Liver tumor segmentation method based on GTF convolution and multi-frequency double attention

Abstract

The invention discloses a liver tumor segmentation method based on GTF convolution and multi-frequency double attention, and aims to solve the problems of shape and size diversity and boundary fuzziness of liver tumors and realize accurate liver tumor segmentation. The method comprises the following steps: S1, preprocessing abdominal CT data, and dividing the CT data into a training set, a verification set and a test set; s2, a GTF (Geometric Tigh Framelet) is introduced, and a GTF convolution is constructed in combination with a convolution operation; s3, fusing GTF convolution and an attention mechanism, and constructing a multi-frequency double-attention module; s4, fusing the internal characteristic distillation loss and segmentation loss, and constructing multi-scale distillation segmentation loss; s5, fusing the GTF convolution, the multi-frequency double-attention module and the multi-scale distillation segmentation loss, and constructing a GTF-UNet model; and S6, performing training, verification optimization and testing on the model by using the training set, the verification set and the test set. According to the method, detail features and multi-scale information can be effectively captured, the segmentation precision of the liver tumor is effectively improved, and the method can be used for automatic segmentation of the liver tumor in the CT image.

Description

Technical Field

[0001] The present invention relates to the field of medical image processing, and in particular to a liver tumor segmentation method based on GTF convolution and multi-frequency dual attention. Background Art

[0002] In the field of medical image processing, accurate segmentation of liver tumors is extremely important for disease diagnosis, treatment planning, and prognosis assessment. With the rapid development of computer technology, image segmentation methods based on deep learning have become a research hotspot.

[0003] Traditional liver tumor segmentation methods often face many challenges. Liver tumors are remarkably diverse in morphology, size, and location, and their boundaries are often blurred, making it extremely difficult to accurately define the tumor area. For example, some small tumors may have low contrast with surrounding liver tissue, while large tumors may have complex internal structures and irregular edges. In addition, abdominal CT images may also be affected by noise, artifacts, and physiological differences between individuals, further reducing the accuracy and reliability of traditional segmentation methods.

[0004] In recent years, the U-Net architecture based on convolutional neural networks (CNN) has shown good performance in image segmentation tasks. However, U-Net and its derivative models still have certain limitations when dealing with liver tumor segmentation. Its ability to capture subtle features and multi-scale information needs to be improved. For liver tumors with blurred boundaries, it is difficult to accurately identify their edge contours, which affects the accuracy of segmentation. At the same time, the receptive field of the network is relatively limited, and it may not be able to fully integrate the global information in the image, resulting in poor segmentation effects for tumors with some special shapes or locations.

[0005] On the other hand, although traditional multi-scale analysis methods such as wavelet transform can extract different frequency information of images to a certain extent, they are still insufficient in terms of integration with deep learning models and adaptability to complex liver tumor characteristics. In order to overcome these problems, it is necessary to explore new technologies and methods to improve the accuracy and robustness of liver tumor segmentation. Therefore, how to utilize the characteristics of wavelet transform and the advantages of U-Net architecture to effectively improve the accuracy and reliability of liver tumor segmentation has become a key issue to be solved in the field of medical image segmentation. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a liver tumor segmentation method based on GTF convolution and multi-frequency dual attention, which can provide users with a more accurate, efficient and highly adaptable liver tumor segmentation solution.

[0007] Specifically, the method comprises the following steps:

[0008] S1: Preprocess abdominal CT data and divide the CT data into training set, validation set and test set;

[0009] S2: Introduce GTF (Geometric Tight Framelet), combine it with convolution operation, and construct GTF convolution;

[0010] S3: Integrate GTF convolution and attention mechanism to build a multi-frequency dual attention module;

[0011] S4: Fusion of internal feature distillation loss and segmentation loss to construct multi-scale distillation segmentation loss;

[0012] S5: Fusion of GTF convolution, multi-frequency dual attention module and multi-scale distillation segmentation loss to build the GTF-UNet model;

[0013] S6: Use the training set, validation set, and test set to train, validate, optimize, and test the model.

[0014] Preferably, S1 comprises the following steps:

[0015] S1.1: Preprocess the acquired CT data, including: cropping to remove irrelevant areas, resampling to ensure data size consistency; using filtering technology to denoise the data, and normalizing the data;

[0016] Preferably, S2 comprises the following steps:

[0017] S2.1: Construct GTF transform and its inverse transform filter;

[0018] S2.2: Use GTF transform cascade decomposition and reconstruction to construct GTF convolution (GTFConv).

