Unsupervised federated learning method for magnetic resonance imaging

Abstract

The present invention relates to the field of image processing technology, and in particular to an unsupervised federated learning magnetic resonance imaging method, the method comprising: first, performing self-supervised training on a local model and updating the parameters of the local model; the local model includes multiple local client models participating in the federated learning; next, weighted aggregation is performed on the local models after the updated parameters to obtain a global model; then, based on the global model, the local model is personalized to obtain an internal personalized model; the internal personalized model is an interpolation between the local model of the local client, the personalized models of other clients, and the global client; finally, external clients are personalized; the external clients are external clients with invisible data distributions. The unsupervised federated learning magnetic resonance imaging method provided by the present invention can provide personalized models for internal and external clients that lack fully sampled reference data and have different data distributions.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of image processing technology, and in particular to an unsupervised federated learning magnetic resonance imaging method. Background Art

[0002] The principle of Magnetic Resonance Imaging (MRI) is as follows: when an external magnetic field is applied, radio frequency (RF) pulses of a specific frequency are used to excite protons in the tissue being measured. The protons absorb a certain amount of energy and resonate. When the RF pulse emission stops, the excited protons gradually release the absorbed energy in the form of scanning signals. The scanning signals are collected and processed using image reconstruction technology to obtain a scanned image of the tissue being measured.

[0003] The existing federated MRI reconstruction methods have the following main problems: (1) The problem of federated learning reconstruction methods relying on fully sampled reference data. Existing federated learning reconstruction methods all rely on a strong assumption: the local client data has fully sampled data as a reference value for model training. However, in reality, fully sampled data is almost impossible to obtain. (2) The performance of the global model in the local client is not necessarily optimal. In a real environment, since each local client has a specific scanner, scanning scheme and different data distribution related to different patient demographics, the global model is unlikely to be optimal on each individual local client. (3) The problem of external dataset offset. Federated learning methods often show excellent test performance when the test set data distribution is the same as the training set data distribution. However, when there is a large difference between the test set data distribution and the training set data distribution, the test performance of the model will drop sharply. Summary of the Invention

[0004] An embodiment of the present application provides an unsupervised federated learning magnetic resonance imaging method, which provides personalized models for internal and external clients that lack fully sampled reference data and have different data distributions.

[0005] To solve the above technical problems, an embodiment of the present application provides an unsupervised federated learning magnetic resonance imaging method, comprising: first, performing self-supervised training on a local model and updating the parameters of the local model; the local model includes multiple local client models participating in federated learning; next, performing weighted aggregation on the local models after parameter update to obtain a global model; then, based on the global model, personalizing the local model to obtain an internal personalized model; so the internal personalized model is an interpolation between the local model of the local client, the personalized models of other clients, and the global client; finally, personalizing the external client; the external client is an external client with an invisible data distribution.

[0006] In some exemplary embodiments, the self-supervised training of the local model and updating the parameters of the local model include: on any local model, using undersampled K-space data as model input data, performing data augmentation on the undersampled space data to obtain at least two K-space data; using the magnetic resonance images corresponding to any two K-space data as inputs of a first network and a second network, respectively, the first network and the second network being networks with the same structure but different parameters, and performing self-supervised training on the local model according to formula (1):

[0007]

[0008] in, and As shown in formula (2):

[0009]

[0010] In formula (2), k represents the local model, x i,k is the undersampled K-space data, x 1,k 、x 2,k Represents two K-space data, y 1,k 、y 2,k They represent the K-space data output by the first network and the second network respectively, and A represents the undersampling encoding matrix of the undersampling K-space data.

[0011] In some exemplary embodiments, the local models after parameter update are weighted and aggregated by formula (3) to obtain a global model:

[0012]

[0013] Among them, k represents the local model, t represents the communication round, Represents the parameters of the local model;

[0014] The global model is an optimized global model, which is optimized by formula (4):

[0015]

[0016] Among them, w g represents the optimal global model, f wg Indicates that the parameter is w g Model, n k represents the number of training samples for client k.

[0017] In some exemplary embodiments, the personalizing the local model based on the global model to obtain an internal personalized model includes: during a communication round of federated learning, treating the client's personalized model as an interpolation of the local optimal model of the local client and the personalized models of other clients to obtain an initial internal personalized model; and updating the parameters of the initial internal personalized model to obtain an internal personalized model.

