A low-dose PET image reconstruction method based on deep neural network

Abstract

The present invention discloses a low-dose PET image reconstruction method based on a deep neural network. Specifically, the method comprises: enhancing the standard-dose reconstructed image data and forward-projecting it to generate noise-free projection domain data; adding Poisson noise to simulate a low-dose situation to generate a simulated data set; generating a sinusoidal mask by dividing the image into blocks and projecting them; constructing a network model using the mask, and training the deep neural network using a hybrid loss function and the generated data set; judging whether the image reconstruction effect meets the requirements based on evaluation indicators: if it does, proceeding to the next step; otherwise, modifying the network structure, adjusting the optimization function, learning rate, and loss function parameters, and retraining; reducing the parameters of the fully connected layer through truncated singular value decomposition; and using the actual collected sinusoidal data as input to the deep neural network model to calculate the reconstructed image. The present invention reduces the computational time of image reconstruction and improves the signal-to-noise ratio of the reconstructed image under low count rate conditions.

Description

Technical Field

[0001] The present invention relates to the field of nuclear medicine imaging technology, and in particular to a low-dose PET (positron emission tomography) image reconstruction method based on deep neural network. Background Art

[0002] Positron emission tomography (PET) is a commonly used medical imaging technique for diagnosing medical diseases. By injecting radioactive tracers into patients, PET can detect metabolic activities and physiological processes in human tissue at the molecular level. However, the radioactivity of the tracer poses a potential radiation risk to patients, potentially causing genetic damage and cancer. Furthermore, reducing the tracer concentration and detection time will result in a decrease in the number of detected photons, leading to severe artifacts and noise in the reconstructed image.

[0003] The commonly used back-projection filtering algorithm and iterative reconstruction post-filtering algorithm both have some shortcomings: the back-projection filtering algorithm has fast computational speed, but the reconstructed image quality is poor and noisy. The iterative reconstruction algorithm takes the noise model into account, which can better restore image details and suppress noise, but it consumes more computing resources and has a long reconstruction time. In addition, in low-dose imaging, due to the low count rate of the acquired sinusoidal pattern and the presence of high statistical noise, the images reconstructed by both algorithms will suffer from severe noise and loss of detail.

[0004] In summary, existing algorithms have problems such as long reconstruction time and low image signal-to-noise ratio in low-dose imaging applications. Summary of the Invention

[0005] The purpose of the present invention is to provide a fast and accurate low-dose PET image reconstruction method based on deep neural network.

[0006] The technical solution to achieve the purpose of the present invention is: a low-dose PET image reconstruction method based on a deep neural network, the steps are as follows:

[0007] Step S1: After data enhancement, the standard dose reconstructed image is forward projected to generate a noise-free sinusoidal graph, and Poisson noise is added to simulate a low-count situation to obtain a simulation data set;

[0008] Step S2: Generate a sinogram mask by dividing the image into blocks and forward projecting it;

[0009] Step S3: Use the mask to build a deep neural network model structure, set training hyperparameters and optimization algorithms, and train the deep neural network model using the hybrid loss function and the data set obtained in step S1;

[0010] Step S4: Based on the evaluation indicators such as structural similarity and peak signal-to-noise ratio, determine whether the image reconstruction effect meets the requirements. If so, proceed to the modulation step S5; if not, change the network structure, modify the values ​​of the optimization function, learning rate and loss function parameters, and go to step S3 for retraining;

[0011] Step S5: reducing network parameters based on truncated singular value decomposition;

[0012] Step S6: Using the sinusoidal data collected by the real PET system as input to the trained deep neural network model, and obtaining a reconstructed image through calculation.

[0013] Compared with the existing technology, the present invention has the following significant advantages: (1) PET image data can be directly reconstructed from the sinusoidal data in the projection domain without the need for iterative reconstruction, which requires a short time and enables rapid imaging in whole-body PET imaging and dynamic imaging; (2) the proposed network can better preserve image details, reduce noise and artifacts in the reconstructed image, and still reduce noise and improve the signal-to-noise ratio in low-count situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flowchart of the present invention's low-dose PET image reconstruction based on deep neural network.

[0015] Figure 2 This is an example diagram of the process of generating simulation data according to the present invention.

[0016] Figure 3 is an example diagram of a sinusoidal mask generated by the present invention.

[0017] Figure 4 This is a diagram of the deep neural network structure used.

