of the input image I at 240 degrees. That is, the SRE-CNN in the example prepares a set of convolution kernels for the input image I in different directions to improve the robustness to input rotation. In this way, even if the input image I is rotated or there are small features in the input image I in different directions, each convolution layer in the above SRE-CNN can extract the same features, so that the SRE-CNN as a whole is robust to rotation.

[0121] In some embodiments, the spatial domain equivariant convolution layer further comprises at least one intermediate equivariant layer, and the intermediate convolution kernel of the intermediate equivariant layer adjacent to the time domain equivariant convolution layer is obtained by rotating using a second rotation operator group in the rotation transformation group;

[0122] The image is reconstructed based on the second feature map to obtain a target magnetic resonance image, comprising:

[0123] In the case where it is determined that each channel of the intermediate convolution kernel needs to be shifted according to the rotation condition, each channel of the intermediate convolution kernel is shifted according to the rotation condition and by using a non-rotation transformation subgroup.

[0124] The second feature map is convolved by the shifted intermediate convolution kernel to obtain a third feature map, and the image is reconstructed based on the third feature map to obtain a target magnetic resonance image.

[0125] The intermediate equivariant layer can be understood as a spatial domain equivariant convolution layer located between the input equivariant layer and the output equivariant layer. The number of intermediate equivariant layers can be one or more, which can be set according to actual needs. In this embodiment, at least one intermediate equivariant layer adjacent to the time domain equivariant convolution layer X described above, i.e., the intermediate equivariant layer M connected to the input equivariant layer, is taken as an example for introduction.

[0126] In the intermediate equivariant layer M, in addition to the cyclic shift of the intermediate convolution kernel of the intermediate equivariant layer M, the intermediate convolution kernel also needs to be rotated, which can be represented as, for example:

[0127] wherein, is the intermediate convolution kernel of the intermediate equivariant layer M. M is a non-rotation transformation group for channel transformation of the intermediate convolution kernel, and does not operate on the intermediate convolution kernel in 2D. T is a subgroup of M.

[0128] In FIG. 5, an example of a discrete rotation transformation group S is represented as In fact, in the embodiments of the present application, S can be set to at most

[0129] Therefore, the intermediate convolution kernel can be rotated by using the second rotation operation subgroup B in S. On this basis, similar to the processing process of the first feature map, in the case where it is determined that each channel of the intermediate convolution kernel needs to be shifted according to the rotation condition, each channel of the intermediate convolution kernel is shifted according to the rotation condition and by using T; the second feature map is convolved by the shifted intermediate convolution kernel to obtain a third feature map, so as to subsequently reconstruct the image based on the third feature map to obtain a target magnetic resonance image.

[0130] In the above embodiments, the intermediate equivariant layer M is built, and the intermediate convolution kernel of the intermediate equivariant layer M is cyclically shifted and rotated, so that the network has equivariance to rotation transformation in the planar spatial domain and along the time domain direction, thereby being capable of fully utilizing the rotational symmetry in the image to improve the reconstruction quality.

[0131] In some embodiments, the spatial domain equivariant convolution layer further comprises an output equivariant layer for image reconstruction based on the third layer feature map to obtain the target magnetic resonance image, comprising:

[0132] The end feature map is extracted through the intermediate equivariant layer closest to the output equivariant layer among the at least one intermediate equivariant layer, wherein the end feature map is obtained based on the third layer feature map;

[0133] The end feature map is processed through the output equivariant layer to obtain a result feature map with a channel number consistent with that of the preliminary magnetic resonance image, so as to reconstruct the target magnetic resonance image based on the result feature map.

[0134] The output equivariant layer can be understood as the spatial domain equivariant convolution layer located at the end of each spatial domain equivariant convolution layer, which can be a pooling layer for reducing the channel number in the embodiments of the present application, but will not change the size of the feature map.

[0135] It should be noted that in the image reconstruction task, the output target magnetic resonance image should maintain the same size and channel number as the input preliminary magnetic resonance image. However, due to the expansion of the convolution kernel number of the convolution kernel through the rotation transformation group in the input equivariant layer and the intermediate equivariant layer, the channel number of the feature map is also increased. Therefore, at the end of the network, the channel number of the feature map expanded by the rotation transformation group needs to be reduced to the same channel number as before the expansion.