[0018] In some exemplary embodiments, the initial internal personalized model is as shown in formula (5):

[0019]

[0020] in, represents the internal personalization model, t represents the communication round, and k represents the local client.

[0021] In some exemplary embodiments, the updating of the parameters of the initial internal personalized model includes: updating the mixed local gradient and global gradient; According to formula (5), the local optimal model of communication round t is shown in formula (6):

[0022]

[0023] After considering the mixed local gradient, the optimized personalized model of communication round t is shown in formula (7):

[0024]

[0025] in, represents the local optimal model, Represents an optimized personalized model.

[0026] In some exemplary embodiments, the external client is personalized using an unsupervised loss function; the unsupervised loss function is shown in formula (8):

[0027]

[0028] Among them, w g represents the optimal global model, f wg Indicates that the parameter is wg Model, n t Represents the number of communication rounds t.

[0029] In some exemplary embodiments, the unsupervised loss function is used for test data adaptation, including noise consistency loss, contrast consistency loss and data consistency loss; the external client is personalized through the unsupervised loss function, including: initializing the external client model as a fixed global model; adding Gaussian noise to the test image to generate an image with perturbation data; inputting the test image and the image with perturbation data into the first network and the second network respectively for image reconstruction to generate reconstructed data; performing noise consistency loss processing, contrast consistency loss processing and data consistency loss processing on the reconstructed data respectively to obtain an external-internal personalized model.

[0030] In some exemplary embodiments, the reconstructed data includes reconstructed data of a test image reconstructed in the first network, reconstructed data of an image with perturbation data reconstructed in the first network, reconstructed data of a test image reconstructed in the second network, and reconstructed data of an image with perturbation data reconstructed in the second network, respectively represented by y 1，test 、y 2，test , y′ 1，test , y′ 2，test express;

[0031] The noise consistency loss function is shown in formula (9):

[0032]

[0033] The contrast consistency loss function is shown in formula (10):

[0034]

[0035] The data consistency loss function is shown in formula (11):

[0036]

[0037] Among them, x test is the undersampled K-space data of the test image, x' test is the undersampled K-space data of the image with perturbation data, and A represents the undersampled encoding matrix of the undersampled K-space data.

[0038] In some exemplary embodiments, according to formula (9), formula (10), and formula (11), a total unsupervised loss function is obtained, as shown in formula (12):

[0039]

[0040] Among them, γ1 is the weight coefficient of contrast consistency loss, and γ2 is the weight coefficient of noise consistency loss.

[0041] The technical solution provided by the embodiments of the present application has at least the following advantages:

[0042] The present invention addresses the issues of personalization for internal and external clients in federated learning and the reliance of fully sampled reference data for network training in federated learning MRI reconstruction methods. The present invention proposes an unsupervised federated learning MRI imaging method with both internal and external personalization, including internal model personalization, external model personalization, and unsupervised learning methods for federated learning MRI image reconstruction. The advantages of the present invention lie in: The method framework performs different personalization processes for internal and external clients, achieving good reconstruction performance for both external and internal client data. Secondly, in the internal personalized model, the personalized model is considered an interpolation between the local model of the local client, the personalized models of other clients, and the global client. The personalized model only uses the parameters of other models and does not involve sharing of other information. Thirdly, in the external personalized model, the model updates the test model in an unsupervised manner, without accessing the local client's training data. The test adaptive model is completely independent of the training model and does not affect the model during the training phase. Finally, no fully sampled reference data is required during the model training phase. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] One or more embodiments are exemplarily described by the pictures in the corresponding drawings. These exemplifications do not constitute limitations on the embodiments. Unless otherwise stated, the pictures in the drawings do not constitute proportional limitations.

[0044] Figure 1 A flowchart of an unsupervised federated learning magnetic resonance imaging method provided in one embodiment of the present application;

[0045] Figure 2 A schematic diagram of personalizing a local model to obtain an internal personalized model according to an embodiment of the present application;

[0046] Figure 3 A schematic diagram of obtaining an external personalized model by personalizing an external client provided in an embodiment of the present application. DETAILED DESCRIPTION

[0047] As can be seen from the background technology, existing federated MRI reconstruction methods have the following three main problems: (1) The federated learning reconstruction method relies on fully sampled reference data. (2) The performance of the global model in the local client is not necessarily optimal. (3) The external dataset offset problem.