[0019] Preferably, S2.1 comprises the following steps:

[0020] Construct basic matrices W0, W1 and W2, which will serve as the key starting modules for generating a series of complex matrix structures; W0 contains the smoothing information of the image, W1 contains the direction and gradient information of the image, and W2 extracts the local changes and contrast information of the image that are opposite to the characteristics of W0;

[0021] definition Where i, j = 0, 1, 2, Represents the Kronecker product, which is combined to generate the GTF transform filter matrix group:

[0022] f0=W 0,0 ,

[0023]

[0024] f 11 =W 2,1 , f 12 =W 1,2 ,

[0025]

[0026] The GTF transform filter bank is defined as in is the low pass filter f L , is a high-pass filter, collectively referred to as f H ;Depend on

[0027] filters t filters=E

[0028] It can be seen that the GTF transform has orthogonality, and the GTF inverse transform filters are obtained t ;

[0029] Preferably, S2.2 comprises the following steps:

[0030] Given a single-channel image X, a GTF-based low-pass filter f L and high pass filter f H , the GTF transform (GT) can be described as:

[0031] [X L ,X H ]=Conv([f L ,f H ],X)

[0032] The resolution of each frequency domain component is half of X. L is the low-frequency component of X, X H is the high frequency component of X; since the GTF transform is orthogonal, the inverse GTF transform (IGT) can be obtained by transposed convolution:

[0033] X=Conv-transposed([f L ,f H ],[X L ,X H ])

[0034] The cascaded GTF transform can be achieved by recursively decomposing the low-frequency components, where

[0035]

[0036] Then, the decomposed frequency domain components are convolved to obtain the intermediate variable Y, where w is the weight of the convolution kernel:

[0037]

[0038] GTF is a geometric tight frame wavelet. According to the linear properties of wavelet transform and inverse transform, we have:

[0039] GT(M+N)=GT(M)+GT(N)

[0040] IGT(M+N)=IGT(M)+IGT(N)

[0041] Use the linear properties of inverse wavelet transform to combine high-level output and low-level Y L :

[0042]

[0043] Finally, perform the inverse GTF transform to reconstruct the image and obtain the output Z of the GTF convolution:

[0044]

[0045] Preferably, S3 comprises the following steps:

[0046] S3.1: Build a dual attention module;

[0047] S3.2: Fuse GTF convolution to build a multi-frequency dual attention module (MFDAM);

[0048] Preferably, S3.1 comprises the following steps:

[0049] The dual attention module is composed of spatial attention and channel attention. The feature map first passes through the channel attention module to compress the spatial dimension and obtain the information of the channel dimension. Then the output of the channel attention module is used as input to calculate the spatial attention to compress the channel dimension and obtain the spatial information of the target area. cs The overall calculation process is as follows:

[0050] A c (F D )=σ(MLP(AvgPool(F D ))+MLP(MaxPool(F D )))

[0051]

[0052] A s (F D ′)=σ(f7×7 ([AvgPool(F D ′); MaxPool(F D ′)]))

[0053]

[0054] That is F D =A cs (F D )

[0055] In the above formula, F D is the input feature, F D ′,F D ″ are the output of the channel attention module and the final output of the dual attention module, represents the element-by-element multiplication operation, σ represents the sigmoid activation function, and f 7×7 represents the filter, A c , A s Denote the channel attention layer and the spatial attention layer respectively, A cs represents the dual attention module;

[0056] Preferably, S3.2 comprises the following steps:

[0057] Based on the one-layer decomposition and reconstruction process of GTF convolution, dual attention modules are introduced at the original input feature level and the frequency domain sub-graph level to form a multi-frequency dual attention module. The specific implementation is as follows:

[0058] F′=A cs (Conv(F in ))

[0059] F L ,F H =GT(F in )

[0060] F Gout =IGT(A cs (Conv(F L ,F H )))

[0061]

[0062] Among them, F in , F out Represent the input features and output features respectively, F L , F H The input features are decomposed into high- and low-frequency sub-graphs by GTF transformation. The high- and low-frequency sub-graphs are subjected to convolution and dual attention modules to obtain attention weights, and then the GTF inverse transformation is performed to reconstruct F Gout, and finally concatenate it with the output F′ at the original input feature level to get the final output F out .