[0136] For example, for the intermediate equivariant layer N closest to the output equivariant layer among the at least one intermediate equivariant layer, the end feature map is extracted through the intermediate equivariant layer N, which is obtained based on the third layer feature map. For example, in the example given in FIG. 5, the intermediate equivariant layer N can be used to perform convolution operation on the third layer feature map to obtain the end feature map. The end feature map is processed through the output equivariant layer to obtain a result feature map with a channel number consistent with that of the preliminary magnetic resonance image, so as to reconstruct the target magnetic resonance image based on the result feature map, the channel number of the target magnetic resonance image being consistent with that of the preliminary magnetic resonance image.

[0137] The above embodiments can make the channel number of the output target magnetic resonance image the same as that of the input preliminary magnetic resonance image by building the output equivariant layer, meeting the image reconstruction requirements.

[0138] Based on any of the above embodiments, it should be noted that clinical medical diagnosis requires higher image accuracy for detailed cardiac structures such as the myocardium and cardiovascular system. These detailed cardiac structures are small in scale and have complex local morphologies; therefore, the network's fitting ability is crucial to the accuracy of the reconstruction results. Based on this, the following optional embodiments are proposed: each convolutional kernel in the magnetic resonance image reconstruction network is a linear combination of at least two parameterized bases based on Fourier unfolding. In other words, the lossless nature of Fourier unfolding is utilized to construct a high-precision parameterized base, and the convolutional kernels in the above embodiments are constructed based on this parameterized base, thereby improving the accuracy of the network's expressive power and thus improving the accuracy of the reconstruction of detailed cardiac structures.

[0139] For example, based on the information-lossless nature of Fourier unfolding, high-precision one-dimensional and two-dimensional parameterized basis functions are constructed. It should be noted that parameterized convolution can be understood as defining the convolution kernel as a linear combination of a set (i.e., at least two) of basis functions (i.e., the basis), and learning the combination coefficients during training, rather than directly learning the numerical values ​​of the convolution kernel. This can be expressed as:

[0140] in, This represents a two-dimensional coordinate system. N represents the number of basis functions. n Describe the nth basis function ψ n The coefficients. In this parameterized form, ψ: To become a learnable convolutional kernel.

[0141] Since the Fourier series expansion is equivalent to the inverse discrete Fourier transform, and its representation error is zero, this embodiment uses a basis for Fourier expansion into one-dimensional (1D) and two-dimensional (2D) parameterized convolutions. Here is an example of the expression for the one-dimensional Fourier parameterized basis:

[0142] in, Let p be a one-dimensional Fourier parameterized basis, where p is the basis unwinding frequency (i.e., the kernel size), and a is the base. k cos function The coefficient, b k sin function The coefficients, k = 0, 1, ..., p-1.

[0143] use Fourier basis in the formula Replacing ψ(x) in the equation ψ(x) gives us parameterized convolution. a in the formula k and b k That is, w in the formula ψ(x)n Thus, the constructed parameterized convolution can be used as the convolution kernel in the above embodiments, thereby solving the problem of low reconstruction accuracy caused by small scale and complex local morphology of cardiac details, and improving the imaging quality.

[0144] The constructed SRE-CNN is optimized according to a training loss function, and the network parameters are iteratively updated by a back propagation algorithm. During the iterative updating process, the output of the network gradually approaches the ground truth magnetic resonance image reconstructed based on the fully sampled k-space data. When the preset number of iterations is reached, the training is stopped, and the network parameters at this time are saved. The training steps include:

[0145] (1) determining hyperparameters, including a discrete rotation transformation group S and a basis expansion frequency p of the parameterized convolution, and inputting the hyperparameters into the SRE-CNN;

[0146] (2) calculating the loss function L of the SRE-CNN;

[0147] (3) updating the network parameters of the SRE-CNN using a stochastic gradient descent algorithm. For example, the loss function determined in the embodiments of the present application is L:

[0148] wherein, N train is the number of the training data set; is the i th magnetic resonance image reconstructed by the network during the iteration process; x i represents the ground truth magnetic resonance image, i.e., the label, reconstructed based on the fully sampled k-space data.

