Super-resolution reconstruction method of prostate MRI based on frequency-domain-aware state-space model

Abstract

The present invention discloses a prostate MRI super-resolution reconstruction method based on a frequency domain perception state space model, relates to the field of medical image processing technology, and is characterized in that it comprises the following steps: S1: image preprocessing is performed on the patient's prostate MRI, and a low-resolution MRI image is obtained by downsampling operation; S2: a space-frequency domain Mamba module is constructed based on spatial and frequency domain information, and the spatial information and frequency domain information of the MRI image are extracted and fused; S3: the low-resolution image features obtained in the S1 are input into a feature extraction encoder and decoder composed of multiple cascaded SFMambas, and multi-level semantic features of the image are extracted to reconstruct a high-resolution MRI image. The technical problem to be solved by the present invention is to provide a prostate MRI super-resolution reconstruction method based on a frequency domain perception state space model, so as to facilitate the realization of prostate MRI super-resolution reconstruction.

Description

Technical Field

[0001] The present invention relates to the technical field of medical image processing, and in particular to a prostate MRI super-resolution reconstruction method based on a frequency domain perception state space model. Background Art

[0002] The prostate MRI super-resolution reconstruction task based on deep learning has the following challenges:

[0003] (1) Low efficiency of MRI image super-resolution reconstruction algorithm: Traditional CNN-based super-resolution reconstruction methods capture the multi-level semantic features of MRI images through different receptive fields, while ignoring the global dependency information of the image. Although the algorithm based on the Transformer architecture can capture the global feature information of the image, its computational complexity is too high, resulting in the model's low efficiency in image super-resolution reconstruction, thus limiting the model's application in clinical settings.

[0004] (2) Low accuracy of MRI image super-resolution algorithm: Although the algorithm based on the state-space model solves the problem of low model efficiency, its traditional scanning method is limited to the spatial information of the image and ignores the frequency domain information of the image. Therefore, its accuracy is affected in the process of image semantic feature extraction. Especially in medical image processing, its frequency domain information is more important for tissue location identification and disease diagnosis. The low accuracy of image semantic feature representation directly leads to poor super-resolution reconstruction effect, which affects its application in clinical practice.

[0005] Therefore, the key to super-resolution reconstruction of medical images based on deep learning is to accurately learn the spatial and frequency domain characteristics of the image, build a state-space model based on frequency domain perception, and design a reasonable model framework according to specific application scenarios and data characteristics. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a prostate MRI super-resolution reconstruction method based on a frequency domain perception state space model, so as to facilitate the realization of prostate MRI super-resolution reconstruction.

[0007] The present invention adopts the following technical solutions to achieve the invention objectives:

[0008] The method for super-resolution reconstruction of prostate MRI based on frequency domain perception state space model is characterized by comprising the following steps:

[0009] S1: Preprocess the patient's prostate MRI image and obtain the patient's low-resolution MRI image through downsampling operation;

[0010] S2: Based on the spatial and frequency domain information, a spatial-frequency Mamba module is constructed to extract and fuse the spatial and frequency domain information of low-resolution MRI images;

[0011] S3: inputting the low-resolution MRI image features obtained in S1 into a feature extraction encoder and decoder composed of multiple cascaded space-frequency domain Mamba modules to extract multi-level semantic features of the image and reconstruct a high-resolution MRI image;

[0012] S4: Introduce a hybrid loss function optimization objective, repeatedly iterate the encoder and decoder processes in S3, optimize the model, and reconstruct the low-resolution MRI image into a high-resolution MRI image.

[0013] As a further limitation of the present technical solution, the processing step of S1 includes:

[0014] S11: preprocessing operations of resizing and standardizing pixel intensity values ​​of MRI images of patients with prostate diseases;

[0015] S12: The preprocessed MRI image is downsampled using bicubic interpolation to reconstruct the high-resolution MRI image into a low-resolution MRI image. The low-resolution MRI image features are represented as , its input space can be expressed as , where R represents the three-dimensional space defined, and Represent the length and width of the image respectively. The number of channels representing images and features is 3.