[0063] Preferably, S4 comprises the following steps:

[0064] S4.1: Calculate the internal feature distillation loss;

[0065] S4.2: Calculate segmentation loss;

[0066] S4.3: Construct multi-scale distillation segmentation loss.

[0067] Preferably, S4.1 comprises the following steps:

[0068] The GTF-UNet main body consists of an encoding block, a decoding block, and a bottleneck, and the block contains a convolutional layer. For the feature map in each block, the number of channels is evenly divided into two parts in the channel dimension, and the first half is used as the shallow channel feature. The second half is used as the deep channel feature Internal feature distillation loss function L IFD Defined as:

[0069]

[0070] In the above formula, represents the feature map of the jth layer in the bth block, B represents the total number of blocks in the network, J represents the total number of layers in the block, and the calculation adopts the L2 norm; in this way, information distillation is performed from shallow channel features to deep channel features;

[0071] Preferably, S4.2 comprises the following steps:

[0072] The segmentation loss combines Dice and cross entropy mixed losses; the segmentation loss L MSD The definition is as follows:

[0073]

[0074]

[0075] L MSD =α×Dice(P,G)+(1-α)×CrossEntropy(O,G)

[0076] Among them, P represents the predicted segmentation map, G represents the real segmentation map, N represents the number of pixels, ∈ is a small positive number, and α is the weight that balances the Dice loss and the cross entropy loss;

[0077] Preferably, S4.3 comprises the following steps:

[0078] Using multi-scale supervision, the internal feature distillation loss function L is integrated IFD and segmentation loss L MSD , and obtain the multi-scale distillation segmentation loss L MDS As shown below:

[0079]

[0080] Among them, w j is the weight assigned to the jth scale, L MSD (j) is the segmentation loss of the j-th scale, and β is used to balance the segmentation loss and the internal feature distillation loss.

[0081] Preferably, S5 comprises the following steps:

[0082] Taking the U-shaped network as the basic architecture, the GTFConv block is embedded in the encoder and decoder, and then MFDAM is fused at the bottleneck of the U-shaped network. Finally, the multi-scale distillation segmentation loss function is used for optimization learning to form the GTF-UNet model.

[0083] Preferably, S6 comprises the following steps:

[0084] Use the training set and validation set to train and optimize the model to obtain the optimal model weight, and then use the test set to test the model.

[0085] The beneficial effects of the method of the present invention are: first, in the data preprocessing stage, by performing operations such as cropping, resampling, denoising and normalization on the collected abdominal CT images, the data quality is improved, the interference of irrelevant information is reduced, and the data is reasonably divided into a training set, a validation set and a test set, laying a good foundation for subsequent model training and testing. In the process of model construction, GTF and convolution operations are innovatively integrated to construct a GTF convolution. On this basis, a multi-frequency dual attention module is constructed based on the GTF convolution. Further, the internal feature distillation loss and the segmentation loss are integrated to construct a multi-scale distillation segmentation loss. Finally, a GTF-UNet model is constructed based on a U-type network. These innovative designs enhance the performance of the model in multiple dimensions, so that it shows excellent ability in capturing detailed features and multi-scale information, significantly enhances the accuracy of edge recognition, and effectively expands the receptive field range of the network, so that the network can accurately and efficiently focus on the liver tumor area, while reducing feature redundancy, avoiding invalid or repeated features from dragging down the model performance, and significantly improving the accuracy of liver tumor segmentation. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the prior art and the drawings required for use in the embodiments. The following drawings are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0087] Figure 1 It is a flow chart of a liver tumor segmentation method based on GTF convolution and multi-frequency dual attention of the present invention;

[0088] Figure 2 This is a model architecture diagram of a liver tumor segmentation method based on GTF convolution and multi-frequency dual attention in the present invention;

[0089] Figure 3 It is a schematic diagram of the GTF convolution structure of a liver tumor segmentation method based on GTF convolution and multi-frequency dual attention of the present invention;

[0090] Figure 4 It is a schematic diagram of the MFDAM structure of a liver tumor segmentation method based on GTF convolution and multi-frequency dual attention of the present invention; Specific implementation plan

[0091] In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all other embodiments obtained by ordinary technicians in this field without creative work based on the embodiments of the present invention are within the scope of protection of the present invention.