[0149] The test steps are as follows: preparing a preliminary magnetic resonance image obtained based on the undersampled k-space data, a coil sensitivity map, and a corresponding ground truth magnetic resonance image to be tested, loading the SRE-CNN obtained by training, and inputting the prepared preliminary magnetic resonance image, coil sensitivity map, and corresponding ground truth magnetic resonance image into the SRE-CNN for forward calculation, so as to perform the test.

[0150] To prove the effectiveness of the SRE-CNN in the above proposed magnetic resonance imaging scheme, experiments were conducted. Under the condition that all experimental conditions are consistent, the SRE-CNN and other three kinds of cardiac cine magnetic resonance reconstruction schemes were carried out 12 times, 16 times and 20 times acceleration retrospective undersampling experiments on a 3T magnetic resonance imaging system to prove the effectiveness of the SRE-CNN. The comparison experiment results of the same data set training test are shown in FIG. 7A (the first place is indicated by bold), and the partially reconstructed images (i.e. the reconstructed target magnetic resonance images) are shown in FIG. 7B. It can be seen that the reconstruction results of the SRE-CNN are far superior to other comparison schemes, which shows that the SRE-CNN has higher expression accuracy and application potential. The three comparison cardiac cine magnetic resonance reconstruction schemes include: 1) L+S-a non-deep learning reconstruction scheme based on compressed sensing; 2) MoDL-a deep learning based reconstruction scheme; 3) R2plus1D-a deep learning and CNN based reconstruction scheme. The test indicators include peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and the time required for single image reconstruction (Time). The Adam optimizer is used to update the parameters, and the corresponding learning rate is 0.001, the batch size is 1, and the iteration is 30 generations. All experiments are completed on the same graphics processing unit (GPU).

[0151] Referring to FIG. 7B, the left side of the figure shows the true value magnetic resonance image (i.e. Label) reconstructed based on full sampling k-space data and the k-space mask used for undersampling acceleration. The right side of the figure shows the visualization results of an example image under 12 times and 20 times acceleration imaging, and shows the reconstructed image and the difference image with the Label, which is located below the reconstructed image. The vertical bar on the right side of each image is an x-t image, that is, all x and t values on a line along the y axis are taken, and the reconstruction effect in the time direction is observed based on such an image. As can be seen from FIG. 7B, compared with other comparison schemes, the SRE-CNN has better characterization of the details of the heart; the difference between the reconstructed image and the Label is the smallest; and on the x-t image, the reconstructed image quality is also higher, which all show the excellent performance and expression accuracy of the SRE-CNN.

[0152] In summary, the above magnetic resonance imaging scheme accurately characterizes the rotational symmetry of the local features of the heart by using group theory and high-precision parameterized bases, taking into account the small size and complex local morphology of the heart details, constructs a high-precision SRE-CNN that is invariant to rotational transformation, and achieves the best reconstruction capability in experiments. This shows that the above magnetic resonance imaging scheme has excellent expression accuracy and great clinical application potential.

[0153] FIG. 8 is a structural block diagram of a magnetic resonance imaging apparatus provided by an embodiment of the present application, which is used to perform the magnetic resonance imaging method provided by any of the above embodiments. Details not described in the embodiment of the magnetic resonance imaging apparatus can refer to the above embodiments of the magnetic resonance imaging method. Referring to FIG. 8, the apparatus can include a preliminary magnetic resonance image reconstruction module 410, a magnetic resonance image reconstruction network acquisition module 420, and a target magnetic resonance image obtaining module 430.

[0154] The preliminary magnetic resonance image reconstruction module 410 is configured to acquire k-space data of a target site to be subjected to magnetic resonance imaging, and reconstruct a preliminary magnetic resonance image based on the k-space data.

[0155] The magnetic resonance image reconstruction network acquisition module 420 is configured to acquire a magnetic resonance image reconstruction network previously built, wherein the magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolution layer constructed based on group theory and having rotational equivariance in a spatial domain.

[0156] The target magnetic resonance image obtaining module 430 is configured to input the preliminary magnetic resonance image into the magnetic resonance image reconstruction network, so as to perform image reconstruction by using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, to obtain a target magnetic resonance image.