[0016] As a further limitation of the present technical solution, the processing step of S2 includes:

[0017] S21: Construct a space-frequency domain Mamba module based on spatial and frequency domain information. First, perform linear mapping and convolution operations on the input features of the module. Let the input and output features of the space-frequency domain Mamba module be represented as and , first through a linear layer and a layer Convolutional layer, which takes input features Mapping , the process can be formalized as:

[0018] (1)

[0019] in: express 1×1 Convolution operation;

[0020] Represents a linear operation;

[0021] S22: Input the feature map output in S21 into the spatial Mamba branch and the frequency domain Mamba branch respectively, and extract the spatial semantic features of the image from two different dimensions and frequency domain semantic features ;

[0022] In the space Mamba branch, the sequence Perform DWConv operation, SiLU activation function conversion, spatial scanning and standardization, where DWConv represents depth-separable convolution, and the spatial scanning strategy uses VMamba scanning mechanism to extract features from the image in both horizontal and vertical directions. The process is expressed as:

[0023] (2)

[0024] in: , , and They represent normalization, 2D scanning, SiLU activation function, and depthwise separable convolution operations respectively;

[0025] In the frequency domain Mamba branch, the feature map output in S21 is transformed into It is decomposed into low-frequency sub-band and high-frequency sub-band features, and then DWConv and SiLU activation function operations are performed to obtain the feature representation of the hidden state space. Finally, the semantic features of the frequency domain Mamba branch are reconstructed and output through the inverse NSST process. In terms of scanning strategy, in order to adapt to the sub-band information characteristics from low to high of the NSST algorithm, a sequential scanning strategy from low frequency to high frequency is introduced. In the scanning direction, horizontal, vertical and flip scanning in two directions are used to successively obtain the low-frequency and high-frequency semantic information of the image. The branch operation process can be formalized as follows:

[0026] (3)

[0027] (4)

[0028] in: , , and They represent frequency domain features, frequency domain scanning strategy, non-subsampled shearlet transform and its inverse operation respectively;

[0029] S23: The S21 After the linear layer, the SiLU activation function is operated, and then the semantic features output by the two branches in S22 are respectively and Perform element-by-element multiplication, and finally connect the semantic features of the two branches in series according to the channel to output the semantic features that combine the image space and frequency domain information. , its mathematical form can be expressed as:

[0030] (5)

[0031] in: represents element-wise product;

[0032] Represents a concatenation operation.

[0033] So far, a spatial-frequency Mamba module (SFMamba) based on spatial and frequency domain information was constructed to extract and fuse the spatial and frequency domain information of MRI images.

[0034] As a further limitation of the present technical solution, the processing step of S3 includes:

[0035] S31: First use The convolution operation transforms the low-resolution MRI image Mapping from input space to initial features ,in, Represents the number of channels of the image and features, and then Alternately perform spatial-frequency domain Mamba module operations and downsampling operations to extract semantic features of different depths of the image from both spatial and frequency domain dimensions , the process can be formalized as:

[0036] (6)

[0037] in: represents the encoder;

[0038] represents the downsampling operation;

[0039] Indicates the encoder SFMamba operation, ;

[0040] S32: The semantic features of the low-resolution MRI image extracted in S31 are reconstructed through a feature decoder. The feature decoder is symmetrical with the feature encoder in structure. Space-frequency domain Mamba module operations and upsampling operations are performed alternately at corresponding positions. At the same time, features in the encoder are fused through jump links to gradually improve the resolution of the feature map, thereby obtaining a semantic feature map of the decoder. , its formula is expressed as:

[0041] (7)

[0042] in: Indicates a serial operation;

[0043] Represents an upsampling operation;

[0044] Indicates execution of the decoder Space-frequency domain Mamba modules, ;

[0045] Finally, through a The convolutional layer converts the semantic features output by the last spatial-frequency domain Mamba module of the decoder into Mapping to residual image Then, the low-resolution MRI images Add it element by element to reconstruct high-resolution MRI images , its formula is expressed as:

[0046] (8)

[0047] in: express Convolution operation.