[0018] Figure 5 is an instance of the image reconstructed by the network. DETAILED DESCRIPTION

[0019] The purpose of the present invention is to provide an image reconstruction method for a low-dose positron emission tomography (PET) device based on a deep neural network, which solves the problems of traditional iterative reconstruction algorithms, such as long reconstruction time, low signal-to-noise ratio of reconstructed images, and blurred details under low count rates.

[0020] Combine Figure 1 The present invention provides a method for reconstructing low-dose positron emission tomography (PET) images based on a deep neural network, comprising the following steps:

[0021] Step S1: After data enhancement, the standard dose reconstructed image is forward projected to generate a noise-free sinusoidal graph, and Poisson noise is added to simulate a low-count situation to obtain a simulation data set;

[0022] Step S2: Generate a sinogram mask by dividing the image into blocks and forward projecting it;

[0023] Step S3: Use the mask to build a deep neural network model structure, set training hyperparameters and optimization algorithms, and train the deep neural network model using the hybrid loss function and the data set obtained in step S1;

[0024] Step S4: Based on the evaluation indicators such as structural similarity and peak signal-to-noise ratio, determine whether the image reconstruction effect meets the requirements. If so, proceed to the modulation step S5; if not, change the network structure, modify the values ​​of the optimization function, learning rate and loss function parameters, and go to step S3 for retraining;

[0025] Step S5: reducing network parameters based on truncated singular value decomposition;

[0026] Step S6: Using the sinusoidal data collected by the real PET system as input to the trained deep neural network model, and obtaining a reconstructed image through calculation.

[0027] As a specific example, in step S1, the process of generating the simulation data set is as follows:

[0028] S11, generating PET images of different shapes by randomly rotating, mirror-flipping, and translating the standard-dose reconstructed PET image up and down and left and right;

[0029] S12, forward-projecting the PET image based on the projection matrix to generate a noise-free sinusoidal graph;

[0030] S13. Normalize the noise-free sinusoidal graph to a specific count rate interval and add Poisson noise to obtain a simulation data set.

[0031] As a specific example, in step S2, a sinusoidal mask is generated as follows:

[0032] S21, dividing the PET image into blocks, each block being surrounded by a buffer;

[0033] S22, forward project the divided image to generate a sine graph, and then Figure 2 The value is used as a mask for the sinogram.

[0034] As a specific example, in step S3, a deep neural network model structure is constructed, and training hyperparameters and an optimization algorithm are set. The optimization algorithm adopts the Adam algorithm, and the network model structure is as follows:

[0035] The deep neural network model structure includes a domain transformation module and an image enhancement module;

[0036] The domain transformation module consists of two parts: mask selection and fully connected layer. The mask selection part uses a pre-generated mask to select the sinogram data of a specific area, inputs it into the fully connected layer, reorganizes the output one-dimensional data into two-dimensional image blocks, and combines these image blocks.

[0037] The image enhancement module consists of a U-Net structure network, which includes three parts: encoder, bottleneck layer and decoder. The encoder has three layers, each layer consists of a residual block, and the output of each layer serves as the input of the next layer and the input of the corresponding encoder layer; the bottleneck layer contains a residual block; the decoder has the same number of layers as the encoder, and each layer contains a pixel rearrangement layer for upsampling and a residual block for feature decoding; the feature map output by the last layer of the decoder is output as a PET image after 1×1 convolution.

[0038] As a specific example, the hybrid loss function and the data set obtained in step S1 are used to train the deep neural network model in step S3, where the hybrid loss function L mix The formula for (x,y) is as follows:

[0039] L mix (x,y)=α1L l1 (x,y)+α2L MS-SSIM (x,y)+βL VGG (x,y)

[0040] Among them, α1, α2 and β are hyperparameters;

[0041] Mean absolute error loss L l1 The (x,y) formula is:

[0042]

[0043] Where x represents the actual PET image, y represents the predicted PET image output by the deep neural network model, and N represents the number of pixels in the real image;

[0044] Multi-scale structural similarity loss L MS-SSIM The (x,y) formula is:

[0045]

[0046] Among them, c j 、s j They represent the calculation of contrast term and structure term after performing j consecutive low-pass filtering and downsampling with a sampling interval of 2 on the original image, and M represents the total number of consecutive low-pass filtering times;

[0047] The formula for the brightness term l(x,y) is:

[0048]

[0049] The formula for the contrast term c(x,y) is:

[0050]

[0051] The formula for the structural term s(x,y) is:

[0052]