[0157] Optionally, the magnetic resonance image reconstruction network further includes a time domain equivariant convolution layer having rotational equivariance in a time domain; and the target magnetic resonance image obtaining module 430 can include:

[0158] The target magnetic resonance image first obtaining submodule is configured to perform image reconstruction by using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer, and by using rotational symmetry of the preliminary magnetic resonance image in the time domain through the time domain equivariant convolution layer, for the spatial domain equivariant convolution layer and the time domain equivariant convolution layer in the magnetic resonance image reconstruction network, to obtain the target magnetic resonance image.

[0159] Optionally, the spatial domain equivariant convolution layer at least includes an input equivariant layer, and an input convolution kernel of the input equivariant layer is obtained by the following module:

[0160] The input convolution kernel obtaining module is configured to rotate a preset convolution kernel by using a first rotation operation subgroup in a preset rotation transformation group, to expand a convolution kernel quantity of the preset convolution kernel, to obtain the input convolution kernel.

[0161] The target magnetic resonance image obtaining module 430 can include:

[0162] The target magnetic resonance image second obtaining submodule is configured to utilize the rotation symmetry of the preliminary magnetic resonance image in the spatial domain to perform feature extraction on the preliminary magnetic resonance image by using an input convolution kernel of an input equivariant layer in the magnetic resonance image reconstruction network, to obtain a first layer feature map defined in a rotation transformation group, and to perform image reconstruction based on the first layer feature map to obtain the target magnetic resonance image.

[0163] On this basis, optionally, the magnetic resonance image reconstruction network further comprises at least one time domain equivariant convolution layer having rotation equivariance in the time domain; and the target magnetic resonance image second obtaining submodule can comprise:

[0164] The channel shifting unit is configured to, in a case where it is determined according to the rotation condition that each channel of the time domain convolution kernel needs to be shifted, shift each channel of the time domain convolution kernel according to the rotation condition and by using a preset non-rotation transformation subgroup, for the time domain convolution kernel of the time domain equivariant convolution layer adjacent to the input equivariant layer in the at least one time domain equivariant convolution layer.

[0165] The target magnetic resonance image obtaining unit is configured to perform convolution operation on the first layer feature map by using the shifted time domain convolution kernel to obtain a second layer feature map, and perform image reconstruction based on the second layer feature map to obtain the target magnetic resonance image.

[0166] On this basis, optionally, the spatial domain equivariant convolution layer further comprises at least one intermediate equivariant layer, and an intermediate convolution kernel of an intermediate equivariant layer adjacent to the time domain equivariant convolution layer in the at least one intermediate equivariant layer is obtained by using a second rotation operation subgroup in the rotation transformation group; and the target magnetic resonance image obtaining unit can comprise:

[0167] The channel shifting subunit is configured to, in a case where it is determined according to the rotation condition that each channel of the intermediate convolution kernel needs to be shifted, shift each channel of the intermediate convolution kernel according to the rotation condition and by using the non-rotation transformation subgroup.

[0168] The target magnetic resonance image obtaining subunit is configured to perform convolution operation on the second layer feature map by using the shifted intermediate convolution kernel to obtain a third layer feature map, and perform image reconstruction based on the third layer feature map to obtain the target magnetic resonance image.

[0169] On this basis, optionally, the spatial domain equivariant convolution layer further comprises an output equivariant layer, and the target magnetic resonance image obtaining subunit is configured to:

[0170] perform convolution operation on the second layer feature map by using the shifted intermediate convolution kernel to obtain a third layer feature map, and extract an end feature map by using the intermediate equivariant layer closest to the output equivariant layer in the at least one intermediate equivariant layer, wherein the end feature map is obtained on the basis of the third layer feature map.

[0171] The output isovar layer is processed to obtain a result feature map with a number of channels consistent with the preliminary magnetic resonance image, and the target magnetic resonance image is reconstructed based on the result feature map.

[0172] Optionally, in any of the above apparatuses, each convolution kernel in the magnetic resonance image reconstruction network is a linear combination of at least two parameterized bases based on Fourier expansion.