[0092] The embodiment of the present invention provides a liver tumor segmentation method based on GTF convolution and multi-frequency dual attention, which is used to achieve accurate segmentation of liver tumors, assist clinical diagnosis and treatment decision-making, and improve the accuracy and efficiency of medical image processing.

[0093] Reference Figure 1 , the method comprises the following steps:

[0094] S1: Preprocess abdominal CT data and divide the CT data into training set, validation set and test set;

[0095] S2: Introduce GTF (Geometric Tight Framelet), combine it with convolution operation, and construct GTF convolution;

[0096] S3: Integrate GTF convolution and attention mechanism to build a multi-frequency dual attention module;

[0097] S4: Fusion of internal feature distillation loss and segmentation loss to construct multi-scale distillation segmentation loss;

[0098] S5: Fusion of GTF convolution, multi-frequency dual attention module and multi-scale distillation segmentation loss to build the GTF-UNet model;

[0099] S6: Use the training set, validation set, and test set to train, validate, optimize, and test the model.

[0100] Further, S1 comprises the following steps:

[0101] S1.1: Preprocess the acquired CT data, including: cropping to remove irrelevant areas, resampling to ensure data size consistency; using filtering technology to denoise the data, and normalizing the data;

[0102] Furthermore, the preprocessing of the collected CT data includes: cropping to remove irrelevant areas, resampling to ensure the consistency of data size; using filtering technology to denoise the data, and normalizing the data. This step specifically includes:

[0103] The collected data include public data sets and data sets provided by cooperative hospitals. Each case image completely covers the entire area of ​​the liver. The CT data is cropped to remove irrelevant areas and resampled to 512×512 size. Then, Gaussian filtering is used to denoise the CT, and the pixel value of each data is normalized to a uniform range (0 to 1);

[0104] The masks corresponding to the liver and background areas are set to 0, and the masks corresponding to the liver tumor areas are set to 1;

[0105] Convert the labeled CT data stored in nii format into data in npz matrix format;

[0106] S1.2: Divide the preprocessed CT data into training set, validation set and test set.

[0107] Furthermore, the step of dividing the preprocessed CT data into a training set, a validation set, and a test set specifically includes:

[0108] The CT data were divided into a training set, a validation set, and a test set in a ratio of 8:1:1.

[0109] Further, refer to Figure 3 , S2 includes the following steps:

[0110] S2.1: Construct GTF transform and its inverse transform filter;

[0111] S2.2: Use GTF transform cascade decomposition and reconstruction to construct GTF convolution (GTFConv).

[0112] Further, S2.1 includes the following steps:

[0113] Construct basic matrices W0, W1 and W2, which will serve as the key starting modules for the subsequent generation of a series of complex matrix structures; among them, W0 contains the smoothing information of the image, W1 contains the direction and gradient information of the image, and W2 extracts the local changes and contrast information of the image that are opposite to the characteristics of W0; according to the characteristics of W0, W1 and W2, define the basic matrix generation function:

[0114]

[0115] Using the basic matrix generation function, the following basic matrix can be generated:

[0116]

[0117] definition Where i, j = 0, 1, 2, Represents the Kronecker product. Here, the size of the basic matrix is ​​set to 3×3, thereby generating the GTF transformation filter matrix group:

[0118] f0=W 0,0 ,

[0119]

[0120] f 11 =W 2,1 , f 12 =W 1,2 ,

[0121]

[0122] The GTF transform filter bank is defined as in is the low pass filter f L , is a high-pass filter, collectively referred to as f H ;Depend on

[0123] filters t filters=E

[0124] It can be seen that the GTF transform has orthogonality, and the GTF inverse transform filters are obtained t ;

[0125] Further, S2.2 includes the following steps:

[0126] Given a single-channel image X, a GTF-based low-pass filter f L and high pass filter f H , setting the convolution step size to 2 and padding to 1, the GTF transform (GT) can be described as:

[0127] [X L ,X H ]=Conv([f L ,f H ],X)

[0128] The output of the convolution has 18 channels, and the resolution of each channel is half of X. L is the low-frequency component of X, X H is the high frequency component of X; since the GTF transform is orthogonal, the inverse GTF transform (IGT) can be obtained by transposed convolution:

[0129] X=Conv-transposed([f L ,f H ],[X L ,X H ])