[0053] Among them, μ x ,μ y represent the mean of x and y, σ x ,σ y represent the standard deviation of x and y, σ xy Represents the covariance of x and y, C1, C2, C3 are constant values ​​that satisfy:

[0054] C1=(K1L) 2

[0055] C2=(K2L) 2

[0056] C3=C2 / 2

[0057] Where K1 = 0.01, K2 = 0.03, L represents the numerical range;

[0058] Perceptual difference loss L VGG The formula for (x,y) is as follows:

[0059]

[0060] Where C is the number of channels of features calculated and output by the first three convolutional layers of the VGG network, H and W are the height and width of the feature map, respectively. During the calculation, the single-channel PET image is copied and spliced ​​into a three-channel image before being input into the VGG network.

[0061] As a specific example, the process of reducing network parameters based on truncated singular value decomposition in step S5 is as follows:

[0062] S51. Decompose the singular value of the fully connected layer weight matrix W into W = UΣV T ; U is a left singular matrix, Σ is a diagonal matrix, V T is a right singular matrix;

[0063] S52. Take several largest singular values ​​and singular value vectors to obtain the approximate W of the weight matrix K ≈W, where Σ K is a diagonal matrix composed of several largest singular values, U K and V Kis a matrix consisting of singular value vectors;

[0064] S53. Will U k and Generate two new fully connected layers as the weight matrix and replace the original single fully connected layer.

[0065] The present invention can directly reconstruct PET image data from sinusoidal data in the projection domain, eliminating the need for iterative reconstruction and shortening the time required. This allows for rapid whole-body PET imaging and dynamic imaging. It can also reduce noise and improve the signal-to-noise ratio (SNR) even at low counts. Commonly used clinical algorithms, such as backprojection filtering and ordered subset maximum expectation, still produce low SNRs and blurred image details in low-count scenarios, even after image post-filtering. Compared to these algorithms, the network proposed in the present invention can better preserve image details and reduce noise and artifacts in the reconstructed image.

[0066] Example

[0067] Combine Figure 1 In this embodiment, the image reconstruction of a low-dose positron emission tomography imager based on a deep neural network includes the following steps:

[0068] Step S1: Data enhancement is performed on the standard dose reconstructed PET image, a noise-free sinusoidal graph is generated using system matrix forward projection, and Poisson noise is added to simulate a low count situation;

[0069] Furthermore, the method steps are as follows:

[0070] S11. The 2D PET images were randomly rotated clockwise by -30° to +30°, then randomly mirrored left and right, and randomly translated horizontally and vertically by -10 to 10 units.

[0071] S12. Simulate the system matrix of Biograph mMR based on the multiray tracing algorithm and generate noise-free sinusoidal data using forward projection of the system matrix.

[0072] S13, the count rate of the noise-free sinusoidal data is randomly normalized to between 50,000 and 100,000, and Poisson noise is added to simulate the low count situation. The whole process is as follows Figure 2 shown.

[0073] Step S2: Divide the PET image into multiple sub-blocks, each of which is surrounded by a fixed-width buffer, and use the system matrix to forward project the noise-free sinusoidal data, taking the non-negative value area as a mask;

[0074] Furthermore, the method steps are as follows:

[0075] S21, dividing the PET image of size 128×128 into 16 32×32 sub-blocks, each sub-block is surrounded by a buffer with a width of 4, the values ​​of the sub-blocks and buffers are set to 100, and the values ​​of other areas are set to 0;

[0076] S22, forward project each PET image containing a sub-block using the system matrix to obtain a sinusoidal graph related to the sub-block area, and convert the sinusoidal graph into Figure 2 The non-negative areas are all set to 1, and the rest are set to 0 as the sinogram mask. The process is as follows Figure 3 As shown;

[0077] Step S3: Adjust the deep neural network structure, optimize the algorithm, loss function, and use the generated data set for training.

[0078] The convolutional neural network structure is as follows Figure 4 As shown in the figure, the deep neural network model structure includes a domain transformation module and an image enhancement module. The domain transformation module consists of two parts: a mask selection and a fully connected layer. The mask selection part uses a pre-generated mask to select the sinusoidal data of a specific region, which is input into the fully connected layer. The output of the one-dimensional data is reorganized into two-dimensional image blocks, and these image blocks are combined. The image enhancement module consists of a U-Net network with three parts: an encoder, a bottleneck layer, and a decoder. The encoder has three layers, each consisting of a residual block. The output of each layer serves as the input of the next layer and the corresponding encoder layer. The bottleneck layer contains a residual block. The decoder has the same number of layers as the encoder, and each layer contains a pixel reordering layer for upsampling and a residual block for feature decoding. The feature map output by the last layer of the decoder is subjected to a 1×1 convolution and then outputs the PET image.