[0173] Optionally, the k-space data is undersampled k-space data, and the preliminary magnetic resonance image reconstruction module 410 can include:

[0174] The coil sensitivity map obtaining unit is configured to obtain a coil sensitivity map based on the undersampled k-space data;

[0175] The preliminary magnetic resonance image obtaining unit is configured to perform initial zero-padding reconstruction based on the coil sensitivity map and in combination with the undersampled k-space data to obtain a preliminary magnetic resonance image;

[0176] The target magnetic resonance image obtaining module 430 is configured to:

[0177] The preliminary magnetic resonance image and the coil sensitivity map are input into the magnetic resonance image reconstruction network to reconstruct the target magnetic resonance image by using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain isovar convolution layer in the magnetic resonance image reconstruction network and updating the data consistency of the coil sensitivity map through the magnetic resonance image reconstruction network.

[0178] Optionally, the target part is a heart, and the magnetic resonance imaging is a cardiac cine magnetic resonance imaging.

[0179] The magnetic resonance imaging apparatus provided by the embodiments of the present application can utilize the first rotation operation subgroup in the rotation transformation group to rotate the preset convolution kernel, thereby expanding the number of convolution kernels of the preset convolution kernel to obtain an input convolution kernel. The input convolution kernel can be understood as a convolution kernel prepared for a preliminary magnetic resonance image at different rotation angles, and the input convolution kernel can be used to extract features of the preliminary magnetic resonance image. Therefore, the rotational symmetry of the preliminary magnetic resonance image in the spatial domain can be effectively utilized, and the reconstruction quality of the magnetic resonance image is improved.

[0180] The magnetic resonance imaging apparatus provided by the embodiments of the present application can perform the magnetic resonance imaging method provided by any of the embodiments of the present application, and has the corresponding function modules and beneficial effects of the performing method.

[0181] In the embodiment of the magnetic resonance imaging apparatus, each unit and module included is only divided according to a functional logic, and as long as the corresponding function can be realized; in addition, the names of each functional unit are only for the convenience of mutual differentiation.

[0182] FIG. 9 shows a structural schematic diagram of an electronic device 10 that can be used to implement embodiments of the present application. The electronic device can represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular telephones, smart phones, wearable devices (e.g., headsets, glasses, watches, etc.), and other similar computing devices. The components shown in FIG. 9, their connections and relationships, and their functions, are shown as examples.

[0183] As shown in FIG. 9, the electronic device 10 includes at least one processor 11, and a memory, such as a Read Only Memory (ROM) 12, a Random Access Memory (RAM) 13, etc., which is communicatively connected to the at least one processor 11, wherein the memory stores a computer program that can be executed by the at least one processor. The processor 11 can perform various appropriate actions and processes according to the computer program stored in the Read Only Memory (ROM) 12 or loaded from the storage unit 18 into the Random Access Memory (RAM) 13. In the RAM 13, various programs and data required for the operation of the electronic device 10 can also be stored. The processor 11, the ROM 12, and the RAM 13 are connected to each other through a bus 14. An Input / Output (I / O) interface 15 is also connected to the bus 14.

[0184] A plurality of components in the electronic device 10 are connected to the I / O interface 15, including: an input unit 16, such as a keyboard, a mouse, etc.; an output unit 17, such as various types of displays, a loudspeaker, etc.; a storage unit 18, such as a magnetic disk, an optical disk, etc.; and a communication unit 19, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 19 allows the electronic device 10 to exchange information / data with other devices through a computer network, such as the Internet, and / or various telecommunication networks.

[0185] The processor 11 can be various general and / or special purpose processing components with processing and computing capabilities. Some examples of the processor 11 include a central processing unit (CPU), a graphics processing unit (GPU), various specialized artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, and the like. The processor 11 performs various methods and processes described above, such as a magnetic resonance imaging method.

[0186] In some embodiments, the magnetic resonance imaging method can be implemented as a computer program tangibly embodied in a computer readable storage medium, such as the storage unit 18. In some embodiments, part or all of the computer program can be loaded and / or installed onto the electronic device 10 via the ROM 12 and / or the communication unit 19. When the computer program is loaded onto the RAM 13 and executed by the processor 11, one or more steps of the magnetic resonance imaging method described above can be performed. Alternatively, in other embodiments, the processor 11 can be configured to perform the magnetic resonance imaging method by any other suitable means, such as by means of firmware.