[0048] As a further limitation of the present technical solution, the processing step of S4 includes:

[0049] S41: Introduce a mixed loss function to optimize the training process of the algorithm, which includes spatial loss , low frequency loss and high frequency loss , and finally the loss function of the prostate MRI super-resolution reconstruction model based on the frequency domain perception state space model is:

[0050] (9)

[0051] in: , and They represent trade-off hyperparameters respectively;

[0052] for and , this algorithm uses the mean absolute error as the loss function, and its formula can be expressed as:

[0053] (10)

[0054] (11)

[0055] in: , Represent the reconstructed image and the real image respectively;

[0056] and Respectively represent the low-frequency sub-band and high-frequency sub-band features extracted from the NSST module;

[0057] represents the L1 norm;

[0058] Similarly, for , the algorithm combines the mean absolute error loss and the structural similarity coefficient loss. The structural similarity coefficient loss is similar to the human visual system and can keenly perceive local structural changes. Its formula is expressed as:

[0059] (12)

[0060] in: and is the pixel mean;

[0061] and is the variance;

[0062] is the covariance;

[0063] represents the mean absolute error loss;

[0064] Represents the structural similarity coefficient loss.

[0065] As a further limitation of the technical solution, it includes a data preprocessing module, a space-frequency domain Mamba (SFMamba) module, an encoder-decoder (Encoder-Decoder) module and an iterative optimization loss module.

[0066] Data preprocessing module: responsible for resizing and standardizing the pixel intensity values ​​of the original MRI images of prostate disease patients included in the clinical diagnosis and treatment process, and then reconstructing the low-resolution MRI images of the prostate through downsampling operations;

[0067] Spatial-Frequency Domain Mamba (SFMamba) module: Through the spatial Mamba branch based on the VMamba architecture and the frequency domain Mamba branch based on the non-subsampled truncated wavelet transform (NSST), the deep semantic features of low-resolution MRI images are extracted and fused from different dimensions, the image spatial information and frequency domain information are incorporated, and the image semantic feature representation is learned efficiently and accurately, solving the problems of low efficiency and low accuracy of medical image super-resolution reconstruction algorithms.

[0068] Encoder-Decoder module: By building a symmetric encoder-decoder architecture, based on multi-stage cascaded SFMamba modules and symmetrical downsampling and upsampling operations, the algorithm complexity is further reduced, and more fine-grained image semantic information is efficiently extracted, solving the problem of low computational efficiency of medical image super-resolution reconstruction algorithms.

[0069] Iterative Optimization Loss Module: It is responsible for using the proposed hybrid loss function to iterate and optimize the algorithm multiple times, enhancing the model's ability to efficiently and accurately learn the semantic feature representation of medical images, thereby comprehensively improving the algorithm's super-resolution reconstruction performance.

[0070] Compared with the prior art, the advantages and positive effects of the present invention are:

[0071] The present invention introduces the visual Mamba architecture to efficiently learn the semantic features of medical images, and improves the efficiency of the model in image super-resolution reconstruction; based on the non-subsampled truncated wave transform algorithm, frequency domain information features such as low-frequency and high-frequency subbands in medical images are extracted, and the image frequency domain information is incorporated into the semantic feature representation, the dimension of the image feature representation is increased, and the accuracy of the model learning the semantic features of medical images is comprehensively improved. The above method solves two challenges in the image feature extraction process of most models in the current medical image super-resolution reconstruction task: the high computational complexity of the medical image analysis model and the low accuracy of the medical image semantic feature representation. The present invention introduces a symmetric encoder-decoder framework, based on multiple cascaded space-frequency domain Mamba and corresponding downsampling and upsampling operations, to further improve the model calculation efficiency and solve the problem of low efficiency in the medical image super-resolution reconstruction task. A mixed loss function is introduced to optimize the model training process from three perspectives: spatial loss, low-frequency loss and high-frequency loss, comprehensively improve the accuracy of the model in extracting image semantic features, solve the problem of low accuracy of semantic feature learning in the current medical image super-resolution reconstruction task, and improve the reliability of the algorithm in clinical diagnosis and treatment. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is a schematic diagram of the process of the present invention.

[0073] Figure 2 It is a schematic diagram of the present invention.

[0074] Figure 3 Schematic diagram of the space-frequency domain Mamba module (SFMamba) constructed for the present invention.