[0130] The cascaded GTF transform can be achieved by recursively decomposing the low-frequency components, where

[0131]

[0132] Then, the decomposed frequency domain components are subjected to 5×5 convolution operations to obtain the intermediate variable Y, where w is the weight of the 5×5 convolution:

[0133]

[0134] GTF is a geometric tight frame wavelet. According to the linear properties of wavelet transform and inverse transform, we have:

[0135] GT(M+N)=GF(M)+GT(N)

[0136] IGT(M+N)=IGT(M)+IGT(N)

[0137] Use the linear properties of inverse wavelet transform to combine high-level output and low-level Y L :

[0138]

[0139] Finally, perform the inverse GTF transform to reconstruct the image and obtain the output Z of the GTF convolution:

[0140]

[0141] The number of recursive decomposition layers of GTF convolution in the GTF-UNet model is 3, so the maximum value of i is 3. Set Z (4) =0.

[0142] Further, refer to Figure 4 , S3 includes the following steps:

[0143] S3.1: Build a dual attention module;

[0144] S3.2: Fusion of GTF convolution to build a multi-frequency dual attention module (MFDAM).

[0145] Further, S3.1 includes the following steps:

[0146] The dual attention module is composed of spatial attention and channel attention. The feature map first passes through the channel attention module to compress the spatial dimension and obtain the information of the channel dimension. Then the output of the channel attention module is used as input to calculate the spatial attention to compress the channel dimension and obtain the spatial information of the target area. The overall calculation process A cs As shown below:

[0147] A c (F D )=σ(MLP(AvgPool(F D ))+MLP(MaxPool(F D )))

[0148]

[0149] A s (F D ′)=σ(f 7×7 ([AvgPool(F D ′); MaxPool(F D ′)]))

[0150]

[0151] That is F D =A cs (F D )

[0152] In the above formula, F D is the input feature, F D ′,F D ″ are the output of the channel attention module and the final output of the dual attention module, represents the element-by-element multiplication operation, σ represents the sigmoid activation function, and f 7×7represents a convolution operation with a filter size of 7×7, A c , A s Denote the channel attention layer and the spatial attention layer respectively, A cs represents the dual attention module;

[0153] Further, S3.2 includes the following steps:

[0154] Based on the one-layer decomposition and reconstruction process of GTF convolution, dual attention modules are introduced at the original input feature level and the frequency domain sub-graph level to form a multi-frequency dual attention module. The specific implementation is as follows:

[0155] F′=A cs (Conv(F in ))

[0156] F L ,F H =GT(F in )

[0157] F Gout =IGT(A cs (Conv(F L ,F H )))

[0158]

[0159] Among them, F in , F out Represent the input features and output features respectively, F L , F H The input features are decomposed into high- and low-frequency sub-graphs by GTF transformation. The high- and low-frequency sub-graphs are subjected to convolution and dual attention modules to obtain attention weights, and then the GTF inverse transformation is performed to reconstruct F Gout , and finally concatenate it with the output F′ at the original input feature level to get the final output F out .

[0160] Further, S4 comprises the following steps:

[0161] S4.1: Calculate the internal feature distillation loss;

[0162] S4.2: Calculate segmentation loss;

[0163] S4.3: Construct multi-scale distillation segmentation loss.

[0164] Further, S4.1 includes the following steps:

[0165] The GTF-UNet main body consists of four encoding blocks, four decoding blocks and a bottleneck. Each block contains two convolutional layers. For the feature map in each block, the number of channels is evenly divided into two parts in the channel dimension. The first half is used as the shallow channel feature. The second half is used as the deep channel feature Internal feature distillation loss function L IFD Defined as:

[0166]

[0167] In the above formula, represents the feature map of the jth layer in the bth block, B represents the total number of blocks in the network, J represents the total number of layers in the block, and the calculation adopts the L2 norm; in this way, information distillation is performed from shallow channel features to deep channel features;

[0168] Further, S4.2 includes the following steps:

[0169] The segmentation loss combines Dice and cross entropy mixed losses; the segmentation loss L MSD The definition is as follows:

[0170]

[0171] L MSD =α×Dice(P,G)+(1-α)×CrossEntropy(P,G)

[0172] Among them, P represents the predicted segmentation map, G represents the real segmentation map, N represents the number of pixels, ∈ is a small positive number, and α is the weight that balances the Dice loss and the cross entropy loss;

[0173] Further, S4.3 includes the following steps:

[0174] Using multi-scale supervision, the internal feature distillation loss function L is integrated IFD and segmentation loss L MSD , and obtain the multi-scale distillation segmentation loss L MDS As shown below:

[0175]

[0176] Among them, k is set to 4, w j is the weight assigned to the jth scale, L MSD (j) is the segmentation loss of the j-th scale, and β is used to balance the segmentation loss and the internal feature distillation loss.