[0187] Various implementations of the systems and techniques described above can be realized in digital electronic circuitry, integrated circuitry, a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), a system on chip (SOC), a complex programmable logic device (CPLD), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include implementation in one or more computer programs that are executable and / or interpretable on a programmable system including at least one programmable processor, which can be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device.

[0188] A computer program for implementing the methods of the present application can be written in any combination of one or more programming languages. The computer program can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the computer program, when executed by the processor of the machine, causes the machine to implement the functions / acts specified in the flow diagrams and / or block diagrams. The computer program can be executed entirely on a machine, partially on a machine, partially on a machine as a stand-alone software package, and partially on a remote machine or entirely on a remote machine or server.

[0189] In the context of the present application, a computer-readable storage medium can be a tangible medium that can contain or store computer programs for use by or in connection with an instruction execution system, apparatus, or device. The computer-readable storage medium can include an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. Alternatively, the computer-readable storage medium can be a machine-readable signal medium. Examples of a machine-readable storage medium can include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0190] To provide for interaction with a user, the systems and techniques described here can be implemented on an electronic device having a display device (e.g., a Cathode Ray Tube (CRT) or a Liquid Crystal Display (LCD) or a monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the electronic device. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form, including acoustic, speech, or tactile input.

[0191] The systems and techniques described herein can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a user computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the systems and techniques described herein, or any combination of such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (LAN), a wide area network (WAN), blockchain network, and the Internet.

[0192] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a host product in the cloud computing service system, to solve the defects of large management difficulty and weak business scalability in traditional physical host and VPS service.

[0193] The steps shown above in various forms of flow can be reordered, added to, or deleted from. For example, the steps described in the present application can be executed in parallel, can be executed sequentially, or can be executed in different orders, as long as the desired results of the present application can be achieved.

Claims

1. A magnetic resonance imaging method, comprising: acquiring k-space data of a target site to be subjected to magnetic resonance imaging, and reconstructing a preliminary magnetic resonance image based on the k-space data; obtaining a pre-built magnetic resonance image reconstruction network, wherein the magnetic resonance image reconstruction network at least comprises a spatial domain equivariant convolution layer constructed based on group theory and having rotational equivariance in a spatial domain; inputting the preliminary magnetic resonance image into the magnetic resonance image reconstruction network to perform image reconstruction using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, and obtaining a target magnetic resonance image.

2. The method of claim 1, wherein, The magnetic resonance image reconstruction network further comprises a time domain equivariant convolution layer having rotational equivariance in a time domain; the image reconstruction using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, and obtaining a target magnetic resonance image, comprises: for the spatial domain equivariant convolution layer and the time domain equivariant convolution layer in the magnetic resonance image reconstruction network, performing image reconstruction using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer, and using rotational symmetry of the preliminary magnetic resonance image in the time domain through the time domain equivariant convolution layer, and obtaining a target magnetic resonance image.

3. The method of claim 1, wherein, The spatial domain equivariant convolution layer at least comprises an input equivariant layer, and an input convolution kernel of the input equivariant layer is obtained by the following steps: using a first rotation operation subgroup in a preset rotation transformation group to rotate a preset convolution kernel to expand the number of convolution kernels of the preset convolution kernel, and obtaining the input convolution kernel; the image reconstruction using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, and obtaining a target magnetic resonance image, comprises: performing feature extraction on the preliminary magnetic resonance image using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the input convolution kernel of the input equivariant layer in the magnetic resonance image reconstruction network, obtaining a first layer feature map defined on the first rotation transformation group, and performing image reconstruction based on the first layer feature map to obtain a target magnetic resonance image.

4. The method of claim 3, wherein, The magnetic resonance image reconstruction network further comprises at least one time domain equivariant convolution layer having rotational equivariance in a time domain; the image reconstruction based on the first layer feature map to obtain a target magnetic resonance image, comprises: for a time domain convolution kernel of a time domain equivariant convolution layer adjacent to the input equivariant layer in the at least one time domain equivariant convolution layer, in a case where it is determined that each channel of the time domain convolution kernel needs to be shifted according to a rotation condition of the preliminary magnetic resonance image, shifting each channel of the time domain convolution kernel according to the rotation condition and using a preset non-rotation transformation subgroup; ​ The first layer feature map is convoluted by the shifted time domain convolution kernel to obtain a second layer feature map, and image reconstruction is performed based on the second layer feature map to obtain a target magnetic resonance image.

