Low-dose Sinogram denoising and PET image reconstruction method based on convolutional neural network

Abstract

The present invention discloses a low-dose Sinogram denoising and PET image reconstruction method based on a convolutional neural network, which divides the reconstruction problem into three sub-problems: projection domain denoising, reconstruction from projection domain to image domain, and image domain denoising, and solves them respectively using a pyramid convolution weighted denoising module, an improved filter back projection layer, and an improved denoising convolutional neural network; the pyramid convolution weighted denoising module denoises the low-dose projection domain data Sinogram to generate projection domain data close to the standard dose, the filter back projection layer regards the frequency domain filter as learnable, and reconstructs a noisy reconstruction image from the denoised projection domain data Sinogram, and the improved DnCNN removes a small amount of noise in the reconstructed image, thereby obtaining a high-quality reconstruction image. The present invention solves the problem that is difficult to explain when deep learning is used for image reconstruction, and can still reconstruct high-quality PET images under low-dose conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of biomedical image reconstruction, and in particular relates to a low-dose Sinogram denoising and PET image reconstruction method based on a convolutional neural network. Background Art

[0002] Positron emission tomography (PET) is a nuclear medicine technology used for in vivo functional imaging. It can provide functional information of organs and lesions at the molecular level and plays an irreplaceable role in the diagnosis and treatment of heart diseases, brain diseases and malignant tumors. PET imaging mainly uses the decay of radioactive isotopes for tracking and detection. On the one hand, the projection data directly obtained by the PET scanner only records the information of the events saved by the PET system detector, which cannot be used directly. It needs to be reconstructed by the algorithm before it can be used as a medical image for doctors to directly refer to. So far, PET image reconstruction is still a hot technology in the field of medical image reconstruction research. On the other hand, the image quality of PET reconstruction has always been limited by its injection dose and imaging time. The radioactive drugs in PET imaging will cause radiation to patients, thereby increasing their chances of cancer. According to the principle of As low as reasonably achievable (ALARA) proposed by the International Commission on Radiological Protection, in PET clinical diagnosis, we expect to obtain the results that meet clinical detection with the minimum dose and minimize the radiation dose to patients. Therefore, how to reconstruct high-quality PET images with low-dose data has always been a problem to be solved.

[0003] PET reconstruction algorithms can be divided into three categories: analytical reconstruction algorithms, iterative reconstruction algorithms, and deep learning reconstruction methods. Analytical reconstruction algorithms, such as the filtered back-projection (FBP) algorithm, are based on the central slice theorem. They first filter the sinogram in the frequency domain and then perform back-projection. This type of method has the advantages of being simple and fast, but the reconstructed image contains a lot of noise and wheel-shaped artifacts. Iterative reconstruction algorithms use Poisson or Gaussian models to describe noise and establish the objective function of reconstruction. In order to suppress the noise of the reconstructed image, this type of method often adds prior constraints to the objective function, such as Markov random fields, TV, etc. There are many types of prior forms, and it is difficult to determine which prior form is optimal. Compared with analytical reconstruction algorithms, iterative reconstruction algorithms use noise models, which suppress the noise in the reconstructed image to a certain extent, but it has a large amount of calculation and is slow, and the selection of prior forms and hyperparameters relies on experience, and there is no unified standard. Deep learning methods, such as the relatively mature deep neural network structure U-net, generative adversarial network (GAN), encoding-decoding structure, etc., input sinograms or low-quality reconstruction images obtained by traditional methods into the neural network, and through supervised learning, the neural network outputs high-quality reconstruction images; although these deep learning methods have achieved certain results in reconstruction problems, the networks used in these methods are like black boxes and difficult to explain, and this method ignores the information in the sinogram domain. How to use the original signal in the sinogram domain, combine deep learning technology with traditional reconstruction algorithms, realize denoising from the source of data, and then realize the reconstruction of low-dose sinogram data to high-quality PET images has become a very important research topic. Summary of the invention

[0004] In view of the above, the present invention provides a low-dose Sinogram denoising and PET image reconstruction method based on convolutional neural network, which splits the reconstruction problem into three sub-problems: projection domain denoising, projection domain to image domain reconstruction, and image domain denoising, which are solved by pyramid convolution weighted denoising module, improved filtered back projection layer FBP, and improved denoising convolutional neural network DnCNN respectively.