[0079] The hybrid loss function formula used is as follows:

[0080] L mix (x,y)=a1L l1 (x,y)+α2L MS-SSIM (x,y)+βL VGG (x,y)

[0081] Among them, α1, α2 and β are hyperparameters;

[0082] Mean absolute error loss L l1 The (x,y) formula is:

[0083]

[0084] Where x represents the actual PET image, y represents the predicted PET image output by the deep neural network model, and N represents the number of pixels in the real image;

[0085] Multi-scale structural similarity loss L MS-SSIM The (x,y) formula is:

[0086]

[0087] Among them, c j 、s j They represent the calculation of contrast term and structure term after performing j consecutive low-pass filtering and downsampling with a sampling interval of 2 on the original image, and M represents the total number of consecutive low-pass filtering times;

[0088] The formula for the brightness term l(x,y) is:

[0089]

[0090] The formula for the contrast term c(x,y) is:

[0091]

[0092] The formula for the structural term s(x,y) is:

[0093]

[0094] Among them, μ x ,μ y represent the mean of x and y, σ x ,σ y represent the standard deviation of x and y, σ xy Represents the covariance of x and y, C1, C2, C3 are constant values ​​that satisfy:

[0095] C1=(K1L) 2

[0096] C2=(K2L) 2

[0097] C3=C2 / 2

[0098] Where K1=0.01, K2=0.03, and L represents the numerical range.

[0099] Perceptual difference loss L VGG The formula for (x,y) is as follows:

[0100]

[0101] Where C is the number of channels of features computed by the first three convolutional layers of the VGG network, and H and W are the height and width of the feature map, respectively. During the computation, the single-channel PET image is copied and concatenated into a three-channel image before being fed into the VGG network.

[0102] Step S4, judging whether the image reconstruction effect meets the requirements through evaluation indicators such as structural similarity and peak signal-to-noise ratio, if so, modulate step S5; otherwise, adjust the model structure and parameters, and go to step S3 for retraining.

[0103] Step S5: Based on truncated singular value decomposition, the single fully connected layer corresponding to each sub-block is decomposed into two small fully connected layers to reduce network parameters.

[0104] Furthermore, the method steps are as follows:

[0105] S51. Decompose the original singular value of the weight matrix W with rank 1024 into W = UΣV T ;

[0106] S52, take the 128 largest singular values ​​and the corresponding singular vectors to obtain the approximate weight matrix W K ≈W, where

[0107] Σ K is a diagonal matrix composed of these singular values, U K and V K is the matrix consisting of the corresponding singular vectors,

[0108] S53, use U K and Generate two new fully connected layers as parameters to replace the fully connected layer with weight matrix W;

[0109] Step S6: Reconstruct the image using the trained network for the actual collected sinusoidal data. Figure 5 is an instance of the image reconstructed by the network.

[0110] In summary, the present invention reconstructs PET images directly from low-dose sinusoidal data, eliminating the need for sinusoidal filtering and iterative reconstruction, reducing computational time, and enabling application in whole-body PET imaging and dynamic imaging. Furthermore, the present invention exhibits strong noise immunity, while commonly used image reconstruction algorithms, such as backprojection filtering and iterative reconstruction post-filtering, exhibit severe noise, detail loss, and artifacts in reconstructed images under low-count conditions. The present invention generates a large amount of low-count sinusoidal data during the data set generation phase, thereby improving the network's image reconstruction performance under low-count conditions and enhancing the signal-to-noise ratio and structural similarity of the reconstructed image.