[0177] Further, refer to Figure 2 , S5 comprises the following steps:

[0178] Taking the U-shaped network as the basic architecture, the GTFConv block is embedded in the encoder and decoder, and then MFDAM is fused at the bottleneck of the U-shaped network. Finally, the multi-scale distillation segmentation loss function is used for optimization learning to form the GTF-UNet model.

[0179] Further, S6 comprises the following steps:

[0180] Use the training set and validation set to train and optimize the model to obtain the optimal model weights, then import the optimal model weights into the test code and use the test set to test the model.

[0181] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make other equivalent modifications or substitutions without violating the spirit of the invention, and these equivalent modifications or substitutions are included in the scope defined by the application claims.

Claims

1. A liver tumor segmentation method based on GTF convolution and multi-frequency dual attention, It is characterized in that The method comprises the following steps: S1: Preprocess abdominal CT data and divide the CT data into training set, validation set and test set; S2: Introduce GTF (Geometric Tight Framelet), combine it with convolution operation, and construct GTF convolution; S3: Integrate GTF convolution and attention mechanism to build a multi-frequency dual attention module; S4: Fusion of internal feature distillation loss and segmentation loss to construct multi-scale distillation segmentation loss; S5: Fusion of GTF convolution, multi-frequency dual attention module and multi-scale distillation segmentation loss to build the GTF-UNet model; S6: Use the training set, validation set, and test set to train, validate, optimize, and test the model.

2. According to claim 1, a liver tumor segmentation method based on GTF convolution and multi-frequency dual attention is characterized in that: S1 includes the following steps: S1.1: Preprocess the acquired CT data, including: cropping to remove irrelevant areas and resampling to ensure consistent data size; Filtering technology is used to denoise the data and normalize the data.

3. The method for liver tumor segmentation based on GTF convolution and multi-frequency dual attention according to claim 1, characterized in that: S2 includes the following steps: S2.1: Construct GTF transform and its inverse transform filter; S2.2: Use GTF transform cascade decomposition and reconstruction to construct GTF convolution (GTFConv). Among them, S2.1 includes the following steps: Construct basic matrices W0, W1 and W2, which will serve as the key starting modules for generating a series of complex matrix structures; W0 contains the smoothing information of the image, W1 contains the direction and gradient information of the image, and W2 extracts the local changes and contrast information of the image that are opposite to the characteristics of W0; definition Where i, j = 0, 1, 2, Represents the Kronecker product, which is combined to generate the GTF transform filter matrix group: The GTF transform filter bank is defined as in is the low pass filter f L , is a high-pass filter, collectively referred to as f H ;Depend on filters t filters=E It can be seen that the GTF transform has orthogonality, and the GTF inverse transform filters are obtained t ; Among them, S2.2 includes the following steps: Given a single-channel image X, a GTF-based low-pass filter f L and high pass filter f H , the GTF transform (GT) can be described as: [X L ,X H ]=Conv([f L ,f H ],X) The resolution of each frequency domain component is half of X. L is the low-frequency component of X, X H is the high frequency component of X; since the GTF transform is orthogonal, the inverse GTF transform (IGT) can be obtained by transposed convolution: X=Conv-transposed([d L ,f H ],[X L ,X H ]) The cascaded GTF transform can be achieved by recursively decomposing the low-frequency components, where Then, the decomposed frequency domain components are convolved to obtain the intermediate variable Y, where w is the weight of the convolution kernel: GTF is a geometric tight frame wavelet. According to the linear properties of wavelet transform and inverse transform, we have: GT(M+N)=GT(M)+GT(N) IGT(M+N)=IGT(M)+IGT(N) Use the linear properties of inverse wavelet transform to combine high-level output and low-level Y L : Finally, perform the inverse GTF transform to reconstruct the image and obtain the output Z of the GTF convolution:

4. The method for liver tumor segmentation based on GTF convolution and multi-frequency dual attention according to claim 1, characterized in that: S3 includes the following steps: S3.1: Build a dual attention module; S3.2: Fusion of GTF convolution to build a multi-frequency dual attention module (MFDAM). Among them, S3.1 includes the following steps: The dual attention module is composed of spatial attention and channel attention. The feature map first passes through the channel attention module to compress the spatial dimension and obtain the information of the channel dimension. Then the output of the channel attention module is used as input to calculate the spatial attention to compress the channel dimension and obtain the spatial information of the target area. cs The overall calculation process is as follows: Ac(FD)=σ(MLP(AvgPool(FD))+MLP(MaxPool(FD))) A s (F D ′)=σ(f 7×7 ([AvgPool(F D ′);MaxPool(F D ′)])) That is F D =A cs (F D ) In the above formula, F D is the input feature, F D ′,F D ″ are the output of the channel attention module and the final output of the dual attention module, represents the element-by-element multiplication operation, σ represents the sigmoid activation function, and f 7×7 represents the filter, A c , A s Denote the channel attention layer and the spatial attention layer respectively, A cs represents the dual attention module; Among them, S3.2 includes the following steps: Based on the one-layer decomposition and reconstruction process of GTF convolution, dual attention modules are introduced at the original input feature level and the frequency domain sub-graph level to form a multi-frequency dual attention module. The specific implementation is as follows: F′=A cs (Conv(F in )) F L ,F H =GT(F in ) F Gout =IGT(A cs (Conv(F L ,F H ))) Among them, F in , F out Represent the input features and output features respectively, F L , F H The input features are decomposed into high- and low-frequency sub-graphs by GTF transformation. The high- and low-frequency sub-graphs are subjected to convolution and dual attention modules to obtain attention weights, and then the GTF inverse transformation is performed to reconstruct F Gout , and finally concatenate it with the output F′ at the original input feature level to get the final output F out .

5. The method for liver tumor segmentation based on GTF convolution and multi-frequency dual attention according to claim 1, characterized in that: S4 includes the following steps: S4.1: Calculate the internal feature distillation loss; S4.2: Calculate segmentation loss; S4.3: Construct multi-scale distillation segmentation loss. Among them, S4.1 includes the following steps: The main body of GTF-UNet consists of encoding blocks, decoding blocks and bottlenecks, and the blocks contain convolutional layers. For the feature maps in each block, the number of channels is evenly divided into two parts in the channel dimension, and the first half is used as the shallow channel feature. The second half is used as the deep channel feature Internal feature distillation loss function L IFD Defined as: In the above formula, represents the feature map of the jth layer in the bth block, B represents the total number of blocks in the network, J represents the total number of layers in the block, and the calculation adopts the L2 norm; in this way, information distillation is performed from shallow channel features to deep channel features; Among them, S4.2 includes the following steps: The segmentation loss combines Dice and cross entropy mixed losses; the segmentation loss L MSD The definition is as follows: L MSD =α×Dice(P,G)+(1-α)×CrossEntropy(P,G) Among them, P represents the predicted segmentation map, G represents the true segmentation map, N represents the number of pixels, ∈ is a small positive number, and α is the weight that balances the Dice loss and the cross entropy loss. Among them, S4.3 includes the following steps: Using multi-scale supervision, the internal feature distillation loss function L is integrated IFD and segmentation loss L MSD , and obtain the multi-scale distillation segmentation loss L MDS As shown below: Among them, w j is the weight assigned to the jth scale, L MSD (j) is the segmentation loss of the j-th scale, and β is used to balance the segmentation loss and the internal feature distillation loss.

6. The method for liver tumor segmentation based on GTF convolution and multi-frequency dual attention according to claim 1, characterized in that: S5 includes the following steps: Taking the U-shaped network as the basic architecture, the GTFConv block is embedded in the encoder and decoder, and then MFDAM is fused at the bottleneck of the U-shaped network. Finally, the multi-scale distillation segmentation loss function is used for optimization learning to form the GTF-UNet model.

7. The method for liver tumor segmentation based on GTF convolution and multi-frequency dual attention according to claim 1, characterized in that: S6 includes the following steps: Use the training set and validation set to train and optimize the model to obtain the optimal model weight, and then use the test set to test the model.

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