[0075] Figure 4 Schematic diagram of the spatial scanning strategy and frequency domain scanning strategy of the present invention, wherein: Figure 4 (a) is a schematic diagram of the spatial scanning strategy; Figure 4 (b) Schematic diagram of the frequency domain scanning strategy. DETAILED DESCRIPTION

[0076] A specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific implementation.

[0077] The present invention preprocesses the collected T2-weighted sequence MRI images of patients with prostate diseases, and uses the bi-tricubic interpolation method to downsample the high-resolution MRI images and reconstruct them into low-resolution MRI images as model input. The SFMamba feature extraction basic module is constructed to capture the spatial semantic features of the image through the space-based visual Mamba branch. At the same time, the low-frequency and high-frequency sub-band features of the image are extracted based on the non-subsampled shearlet transform (NSST) algorithm, and the semantic features based on the two dimensions of space and frequency domain are integrated. Based on multiple cascaded SFMamba modules and downsampling operations to encode the semantic features of the image at different depths, multiple SFMamba modules and upsampling operations are symmetrically cascaded to decode the semantic features of the input image. After multiple rounds of iterative training, the proposed hybrid loss function is used to optimize the model from three perspectives of space, low-frequency and high-frequency information to reconstruct the high-resolution MRI image of the prostate.

[0078] The present invention comprises the following steps:

[0079] S1: Perform image preprocessing on the patient's prostate MRI and obtain a low-resolution MRI image through downsampling operation.

[0080] The processing steps of S1 include:

[0081] S11: performing preprocessing operations such as resizing and standardizing pixel intensity values ​​on the MRI images of patients with prostate diseases;

[0082] The MRI resolution of the clinically enrolled prostate disease patients was adjusted to 512×512, and the pixel intensity value was standardized to [0,1].

[0083] S12: The preprocessed MRI image is downsampled using bicubic interpolation to reconstruct the high-resolution MRI image into a low-resolution MRI image. The low-resolution MRI image features are represented as , its input space can be expressed as , where R represents the three-dimensional space defined, and Represent the length and width of the image respectively, The number of channels representing images and features is 3.

[0084] S2: A spatial-frequency Mamba module (SFMamba) is constructed based on the spatial and frequency domain information to extract and fuse the spatial and frequency domain information of MRI images.

[0085] like Figure 3 As shown in Figure 1, we construct a SFMamba basic module consisting of spatial Mamba and frequency domain Mamba to obtain multi-level semantic information of the image from two dimensions: spatial and frequency domain. Among them, the two sub-modules of spatial Mamba and frequency domain Mamba adopt different scanning strategies (such as Figure 4 As shown in Figure 3), to achieve the extraction of multi-level semantic features.

[0086] The processing steps of S2 include:

[0087] S21: Construct a space-frequency Mamba module based on spatial and frequency domain information. First, perform linear mapping and convolution operations on the input features of the module. Let the input and output features of the space-frequency Mamba module be represented as and , first through a linear layer and a layer Convolutional layer, which takes input features Mapping , the process can be formalized as:

[0088] (1)

[0089] in: express 1×1 Convolution operation;

[0090] Represents a linear operation;

[0091] S22: Input the feature map output in S21 into the spatial Mamba branch and the frequency domain Mamba branch respectively, and extract the spatial semantic features of the image from two different dimensions and frequency domain semantic features ;

[0092] In the space Mamba branch, the sequence Perform DWConv operation, SiLU activation function conversion, spatial scanning and standardization, where DWConv represents depth-separable convolution, and the spatial scanning strategy uses VMamba scanning mechanism to extract features from the image in both horizontal and vertical directions. The process is expressed as:

[0093] (2)

[0094] in: , , and They represent normalization, 2D scanning, SiLU activation function, and depthwise separable convolution operations respectively;

[0095] In the frequency domain Mamba branch, the feature map output in S21 is transformed into It is decomposed into low-frequency sub-band and high-frequency sub-band features, and then DWConv and SiLU activation function operations are performed to obtain the feature representation of the hidden state space. Finally, the semantic features of the frequency domain Mamba branch are reconstructed and output through the inverse NSST process. In terms of scanning strategy, in order to adapt to the sub-band information characteristics from low to high of the NSST algorithm, a sequential scanning strategy from low frequency to high frequency is introduced. In the scanning direction, horizontal, vertical and flip scanning in two directions are used to successively obtain the low-frequency and high-frequency semantic information of the image. The branch operation process can be formalized as follows:

[0096] (3)

[0097] (4)

[0098] in: , , and They represent frequency domain features, frequency domain scanning strategy, non-subsampled shearlet transform and its inverse operation respectively;

[0099] S23: The S21 After the linear layer, the SiLU activation function is operated, and then the semantic features output by the two branches in S22 are respectively and Perform element-by-element multiplication, and finally connect the semantic features of the two branches in series according to the channel to output the semantic features that combine the image space and frequency domain information. , its mathematical form can be expressed as:

[0100] (5)

[0101] in: represents element-wise product;

[0102] Represents a concatenation operation.

[0103] So far, a spatial-frequency Mamba module (SFMamba) based on spatial and frequency domain information was constructed to extract and fuse the spatial and frequency domain information of MRI images.

[0104] S3: The low-resolution MRI image features obtained in S1 are input into a feature extraction encoder and decoder composed of multiple cascaded space-frequency domain Mamba modules to extract multi-level semantic features of the image and reconstruct a high-resolution MRI image.

[0105] like Figure 2 As shown, the SFMamba module constructed by S2 is used as the basic module for image semantic feature extraction. On this basis, the encoder realizes the extraction of semantic features of low-resolution MRI images by alternating SFMamba and downsampling operations, and the decoder realizes the analysis of image semantic information by alternating SFMamba and upsampling operations, thereby realizing the reconstruction of images from low resolution to high resolution.

[0106] The processing steps of S3 include:

[0107] S31: constructing an image semantic feature encoder based on the space-frequency domain Mamba module constructed in S2, wherein semantic features of different depths in the image are extracted through multiple cascaded space-frequency domain Mamba modules, and the spatial dimension of the feature map is reduced by adding a downsampling operation after each space-frequency domain Mamba module, thereby effectively reducing the computational complexity of the algorithm while extracting deep feature representations of the image;

[0108] First use The convolution operation transforms the low-resolution MRI image Mapping from input space to initial features ,in, Represents the number of channels of the image and features, and then Alternately perform spatial-frequency domain Mamba module operations and downsampling operations to extract semantic features of different depths of the image from both spatial and frequency domain dimensions , the process can be formalized as:

[0109] (6)

[0110] in: represents the encoder;

[0111] represents the downsampling operation;

[0112] Indicates the encoder SFMamba operation, ;

[0113] S32: The semantic features of the low-resolution MRI image extracted in S31 are reconstructed through a feature decoder. The feature decoder is symmetrical with the feature encoder in structure. Space-frequency domain Mamba module operations and upsampling operations are performed alternately at corresponding positions. At the same time, features in the encoder are fused through jump links to gradually improve the resolution of the feature map, thereby obtaining a semantic feature map of the decoder. , its formula is expressed as:

[0114] (7)

[0115] in: Indicates a serial operation;

[0116] Represents an upsampling operation;

[0117] Indicates execution of the decoder Space-frequency domain Mamba modules, ;

[0118] Finally, through a The convolutional layer converts the semantic features output by the last spatial-frequency domain Mamba module of the decoder into Mapping to residual image Then, the low-resolution MRI images Add it element by element to reconstruct high-resolution MRI images , its formula is expressed as:

[0119] (8)

[0120] in: express Convolution operation.

[0121] S4: Introduce a hybrid loss function optimization objective, repeatedly iteratively optimize the encoder and decoder processes in S2 and S3, and reconstruct the low-resolution MRI image into a high-resolution MRI image.

[0122] The model is iterated repeatedly, and a mixed loss function is introduced as the optimization objective. The model is optimized from both spatial and frequency domain dimensions to realize the image reconstruction process from low resolution to high resolution, thereby comprehensively improving the accuracy of super-resolution reconstruction of prostate MRI images.