[0048] To address the above three problems, the present invention proposes a federated semi-supervised learning magnetic resonance image reconstruction method, which provides a unified framework and provides personalized models for internal and external clients that lack fully sampled reference data and have different data distributions.

[0049] Generally, federated learning is a decentralized method to jointly learn a global model for multiple clients, which not only alleviates the problem of insufficient data for a single client, but also effectively protects the data privacy of each client. However, since each local client has a specific scanner, scanning scheme, and different data distribution related to different patient demographics, the global model is unlikely to be optimal on each individual local client. Researchers in related technologies have all raised the issue of local model personalization. Among them, one related technology proposes to use a local batch normalization method to alleviate the problem of feature offset and personalize the local model. Another related technology proposes to divide the network into a basic network layer and a personalized network layer, where the basic part is aggregated using the FedAvg method, and the personalized network layer is only trained on local data and is not transferred to the global model for aggregation. However, these methods only consider the personalization of each local model within federated learning, and do not consider the model personalization of unseen data distribution outside federated learning.

[0050] There are currently three mainstream approaches to model personalization for unseen data distributions outside of federated learning. The first is domain generalization, which involves sharing additional frequency information between local clients to enhance the generalization of the global model to data from unseen data distributions. The second is domain adaptation, which involves learning about domain drift between a labeled source domain and an unlabeled target domain. The third is test-time adaptation, where related technologies design a self-supervised task related to the main task to update the model; another approach uses a pre-trained model to adapt to test data by updating the parameters of the batch normalization layer through entropy minimization. Furthermore, a related technique proposes considering both internal client personalization and external client personalization in the medical image segmentation problem. However, all of these methods are fully supervised during the training phase.

[0051] Based on this, the existing federated learning MRI reconstruction methods have the following technical problems: (1) The existing methods based on local model personalization cannot be generalized to the client of the federated learning external invisible data distribution. (2) The existing model personalization methods based on external invisible data distribution cannot be implemented in many practical scenarios. For example, the domain generalization method shares some frequency information, which may still lead to data privacy leakage; the unsupervised domain adaptation method requires the coexistence of test data and training data, which cannot be met in many practical situations; the test time adaptation method uses a pre-trained model to update the parameters of the batch normalization layer by entropy minimization to adapt to the test data, which is not suitable for reuse of the trained model. (3) All of the above federated learning methods require full sampling reference data during the training phase.

[0052] In order to solve the above technical problems, an embodiment of the present application provides an unsupervised federated learning magnetic resonance imaging method, comprising the following steps: first, performing self-supervised training on a local model and updating the parameters of the local model; the local model includes multiple local client models participating in federated learning; next, performing weighted aggregation on the local models after parameter update to obtain a global model; then, based on the global model, personalizing the local model to obtain an internal personalized model; the internal personalized model is an interpolation between the local model of the local client, the personalized models of other clients, and the global client; finally, personalizing the external client; the external client is an external client with invisible data distribution. This application provides an unsupervised federated learning magnetic resonance imaging method, performs different personalized designs for internal clients and external clients respectively, and provides personalized models for internal and external clients that lack fully sampled reference data and have different data distributions.

[0053] The following detailed description of the various embodiments of the present application is provided in conjunction with the accompanying drawings. However, those skilled in the art will appreciate that many technical details are provided in the various embodiments of the present application to facilitate a better understanding of the present application. However, even without these technical details and the various variations and modifications based on the following embodiments, the technical solutions claimed in the present application can still be implemented.

[0054] refer to Figure 1 , an embodiment of the present application provides an unsupervised federated learning magnetic resonance imaging method, comprising the following steps:

[0055] Step S1: perform self-supervisory training on the local model and update the parameters of the local model; the local model includes multiple local client models participating in federated learning.

[0056] Step S2: Perform weighted aggregation on the local models after parameter update to obtain a global model.

[0057] Step S3: Based on the global model, the local model is personalized to obtain an internal personalized model; the internal personalized model is an interpolation between the local model of the local client, the personalized models of other clients, and the global client.