Claims

1. A low-dose PET image reconstruction method based on deep neural network, characterized in that: Here are the steps: Step S1: After data enhancement, the standard dose reconstructed image is forward projected to generate a noise-free sinusoidal graph, and Poisson noise is added to simulate a low-count situation to obtain a simulation data set; Step S2: Generate a sinogram mask by dividing the image into blocks and forward projecting it; Step S3: Use the mask to build a deep neural network model structure, set training hyperparameters and optimization algorithms, and train the deep neural network model using the hybrid loss function and the data set obtained in step S1; Step S4: Based on the evaluation indicators such as structural similarity and peak signal-to-noise ratio, determine whether the image reconstruction effect meets the requirements. If so, proceed to the modulation step S5; if not, change the network structure, modify the values ​​of the optimization function, learning rate and loss function parameters, and go to step S3 for retraining; Step S5: reducing network parameters based on truncated singular value decomposition; Step S6: Using the sinusoidal data collected by the real PET system as input to the trained deep neural network model to obtain a reconstructed image through calculation; In step S3, a deep neural network model structure is constructed, and training hyperparameters and optimization algorithms are set. The optimization algorithm uses the Adam algorithm, and the network model structure is as follows: The deep neural network model structure includes a domain transformation module and an image enhancement module; The domain transformation module consists of two parts: mask selection and fully connected layer. The mask selection part uses a pre-generated mask to select the sinogram data of a specific area, inputs it into the fully connected layer, reorganizes the output one-dimensional data into two-dimensional image blocks, and combines these image blocks. The image enhancement module consists of a U-Net network, which includes an encoder, a bottleneck layer, and a decoder. The encoder has three layers, each consisting of a residual block. The output of each layer serves as the input of the next layer and the corresponding encoder layer. The bottleneck layer contains a residual block. The decoder has the same number of layers as the encoder, and each layer contains a pixel reordering layer for upsampling and a residual block for feature decoding. The feature map output by the last layer of the decoder is subjected to a 1×1 convolution and then outputs the PET image. In step S3, the deep neural network model is trained using the mixed loss function and the data set obtained in step S1, wherein the mixed loss function L mix The formula for (x,y) is as follows: L mix (x,y)=α1L l1 (x,y)+α2L MS-SSIM (x,y)+βL VGG (x,y) Among them, α1, α2 and β are hyperparameters; Mean absolute error loss L l1 The (x,y) formula is: Where x represents the actual PET image, y represents the predicted PET image output by the deep neural network model, and N represents the number of pixels in the real image; Multi-scale structural similarity loss L MS-SSIM The (x,y) formula is: Among them, c j 、s j They represent the calculation of contrast term and structure term after performing j consecutive low-pass filtering and downsampling with a sampling interval of 2 on the original image, and M represents the total number of consecutive low-pass filtering times; The formula for the brightness term l(x,y) is: The formula for the contrast term c(x,y) is: The formula for the structural term s(x,y) is: Among them, μ x ,μ y represent the mean of x and y, σ x ,σ y represent the standard deviation of x and y, σ xy Represents the covariance of x and y, C1, C2, C3 are constant values ​​that satisfy: C1=(K1L) 2 C2=(K2L) 2 C3=C2 / 2 Where K1 = 0.01, K2 = 0.03, L represents the numerical range; Perceptual difference loss L VGG The formula for (x,y) is as follows: Where C is the number of channels of features calculated and output by the first three convolutional layers of the VGG network, H and W are the height and width of the feature map, respectively. During the calculation, the single-channel PET image is copied and spliced ​​into a three-channel image before being input into the VGG network.

2. The low-dose PET image reconstruction method based on deep neural network according to claim 1, characterized in that: In step S1, the generation process of the simulation data set is as follows: S11, generating PET images of different shapes by randomly rotating, mirror-flipping, and translating the standard-dose reconstructed PET image up and down and left and right; S12, forward-projecting the PET image based on the projection matrix to generate a noise-free sinusoidal graph; S13. Normalize the noise-free sinusoidal graph to a specific count rate interval and add Poisson noise to obtain a simulation data set.

3. The low-dose PET image reconstruction method based on deep neural network according to claim 1, characterized in that In step S2, a sinogram mask is generated as follows: S21, dividing the PET image into blocks, each block being surrounded by a buffer; S22. Forward project the divided image to generate a sinogram, and binarize the sinogram as a mask of the sinogram.

4. The low-dose PET image reconstruction method based on deep neural network according to claim 1, characterized in that The process of reducing network parameters based on truncated singular value decomposition in step S5 is as follows: S51. Decompose the singular value of the fully connected layer weight matrix W into W = UΣV T ; U is a left singular matrix, Σ is a diagonal matrix, V T is a right singular matrix; S52. Take several largest singular values ​​and singular value vectors to obtain the approximate W of the weight matrix K ≈W, where ∑ K is a diagonal matrix composed of several largest singular values, U K and V K is a matrix consisting of singular value vectors; S53. Will U K and Generate two new fully connected layers as the weight matrix and replace the original single fully connected layer.

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