[0005] A low-dose Sinogram denoising and PET image reconstruction method based on convolutional neural network comprises the following steps:

[0006] (1) Obtaining the simulated normal-dose Sinogram projection data and reconstructing the corresponding PET image;

[0007] (2) Downsampling the normal-dose Sinogram projection data using Poisson distribution to obtain low-dose Sinogram projection data;

[0008] (3) acquiring a large number of samples according to steps (1) and (2), each sample including low-dose Sinogram projection data, normal-dose Sinogram projection data and their corresponding PET images;

[0009] (4) The PET reconstruction problem is divided into the following three sub-problems:

[0010] Sub-problem 1 is a Sinogram projection domain denoising problem. The low-dose Sinogram projection data is denoised by a neural network to generate Sinogram projection data Y close to the standard dose. 1 ;

[0011] Subproblem 2 is a reconstruction problem, which is based on the Sinogram projection data Y 1 The PET reconstructed image X with a small amount of noise is obtained by using the improved filtered back projection algorithm (FBP). 1 ;

[0012] Subproblem 3 is also a denoising problem. The image X is reconstructed from PET. 1 After denoising by neural network, a high-quality PET reconstructed image X is obtained;

[0013] (5) Divide all samples into training sets and test sets, and build a network model consisting of a denoising module D1, a reconstruction module, and a denoising module D2 connected in sequence;

[0014] The low-dose Sinogram projection data in the training set samples are used as the input of the denoising module D1, and the normal-dose Sinogram projection data are used as the true value label output by the denoising module D1; the output result of the denoising module D1 is used as the input of the reconstruction module, and the PET image corresponding to the normal-dose Sinogram projection data is used as the true value label output by the reconstruction module; the output result of the reconstruction module is used as the input of the denoising module D2, and the PET image corresponding to the normal-dose Sinogram projection data is used as the true value label output by the denoising module D2, so as to train the entire network model;

[0015] (6) The low-dose Sinogram projection data in the test set samples are input into the trained network model to reconstruct the corresponding PET image, which is then compared with the PET image corresponding to the normal-dose Sinogram projection data.

[0016] Furthermore, in step (1), the normal dose Sinogram projection data is reconstructed using an OSEM (Ordered Subsets Expectation Maximization) reconstruction algorithm to obtain the corresponding PET image.

[0017] Furthermore, the specific implementation method of step (2) is as follows: for the Sinogram projection data of normal dose, firstly, a random number matrix of the same size as the Sinogram matrix is ​​generated based on the Poisson distribution using the built-in library function of Python. By setting different normalization coefficients, the mean of the random number matrix can be set to different sizes. Then, by matrix dot multiplication operation, the mean of the Sinogram matrix can be reduced to one-n of the original value, thereby obtaining the Sinogram projection data of low dose, where n is the downsampling ratio.

[0018] Furthermore, the denoising module D1 adopts a pyramid convolution weighted denoising module, which is composed of 7 convolution blocks connected in sequence from input to output, the convolution block is composed of a pixel attention layer and a multi-scale convolution layer, the pixel attention layer is composed of two 3×3 2D convolution layers and a sigmoid activation function, the multi-scale convolution layer uses convolution kernels of sizes 3×1, 1×3, 5×1, 1×5 and 7×1, 1×7 for convolution operations, and the operation results of each convolution kernel are spliced ​​together as output.

[0019] Furthermore, the reconstruction module is based on an improved filtered back-projection algorithm, including two parts: frequency domain filtering and back-projection. The back-projection part is the same as the traditional filtered back-projection algorithm, while the frequency domain filtering part uses a learnable filter, and the projection data at each angle corresponds to an independent one-dimensional frequency domain filter.

[0020] Furthermore, the denoising module D2 adopts an improved denoising convolutional neural network (DnCNN), which is composed of 8 2D convolutional layers and 1 normalization layer connected in sequence from input to output. Each 2D convolutional layer contains 64 3×3 convolution kernels. Except for the 8th convolutional layer, the outputs of the first 7 convolutional layers are processed using the activation function ReLU and batch normalization BN. Then, the input of the denoising module D2 is subtracted from the output of the 8th convolutional layer, and then a high-quality PET reconstructed image can be output through the normalization layer.