[0058] Step S4: Perform personalized processing on the external client; the external client is an external client for which invisible data distribution is not available.

[0059] The present invention primarily addresses the personalization issues of internal and external clients in federated learning and the reliance of magnetic resonance imaging reconstruction methods in federated learning on fully sampled reference data for network training. Therefore, the present invention proposes an unsupervised federated magnetic resonance imaging reconstruction method with both internal and external personalization. The method primarily comprises: internal model personalization and external model personalization in federated learning magnetic resonance imaging reconstruction, as well as an unsupervised learning method. The unsupervised federated learning magnetic resonance imaging method provided by the present invention can provide personalized models for internal and external clients that lack fully sampled reference data and have different data distributions.

[0060] The unsupervised federated learning magnetic resonance imaging method provided by the present invention is described in detail below.

[0061] In some embodiments, in step S1, the local model is self-supervised trained to update the parameters of the local model, including: on any local model, using undersampled K-space data as model input data, performing data augmentation on the undersampled space data to obtain at least two K-space data; using the magnetic resonance images corresponding to any two K-space data as inputs of a first network and a second network, respectively, the first network and the second network being networks with the same structure but different parameters, and performing self-supervised training on the local model according to formula (1):

[0062]

[0063] in, and As shown in formula (2):

[0064]

[0065] In formula (2), k represents the local model, x i,k is the undersampled K-space data, x 1,k 、x 2,k Represents two K-space data, y 1,k 、y 2,k They represent the K-space data output by the first network and the second network respectively, and A represents the undersampling encoding matrix of the undersampling K-space data.

[0066] It should be noted that formula (2) is illustrated by an example in which data augmentation processing is performed on undersampled spatial data to obtain two K-space data. The following is a detailed explanation of an embodiment in which data augmentation processing is performed on undersampled spatial data to obtain two K-space data.

[0067] Specifically, step S1 is mainly a self-supervised training process for the local model. On any local model k, with undersampled K-space data x i,k As the model input data, the undersampled K-space data x i,k Perform data augmentation processing to obtain K space data x 1,k and x 2,k , x 1,k and x 2,k The corresponding magnetic resonance images are used as inputs of the first network (network 1) and the second network (network 2), y 1,k and y 2,k Represent the K-space data output by network 1 and network 2 respectively. The self-supervised loss function of the model is shown in formula (1), where and The function is shown in formula (2).

[0068] It should be noted that A in formula (2) represents the undersampled K-space data x i,k The first and second networks have the same structure but different parameters, which can be MoDL. This framework mainly solves the problem that the federated learning training phase relies on fully sampled reference data for supervision.

[0069] In some embodiments, step S2 is to perform weighted aggregation on the local models after parameter update using formula (3) to obtain a global model:

[0070]

[0071] Among them, k represents the local model, t represents the communication round, Represents the parameters of the local model;

[0072] The global model is an optimized global model, which is optimized by formula (4):

[0073]

[0074] Among them, w g represents the optimal global model, f wg Indicates that the parameter is w g Model, n k represents the number of training samples for client k.

[0075] Step S2 is mainly the aggregation of the federated learning model. Figure 2 A schematic diagram of the internal personalization model is shown, Figure 2 As shown, in a communication round t of federated learning, each local model (Global model) k updates the local model parameters after E local training The global model then performs weighted aggregation on all local models to obtain the global model, as shown in formula (3). The goal of federated learning is to find the optimal global model w by solving the overall empirical risk minimization problem. g In fully supervised federated learning, the objective function is shown in formula (4). The global model is optimized by formula (4) to obtain the optimal global model w g .

[0076] In some embodiments, in step S3, the local model is personalized based on the global model to obtain an internal personalized model, including: during a communication round of federated learning, the personalized model of the client is regarded as an interpolation of the local optimal model of the local client and the personalized models of other clients to obtain an initial internal personalized model; and the parameters of the initial internal personalized model are updated to obtain the internal personalized model.

[0077] In some embodiments, the initial internal personalized model in step S3 is as shown in formula (5):

[0078]

[0079] in, represents the internal personalization model, t represents the communication round, and k represents the local client.

[0080] In some embodiments, updating the parameters of the initial internal personalized model includes updating a mixed local gradient and a global gradient.