[0123] The processing steps of S4 include:

[0124] S41: Introduce a mixed loss function to optimize the training process of the algorithm, which includes spatial loss , low frequency loss and high frequency loss , and finally the loss function of the prostate MRI super-resolution reconstruction model based on the frequency domain perception state space model is:

[0125] (9)

[0126] in: , and They represent trade-off hyperparameters, which are empirically set to 0.6, 0.3, and 0.1;

[0127] for and , this algorithm uses the mean absolute error as the loss function, and its formula can be expressed as:

[0128] (10)

[0129] (11)

[0130] in: , Represent the reconstructed image and the real image respectively;

[0131] and Respectively represent the low-frequency sub-band and high-frequency sub-band features extracted from the NSST module;

[0132] represents the L1 norm;

[0133] Similarly, for , the algorithm combines the mean absolute error loss and the structural similarity coefficient (SSIM) loss. The structural similarity coefficient loss is similar to the human visual system and can keenly perceive local structural changes. Its formula is expressed as:

[0134] (12)

[0135] in: and is the pixel mean;

[0136] and is the variance;

[0137] is the covariance;

[0138] represents the mean absolute error loss;

[0139] Represents the structural similarity coefficient loss.

[0140] It includes data preprocessing module, space-frequency domain Mamba (SFMamba) module, encoder-decoder module and iterative optimization loss module.

[0141] Data preprocessing module: responsible for resizing and standardizing the pixel intensity values ​​of the original MRI images of prostate disease patients included in the clinical diagnosis and treatment process, and then reconstructing the low-resolution MRI images of the prostate through downsampling operations;

[0142] Spatial-Frequency Domain Mamba (SFMamba) module: Through the spatial Mamba branch based on the VMamba architecture and the frequency domain Mamba branch based on the non-subsampled truncated wavelet transform (NSST), the deep semantic features of low-resolution MRI images are extracted and fused from different dimensions, the image spatial information and frequency domain information are incorporated, and the image semantic feature representation is learned efficiently and accurately, solving the problems of low efficiency and low accuracy of medical image super-resolution reconstruction algorithms.

[0143] Encoder-Decoder module: By building a symmetric encoder-decoder architecture, based on multi-stage cascaded SFMamba modules and symmetrical downsampling and upsampling operations, the algorithm complexity is further reduced, and more fine-grained image semantic information is efficiently extracted, solving the problem of low computational efficiency of medical image super-resolution reconstruction algorithms.

[0144] Iterative Optimization Loss Module: It is responsible for using the proposed hybrid loss function to iterate and optimize the algorithm multiple times, enhancing the model's ability to efficiently and accurately learn the semantic feature representation of medical images, thereby comprehensively improving the algorithm's super-resolution reconstruction performance.

[0145] The above disclosure is only a specific embodiment of the present invention, but the present invention is not limited thereto, and any changes that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A prostate MRI super-resolution reconstruction method based on a frequency-domain-aware state-space model, characterized in that: The following steps are involved: S1: Preprocess the patient's prostate MRI image and obtain the patient's low-resolution MRI image through downsampling operation; S2: Based on the spatial and frequency domain information, a spatial-frequency Mamba module is constructed to extract and fuse the spatial and frequency domain information of low-resolution MRI images; S3: inputting the low-resolution MRI image features obtained in S1 into a feature extraction encoder and decoder composed of multiple cascaded space-frequency domain Mamba modules to extract multi-level semantic features of the image and reconstruct a high-resolution MRI image; S4: introducing a hybrid loss function optimization objective, repeatedly iterating the encoder and decoder processes in S3, optimizing the model, and reconstructing the low-resolution MRI image into a high-resolution MRI image; The processing steps of S1 include: S11: preprocessing operations of resizing and standardizing pixel intensity values ​​of MRI images of patients with prostate diseases; S12: The preprocessed MRI image is downsampled using bicubic interpolation to reconstruct the high-resolution MRI image into a low-resolution MRI image. The low-resolution MRI image features are represented as , its input space can be expressed as , where R represents the three-dimensional space defined, and Represent the length and width of the image respectively, and 3 represents the number of channels of the image and feature is 3; The processing steps of S2 include: S21: Construct a space-frequency Mamba module based on spatial and frequency domain information. First, perform linear mapping and convolution operations on the input features of the module. Let the input and output features of the space-frequency Mamba module be represented as and , first through a linear layer and a layer Convolutional layer, which takes input features Mapping , the process can be formalized as: （1） in: express 1×1 Convolution operation; Represents a linear operation; S22: Input the feature map output in S21 into the spatial Mamba branch and the frequency domain Mamba branch respectively, and extract the spatial semantic features of the image from two different dimensions and frequency domain semantic features ; In the space Mamba branch, the sequence Perform DWConv operation, SiLU activation function conversion, spatial scanning and standardization, where DWConv represents depth-separable convolution, and the spatial scanning strategy uses VMamba scanning mechanism to extract features from the image in both horizontal and vertical directions. The process is expressed as: （2） in: , , and They represent normalization, 2D scanning, SiLU activation function, and depthwise separable convolution operations respectively; In the frequency domain Mamba branch, the feature map output in S21 is transformed into It is decomposed into low-frequency sub-band and high-frequency sub-band features, and then DWConv and SiLU activation function operations are performed to obtain the feature representation of the hidden state space. Finally, the semantic features of the frequency domain Mamba branch are reconstructed and output through the inverse NSST process. In terms of scanning strategy, in order to adapt to the sub-band information characteristics from low to high of the NSST algorithm, a sequential scanning strategy from low frequency to high frequency is introduced. In the scanning direction, horizontal, vertical and flip scanning in two directions are used to successively obtain the low-frequency and high-frequency semantic information of the image. The branch operation process can be formalized as follows: （3） （4） in: , , and They represent frequency domain features, frequency domain scanning strategy, non-subsampled shearlet transform and its inverse operation respectively; S23: The S21 After the linear layer, the SiLU activation function is performed, and then the semantic features output by the two branches in S22 are respectively and Perform element-by-element multiplication, and finally connect the semantic features of the two branches in series according to the channel, and output the semantic features that combine the image space and frequency domain information. , its mathematical form can be expressed as: （5） in: represents element-wise product; Represents a concatenation operation.