[0021] Furthermore, the specific process of training the network model in step (5) is as follows:

[0022] 5.1 Initialize the parameters of the network model; Kaiming is used to initialize the parameters in the denoising module D1, the Ramp filter is used to initialize all frequency domain filters in the reconstruction module, and the truncated normal distribution is used to initialize the parameters in the denoising module D2;

[0023] 5.2 Input the low-dose Sinogram projection data in the training set samples into the network model. In stage 1, train for 50 epochs to make the denoising module D1 converge; in stage 2, train for another 50 epochs to make the reconstruction module converge; in stage 3, collaborative training for 100 epochs to make the entire network model converge, and finally calculate the output of each layer through the forward propagation formula to obtain the final output of the network model;

[0024] 5.3 Calculate the loss function between the output of the three stages of the network model and the true value label:

[0025]

[0026] Among them: loss j is the loss function of the jth stage, X j (i) is the estimated value of the network model output corresponding to the i-th sample in the j-th stage, is the true value label of the i-th sample in the j-th stage, and N is the number of training samples in this stage;

[0027] 5.4 Calculate the partial derivative of the loss function and update the learnable parameters in the network model through the Adam algorithm;

[0028] 5.5 Repeat steps 5.2 to 5.4 until the parameters of the entire network model converge.

[0029] The present invention combines the traditional filtered back projection algorithm and convolutional neural network, and proposes an interpretable deep neural network structure for PET image reconstruction. The reconstruction problem is divided into three sub-problems: projection domain denoising, projection domain to image domain reconstruction, and image domain denoising, which are solved by pyramid convolution weighted denoising module, improved filtered back projection layer FBP, and improved denoising convolutional neural network DnCNN respectively. The pyramid convolution weighted denoising module denoises the low-dose projection domain data Sinogram to generate projection domain data close to the standard dose. The filtered back projection layer regards the frequency domain filter as learnable, and reconstructs the noisy reconstruction image from the denoised projection domain data Sinogram. The improved DnCNN removes a small amount of noise in the reconstructed image, thereby obtaining a high-quality reconstruction image. The present invention solves the problem that deep learning is difficult to explain when used for image reconstruction, and can still reconstruct high-quality PET images under low-dose conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a structural diagram of the network model SDFD-Net of the present invention.

[0031] Figure 2 Low doses in different frames for different methods 18 Schematic diagram of comparison of F-FDG reconstruction results.

[0032] Figure 3 Low doses in different frames for different methods 18 Schematic diagram of comparison of F-FDG reconstructed image quality indicators. DETAILED DESCRIPTION

[0033] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0034] The present invention combines a convolutional neural network with a filtered back-projection algorithm to perform low-dose Sinogram denoising and PET image reconstruction, and specifically includes the following steps:

[0035] (1) Data collection. The GATE toolkit was used to generate the simulation data required for the experiment. Monte Carlo simulation was used to generate normal-dose 3D dynamic Sinogram and PET data. Poisson distribution was used to downsample the normal-dose Sinogram projection data to obtain low-dose Sinogram projection data. Poisson downsampling was repeated 10 times to obtain a large number of samples, each of which included low-dose Sinogram projection data, normal-dose Sinogram projection data, and their corresponding PET images.

[0036] (2) Decompose and reconstruct the problem and determine the structure of the neural network. Figure 1 As shown, the reconstruction problem is divided into three sub-problems:

[0037] Y 1 =F 1 (Y), X 1 =F 2 (Y 1 ), X=F 3 (X 1 )

[0038] Sub-problem 1 is a denoising problem in the Sinogram projection domain. The original low-dose projection data Y is processed by the neural network F 1 (Y) Denoising, generating Sinogram projection data Y close to the standard dose 1 ; Sub-problem 2 is a reconstruction problem, which consists of the denoised projection data Y 1 The improved filtered back projection algorithm F 2 (Y 1 ) to obtain a preliminary reconstruction image X containing a small amount of noise 1 ; Sub-problem 3 is also a denoising problem, which consists of the initial reconstruction of image X 1 Through the neural network F 3 (X 1 ) to obtain a high-quality PET reconstructed image X.

[0039] (3) Training phase:

[0040] Initialize the parameters of SDFD-Net; use Kaiming initialization to initialize the parameters of the pyramid convolution weighted denoising module, use the ramp filter to initialize all frequency domain filters of the FBP layer, and use the truncated normal distribution to initialize the parameters in the improved DnCNN. Input the low-dose Sinogram of the training set into SDFD-Net, first train 50 epochs in stage 1 to converge the pyramid convolution weighted denoising module, then train 50 epochs in stage 2 to converge the FBP layer, and finally train the entire network for 100 epochs to converge the entire SDFD-Net. Calculate the output of each layer through the forward propagation formula to obtain the final output of SDFD-Net. In the verification stage, the trained model is verified every five epochs to supervise the effectiveness of the model training so that the parameters of the training stage can be adjusted in time.