[0081] First, let Then, according to formula (5), the local optimal model of communication round t is shown in formula (6):

[0082]

[0083] After considering the mixed local gradient, the optimized personalized model of communication round t is shown in formula (7):

[0084]

[0085] in, represents the local optimal model, Represents an optimized personalized model.

[0086] Step S3 is mainly to design the framework of the internal personalized model, such as Figure 2 As shown, Inside client represents the internal personalized model. Due to the statistical heterogeneity of local client data, the performance of the global model of federated learning on the local client is not necessarily optimal. Therefore, the present invention proposes a personalized federated learning optimization framework for unsupervised MRI reconstruction, which is mainly aimed at the personalization of the local model. Based on the aggregation of the federated learning model in step S2, the present invention designs an internal personalized model, which is the internal personalized model that is obtained by combining the desired internal personalized model with the local personalized model. It is considered as an interpolation between the local model of local client k, the personalized models of other clients, and the global client.

[0087] Specifically, first, at communication round t, the personalized model of client k is regarded as the interpolation of the local optimal model of local client k and the personalized models of other clients to obtain the initial internal personalized model, which is shown in formula (5). Considering that for local model training, the local model is either updated with local gradients or updated with global gradients, the local model is equivalent to the interpolation of the local model of non-federated learning and the global model of federated learning. Therefore, in order to further increase the parameter space of the model, the present invention adjusts the parameter update of the personalized model to a mixed local gradient and global gradient update. Therefore, let According to formula (5), the local optimal model of communication round t It can be expressed as formula (6). After considering the mixed gradient, the optimized personalized model of communication round t It can be expressed as formula (7). In formula (7), when When , formula (7) degenerates into the aggregation strategy of FedAvg.

[0088] In some embodiments, in step S4, the external client is personalized using an unsupervised loss function; the unsupervised loss function is shown in formula (8):

[0089]

[0090] Among them, w g represents the optimal global model, f wg Indicates that the parameter is w g Model, n t Represents the number of communication rounds t.

[0091] It should be noted that step S4 is mainly about designing the framework of the external personalized model. For external clients with unseen data distribution, the present invention proposes a test time adaptive method based on unsupervised magnetic resonance reconstruction. The unsupervised loss function in formula (8) is used to personalize the external client, mainly to solve the problem of external client performance optimization.

[0092] In some embodiments, the unsupervised loss function is used for test data adaptation, including noise consistency loss, contrast consistency loss and data consistency loss; the external client is personalized through the unsupervised loss function, including: initializing the external client model to a fixed global model; adding Gaussian noise to the test image to generate an image with perturbation data; inputting the test image and the image with perturbation data into the first network and the second network respectively for image reconstruction to generate reconstructed data; performing noise consistency loss processing, contrast consistency loss processing and data consistency loss processing on the reconstructed data respectively to obtain an external-internal personalized model.

[0093] In some embodiments, the reconstructed data includes the reconstructed data of the test image reconstructed in the first network, the reconstructed data of the image with perturbation data reconstructed in the first network, the reconstructed data of the test image reconstructed in the second network, and the reconstructed data of the image with perturbation data reconstructed in the second network, respectively. 1，test 、y 2，test , y′ 1，test , y′ 2，test express;

[0094] The noise consistency loss function is shown in formula (9):

[0095]

[0096] The contrast consistency loss function is shown in formula (10):

[0097]

[0098] The data consistency loss function is shown in formula (11):

[0099]

[0100] Among them, x test is the undersampled K-space data of the test image, x' test is the undersampled K-space data of the image with perturbation data, and A represents the undersampled encoding matrix of the undersampled K-space data.

[0101] It should be noted that since the test data is unlabeled, the present invention designs an unsupervised loss function for test data adaptation, including noise consistency loss, contrast consistency loss, and data consistency loss. Specifically, the personalized model is initialized to a fixed global model. In order to increase the robustness of the personalized model, for a given test image x test Then add Gaussian noise to generate perturbation data x' test . Figure 3 A schematic diagram of an external personalization model is shown, such as Figure 3 As shown, Outside client represents the external personalized model, x test and x' test Input the first network (network 1) and the second network (network 2) respectively for image reconstruction, and generate reconstruction data y 1，test 、y 2，test , y′ 1，test , y′ 2，test .