2. The method for prostate MRI super-resolution reconstruction based on frequency domain perception state space model according to claim 1, characterized in that: The processing steps of S3 include: S31: First use The convolution operation transforms the low-resolution MRI image Mapping from input space to initial features ,in, Represents the number of channels of the image and features, and then Alternately perform spatial-frequency domain Mamba module operations and downsampling operations to extract semantic features of different depths of the image from both spatial and frequency domain dimensions , the process can be formalized as: （6） in: represents the encoder; represents the downsampling operation; Indicates the encoder SFMamba operation, ; S32: The semantic features of the low-resolution MRI image extracted in S31 are reconstructed through a feature decoder. The feature decoder is symmetrical with the feature encoder in structure. Space-frequency domain Mamba module operations and upsampling operations are performed alternately at corresponding positions. At the same time, features in the encoder are fused through jump links to gradually improve the resolution of the feature map, thereby obtaining a semantic feature map of the decoder. , its formula is expressed as: （7） in: Indicates a serial operation; Represents an upsampling operation; Indicates execution of the decoder Space-frequency domain Mamba modules, ; Finally, through a The convolutional layer converts the semantic features output by the last spatial-frequency domain Mamba module of the decoder into Mapping to residual image Then, the low-resolution MRI images Add it element by element to reconstruct high-resolution MRI images , its formula is expressed as: （8） in: express Convolution operation.

3. The method for prostate MRI super-resolution reconstruction based on frequency domain perception state space model according to claim 2, characterized in that: The processing steps of S4 include: S41: Introduce a mixed loss function to optimize the training process of the algorithm, which includes spatial loss , low frequency loss and high frequency loss , and finally the loss function of the prostate MRI super-resolution reconstruction model based on the frequency domain perception state space model is: （9） in: , and They represent trade-off hyperparameters respectively; for and , this algorithm uses the mean absolute error as the loss function, and its formula can be expressed as: （10） （11） in: , Represent the reconstructed image and the real image respectively; and Respectively represent the low-frequency sub-band and high-frequency sub-band features extracted from the NSST module; represents the L1 norm; Similarly, for , the algorithm combines the mean absolute error loss and the structural similarity coefficient loss. The structural similarity coefficient loss is similar to the human visual system and can keenly perceive local structural changes. Its formula is expressed as: （12） in: and is the pixel mean; and is the variance; is the covariance; represents the mean absolute error loss; Represents the structural similarity coefficient loss.

Images