[0041] Calculate the loss function between the output and label of the three stages of SDFD-Net:

[0042]

[0043] in: is the estimated value of the jth stage of the i-th sample output by SDFD-Net, X j (i) is the label of the jth stage of the ith sample. The partial derivative of the loss function is calculated, and the learnable parameters in SDFD-Net are updated through the Adam algorithm. The forward propagation and reverse derivation are repeated to continuously update the parameters of SDFD-Net until the value of the loss function is small enough and the model converges.

[0044] The specific training and reconstruction process is as follows:

[0045]

[0046] (4) Testing phase

[0047] The low-dose projection data Sinogram to be reconstructed is input into the trained SDFD-Net to directly obtain a high-quality reconstructed image.

[0048] Below we conduct experiments based on Monte Carlo simulation data to verify the effectiveness of the present invention. The entire algorithm of this embodiment is tested in a PC system, where the CPU is Core i9-10900k and the graphics card model is GeForce RTX 3080 (10GB video memory). In programming, the Pytorch1.10.0 platform is used to build the neural network. The platform is based on the Python language and can be used in combination in multiple program development environments.

[0049] The simulated tracer is 18 F-FDG, the phantom is a 3D brain phantom, and the equipment used in the GATE simulation is a 655k brain scanner from Hamamatsu Photonics Co., Ltd. The simulated scanning time is 40 minutes, the time frame is 18 frames, and the simulation data is randomly divided into a training set (1200 sinograms), a validation set (300 sinograms), and a test set (500 sinograms).

[0050] Figure 2 Shown are low doses of different methods in different frames 18 Comparison of F-FDG reconstruction images, from left to right, they are the reconstruction images of the FBP-Net algorithm, the reconstruction images of the U-Net algorithm, the reconstruction images of the DeepPET algorithm, the reconstruction images of the present invention, and the true value images reconstructed by the OSEM algorithm; from top to bottom, they are the reconstruction images of the 3rd, 9th, and 17th frames, respectively. As can be seen from the figure, the reconstruction images of the present invention are rich in details and low in noise, and are closest to the true value images; some non-existent structures appear at the edges of the reconstruction images of the U-Net and DeepPET algorithms, and the reconstruction images of FBP-Net are too smooth, losing some details, and are difficult to cope with low-dose reconstruction; therefore, the method of the present invention can obtain high-quality PET reconstruction images, and can still reconstruct high-quality images even under low-dose conditions. Figure 3 Low doses in different frames for different methods 18 The comparison indicators (SSIM and PSNR) of the F-FDG reconstruction images clearly show the quantitative advantages of the present invention.