[0102] In order to make the reconstructed data of network 1 and network 2 consistent, the contrast consistency loss is designed as formula (10). In order to maintain the data consistency between the K-space sampling points in the reconstructed data and the input data, the data consistency loss is designed as formula (11).

[0103] In some embodiments, according to formula (9), formula (10), and formula (11), the total unsupervised loss function is obtained, as shown in formula (12):

[0104]

[0105] Among them, γ1 is the weight coefficient of contrast consistency loss, and γ2 is the weight coefficient of noise consistency loss.

[0106] It should be noted that the entire external model personalization process in step S4 is performed in an unsupervised manner, which does not affect the model in the training phase.

[0107] In summary, the present invention proposes an unsupervised federated magnetic resonance image reconstruction method with both internal and external personalization. Different personalization designs are performed on the internal and external clients, achieving good reconstruction performance for both external and internal client data. The present invention not only proposes an unsupervised federated learning magnetic resonance imaging method, but also proposes an internal model personalization method and an external model personalization method. A test-time adaptive unsupervised loss function is designed, allowing the entire external model personalization process to be performed in an unsupervised manner without affecting the model during the training phase.

[0108] In summary, compared with the existing federated learning magnetic resonance image reconstruction technology, the advantages of the present invention are:

[0109] (1) Unsupervised reconstruction of federated learning magnetic resonance reconstruction is achieved.

[0110] (2) Under a unified framework, internal model personalization and external model personalization in federated learning MRI reconstruction are realized.

[0111] (3) The internal personalized model adopts the interpolation form of multiple models, which increases the parameter space of the model and makes the personalized model have better performance.

[0112] (4) The external personalized model is completely independent of the model's testing phase and does not require the simultaneous presence of test data and training data.

[0113] Based on the above technical solutions, the embodiments of the present application primarily address the issues of personalization of internal and external clients in federated learning, as well as the reliance of federated learning MRI reconstruction methods on fully sampled reference data for network training. A method for unsupervised federated learning MRI imaging with both internal and external personalization is proposed, comprising: internal model personalization, external model personalization, and unsupervised learning methods for federated learning MRI image reconstruction. The advantages of the present invention lie in: the method framework performs different personalization processes on internal and external clients, achieving good reconstruction performance for both external and internal client data. Secondly, in the internal personalized model, the personalized model is considered an interpolation between the local model of the local client, the personalized models of other clients, and the global client. The personalized model only uses the parameters of other models and does not involve sharing of other information. Thirdly, in the external personalized model, the model updates the test model in an unsupervised manner, without accessing the local client's training data. The test adaptive model is completely independent of the training model and does not affect the model during the training phase. Finally, no fully sampled reference data is required during the model training phase.

[0114] Those skilled in the art will appreciate that the above-described embodiments are specific examples for implementing the present application, and that in actual applications, various changes in form and detail may be made thereto without departing from the spirit and scope of the present application. Any person skilled in the art may make changes and modifications without departing from the spirit and scope of the present application. Therefore, the scope of protection of the present application shall be subject to the scope defined in the claims.

Claims

1. An unsupervised federated learning magnetic resonance imaging method, characterized in that: include: Performing self-supervised training on a local model and updating parameters of the local model; the local model includes multiple local client models participating in federated learning; Perform weighted aggregation on the local models after parameter update to obtain the global model; Based on the global model, the local model is personalized to obtain an internal personalized model; the internal personalized model is an interpolation between the local model of the local client, the personalized models of other clients, and the global client; Personalize external clients; The external client is an external client for invisible data distribution; The personalizing the local model based on the global model to obtain an internal personalized model includes: During a communication round of federated learning, the client's personalized model is regarded as the interpolation of the local optimal model of the local client and the personalized models of other clients to obtain the initial internal personalized model; Updating parameters of the initial internal personalized model to obtain an internal personalized model; Personalize external clients through unsupervised loss functions; The unsupervised loss function is shown in formula (8): Among them, w g represents the optimal global model, f wg Indicates that the parameter is w g Model, n t represents the number of communication rounds t, Represents the network input data of client i in communication round t, function represents the global model loss function at communication round t.