5. The method of claim 4, wherein, The spatial domain equivariant convolution layer further comprises at least one intermediate equivariant layer, and an intermediate convolution kernel of an intermediate equivariant layer adjacent to the time domain equivariant convolution layer is obtained by rotating using a second rotation operation subgroup in the rotation transformation group; The image reconstruction based on the second layer feature map to obtain a target magnetic resonance image comprises: In the case where it is determined according to the rotation condition that each channel of the intermediate convolution kernel needs to be shifted, each channel of the intermediate convolution kernel is shifted according to the rotation condition and using the non-rotation transformation subgroup; The second layer feature map is convoluted by the shifted intermediate convolution kernel to obtain a third layer feature map, and image reconstruction is performed based on the third layer feature map to obtain a target magnetic resonance image.

6. The method of claim 5, wherein, The spatial domain equivariant convolution layer further comprises an output equivariant layer, and the image reconstruction based on the third layer feature map to obtain a target magnetic resonance image comprises: An end feature map is extracted through the intermediate equivariant layer closest to the output equivariant layer in the at least one intermediate equivariant layer, wherein the end feature map is obtained based on the third layer feature map; The end feature map is processed through the output equivariant layer to obtain a result feature map with a channel number consistent with the preliminary magnetic resonance image, and a target magnetic resonance image is reconstructed based on the result feature map.

7. The method of any one of claims 3-6, wherein, Each convolution kernel in the magnetic resonance image reconstruction network is a linear combination based on at least two parameterized bases of Fourier expansion.

8. The method of claim 1, wherein, The k-space data is undersampled k-space data, and the reconstruction of a preliminary magnetic resonance image based on the k-space data comprises: Based on the undersampled k-space data, a coil sensitivity map is obtained; Based on the coil sensitivity map, initial zero-padding reconstruction is performed in combination with the undersampled k-space data to obtain a preliminary magnetic resonance image; The input of the preliminary magnetic resonance image into the magnetic resonance image reconstruction network to perform image reconstruction using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network to obtain a target magnetic resonance image comprises: The input of the preliminary magnetic resonance image and the coil sensitivity map into the magnetic resonance image reconstruction network to perform image reconstruction using the rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network and data consistency update of the coil sensitivity map through the magnetic resonance image reconstruction network to reconstruct a target magnetic resonance image.

9. The method of claim 1, wherein, The target site is a heart, and the magnetic resonance imaging is cardiac cine magnetic resonance imaging.

10. A magnetic resonance imaging apparatus, comprising: A preliminary magnetic resonance image reconstruction module is configured to acquire k-space data of a target region to be imaged by magnetic resonance imaging, and reconstruct a preliminary magnetic resonance image based on the k-space data; A magnetic resonance image reconstruction network acquisition module is configured to acquire a magnetic resonance image reconstruction network previously built, wherein the magnetic resonance image reconstruction network at least includes a spatial domain equivariant convolution layer constructed based on group theory and having rotational equivariance in a spatial domain; A target magnetic resonance image obtaining module is configured to input the preliminary magnetic resonance image into the magnetic resonance image reconstruction network, and perform image reconstruction by using rotational symmetry of the preliminary magnetic resonance image in the spatial domain through the spatial domain equivariant convolution layer in the magnetic resonance image reconstruction network, to obtain a target magnetic resonance image. 11.An electronic device, comprising: at least one processor; and a memory connected to the at least one processor in communication; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to make the at least one processor execute the magnetic resonance imaging method according to any one of claims 1-9. 12.A computer readable storage medium, the computer readable storage medium stores computer instructions for making a processor execute the magnetic resonance imaging method according to any one of claims 1-9. 13.A computer program product, the computer program product comprises a computer program, the computer program implements the magnetic resonance imaging method according to any one of claims 1-9 when executed by a processor.

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