[0051] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art to the present invention based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A low-dose Sinogram denoising and PET image reconstruction method based on convolutional neural network, comprising the following steps: (1) Acquire the simulated normal-dose Sinogram projection data, and use the OSEM reconstruction algorithm to reconstruct the normal-dose Sinogram projection data to obtain its corresponding PET image; (2) The normal-dose Sinogram projection data is downsampled using Poisson distribution to obtain low-dose Sinogram projection data. The specific implementation method is as follows: for the normal-dose Sinogram projection data, a random number matrix of the same size as the Sinogram matrix is ​​first generated based on the Poisson distribution using the Python built-in library function. By setting different normalization coefficients, the mean of the random number matrix is ​​set to different sizes. Then, by performing matrix dot multiplication, the mean of the Sinogram matrix is ​​reduced to one-n of the original, thereby obtaining low-dose Sinogram projection data, where n is the downsampling ratio. (3) acquiring a large number of samples according to steps (1) and (2), each sample including low-dose Sinogram projection data, normal-dose Sinogram projection data and their corresponding PET images; (4) The PET reconstruction problem is divided into the following three sub-problems: Sub-problem 1 is a Sinogram projection domain denoising problem, which generates Sinogram projection data Y1 close to the standard dose by denoising the low-dose Sinogram projection data through a neural network; Sub-problem 2 is a reconstruction problem, in which the Sinogram projection data Y1 is used to obtain a PET reconstructed image X1 containing a small amount of noise through an improved filtered back-projection algorithm; Sub-problem 3 is also a denoising problem. The PET reconstructed image X1 is denoised by a neural network to obtain a high-quality PET reconstructed image X. (5) Divide all samples into training sets and test sets, and build a network model consisting of a denoising module D1, a reconstruction module, and a denoising module D2 connected in sequence; The low-dose Sinogram projection data in the training set samples are used as the input of the denoising module D1, and the normal-dose Sinogram projection data are used as the true value label output by the denoising module D1; the output result of the denoising module D1 is used as the input of the reconstruction module, and the PET image corresponding to the normal-dose Sinogram projection data is used as the true value label output by the reconstruction module; the output result of the reconstruction module is used as the input of the denoising module D2, and the PET image corresponding to the normal-dose Sinogram projection data is used as the true value label output by the denoising module D2, so as to train the entire network model; The denoising module D1 adopts a pyramid convolution weighted denoising module, which is composed of 7 convolution blocks connected in sequence from input to output. The convolution block is composed of a pixel attention layer and a multi-scale convolution layer. The pixel attention layer is composed of two 3×3 2D convolution layers and a sigmoid activation function. The multi-scale convolution layer uses convolution kernels of 3×1, 1×3, 5×1, 1×5, 7×1, and 1×7 sizes for convolution operations, and splices the operation results of each convolution kernel together as output; The reconstruction module is based on an improved filtering back-projection algorithm, including two parts: frequency domain filtering and back-projection. The back-projection part is the same as the traditional filtering back-projection algorithm, while the frequency domain filtering part uses a learnable filter, and the projection data at each angle corresponds to an independent one-dimensional frequency domain filter. The denoising module D2 adopts an improved denoising convolutional neural network, which is composed of 8 2D convolutional layers and 1 normalization layer connected in sequence from input to output. Each 2D convolutional layer contains 64 3×3 convolution kernels. Except for the 8th convolutional layer, the outputs of the first 7 convolutional layers are processed by activation function ReLU and batch normalization BN. Then, the output of the 8th convolutional layer is subtracted from the input of the denoising module D2, and then a high-quality PET reconstructed image is obtained by outputting it through the normalization layer. (6) Inputting the low-dose Sinogram projection data in the test set samples into the trained network model, reconstructing the corresponding PET image, and comparing it with the PET image corresponding to the normal-dose Sinogram projection data; The above-mentioned low-dose Sinogram denoising and PET image reconstruction method combines the traditional filtered back projection algorithm and convolutional neural network, and proposes an interpretable deep neural network structure for PET image reconstruction. The reconstruction problem is divided into three sub-problems: projection domain denoising, projection domain to image domain reconstruction, and image domain denoising, which are solved by pyramid convolution weighted denoising module, improved filtered back projection layer FBP, and improved denoising convolutional neural network DnCNN respectively; the pyramid convolution weighted denoising module denoises the low-dose projection domain data Sinogram to generate projection domain data close to the standard dose, the filtered back projection layer regards the frequency domain filter as learnable, and reconstructs the noisy reconstruction image from the denoised projection domain data Sinogram, and the improved DnCNN removes a small amount of noise in the reconstructed image, thereby obtaining a high-quality reconstruction image.

2. The low-dose Sinogram denoising and PET image reconstruction method according to claim 1, characterized in that: The specific process of training the network model in step (5) is as follows: 5.1 Initialize the parameters of the network model; Kaiming is used to initialize the parameters in the denoising module D1, the Ramp filter is used to initialize all frequency domain filters in the reconstruction module, and the truncated normal distribution is used to initialize the parameters in the denoising module D2; 5.2 Input the low-dose Sinogram projection data in the training set samples into the network model. In stage 1, train for 50 epochs to make the denoising module D1 converge; in stage 2, train for another 50 epochs to make the reconstruction module converge; in stage 3, collaborative training for 100 epochs to make the entire network model converge, and finally calculate the output of each layer through the forward propagation formula to obtain the final output of the network model; 5.3 Calculate the loss function between the output of the three stages of the network model and the true value label: Among them: loss j is the loss function of the jth stage, X j (i) is the estimated value of the network model output corresponding to the i-th sample in the j-th stage, is the true value label of the i-th sample in the j-th stage, and N is the number of training samples in this stage; 5.4 Calculate the partial derivative of the loss function and update the learnable parameters in the network model through the Adam algorithm; 5.5 Repeat steps 5.2 to 5.4 until the parameters of the entire network model converge.

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