2. The unsupervised federated learning magnetic resonance imaging method according to claim 1, characterized in that The self-supervised training of the local model and updating the parameters of the local model include: On any local model, using undersampled K-space data as model input data, performing data augmentation on the undersampled K-space data to obtain at least two K-space data; The magnetic resonance images corresponding to any two K-space data are used as the input of the first network and the second network respectively. The first network and the second network have the same structure but different parameters. The local model is self-supervised trained using formula (1): in, is the sum of the loss functions between the output data and input data of the first network and the second network, is the loss function between the output data of the first network and the output data of the second network, and α is the balance weight between the two loss functions; and As shown in formula (2): In formula (2), k represents the local model, x i,k is the undersampled K-space data, y 1,k 、y 2,k They represent the K-space data output by the first network and the second network respectively, A represents the undersampling encoding matrix of the undersampling K-space data, and I represents the all-1 matrix.

3. The unsupervised federated learning magnetic resonance imaging method according to claim 1, wherein: The local models after parameter update are weighted and aggregated using formula (3) to obtain the global model: Among them, k represents the local model, t represents the communication round, represents the local model weight of client k in communication round t; K represents the total number of clients, p k represents the weight aggregation coefficient of client k; The global model is an optimized global model, which is optimized by formula (4): Among them, w g represents the optimal global model, f wg Indicates that the parameter is w g Model, n k represents the number of training samples of client k, K represents the total number of clients, represents the input image of client k in fully supervised federated learning, represents the reference image of client k in fully supervised federated learning, function represents the loss function of client k in fully supervised federated learning.

4. The unsupervised federated learning magnetic resonance imaging method according to claim 1, wherein: The initial internal personalized model is shown in formula (5): in, represents the personalized model of client k in communication round t, t represents the communication round, k represents the local client, K represents the total number of clients, β represents the weight coefficient for balancing the local optimal model and the personalized models of other clients, represents the local optimal model of client k in communication round t, represents the sum of personalized models of all clients except client k.

5. The unsupervised federated learning magnetic resonance imaging method according to claim 4, characterized in that Updating parameters of the initial internal personalized model, including: updating a mixed local gradient and a global gradient; make According to formula (5), the local optimal model of communication round t is shown in formula (6): After considering the mixed local gradient, the optimized personalized model of communication round t is shown in formula (7): in, represents the local optimal model of client k in communication round t, represents the personalized model of client k in communication round t, β represents the weight coefficient for balancing the local optimal model and the personalized models of other clients in Formula 2, K represents the total number of clients, μ represents the weight coefficient for balancing the local gradient and the global gradient, represents the local gradient of client k in communication round t-1, represents the global aggregate gradient, σ represents the gradient descent parameter, represents the gradient of each training step.

6. The unsupervised federated learning magnetic resonance imaging method according to claim 1, characterized in that The unsupervised loss function is used to test data adaptation, including noise consistency loss, contrast consistency loss and data consistency loss; Personalization for external clients via unsupervised loss functions, including: Initialize the external client model to a fixed global model; Add Gaussian noise to the test image to generate an image with perturbed data; Inputting the test image and the image with the disturbance data into the first network and the second network respectively for image reconstruction to generate reconstructed data; The reconstructed data are subjected to noise consistency loss processing, contrast consistency loss processing and data consistency loss processing respectively to obtain an external and internal personalized model.

7. The unsupervised federated learning magnetic resonance imaging method according to claim 6, characterized in that The reconstructed data includes the reconstructed data of the test image reconstructed in the first network, the reconstructed data of the image with perturbation data reconstructed in the first network, the reconstructed data of the test image reconstructed in the second network, and the reconstructed data of the image with perturbation data reconstructed in the second network, respectively represented by y 1，test 、y 2,test , y′ 1,test , y′ 2，test express; The noise consistency loss function is shown in formula (9): The contrast consistency loss function is shown in formula (10): The data consistency loss function is shown in formula (11): Among them, x test is the undersampled K-space data of the test image, A represents the undersampled encoding matrix of the undersampled K-space data, and I represents the all-1 matrix.

8. The unsupervised federated learning magnetic resonance imaging method according to claim 7, characterized in that: According to formula (9), formula (10), and formula (11), the total unsupervised loss function is obtained, as shown in formula (12): Among them, γ1 is the weight coefficient of contrast consistency loss, and γ2 is the weight coefficient of noise consistency loss.

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