CN116152373A - Low-dose CT image reconstruction method combining neural network and convolutional dictionary learning - Google Patents
Low-dose CT image reconstruction method combining neural network and convolutional dictionary learning Download PDFInfo
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Abstract
The invention relates to a CT image reconstruction method combining convolutional neural network and convolutional dictionary learning. The method utilizes the priori of the network self-adaptive learning model, so that the model can be better suitable for reconstructing an image, the convolution dictionary learning is based on the whole image, the problem of boundary aggregation artifact can be effectively solved, and the network optimization is more visual due to the interpretability. The combination of the two can effectively remove noise and artifacts in the low-dose image, and can better keep image details.
Description
Technical Field
The invention relates to a low-dose CT image reconstruction method, in particular to a low-dose CT image reconstruction method combining neural network and convolution dictionary learning.
Background
The computed tomography (Computed Tomography, CT) technique has been widely used for clinical diagnosis, but a large amount of radiation causes irreversible damage to the human body, so the low-dose CT image reconstruction has important clinical research value. Existing reconstruction algorithms include filtered backprojection algorithms, iterative reconstruction algorithms, and statistical iterative reconstruction algorithms. The filtered back projection algorithm (FBP algorithm) has high requirements on data completeness, and can not generate ideal diagnostic image quality under the condition of low dosage; the iterative algorithm of algebraic iterative reconstruction, simultaneous algebraic iterative reconstruction and the like can improve the problem to a certain extent, but due to lack of additional prior knowledge, satisfactory results are difficult to obtain; statistical iterative algorithms incorporating image prior information in the reconstruction process have been shown to better remove noise and artifacts resulting from reduced radiation doses, with their associated objective functions generally consisting of two parts, the data fidelity term and the regularization term. The compressed sensing (Compressed Sensing, CS) theory proposed by Candes et al has demonstrated that data well below the nyquist sampling rate can be used to accurately recover the original signal. With the rise of CS, an image reconstruction method based on sparse representation is rapidly developed, and the total variation algorithm achieves the purpose of denoising by utilizing gradient minimization, but the image is assumed to be piecewise smooth, so that the reconstructed image has ladder artifacts; the image reconstruction method based on dictionary learning learns the dictionary from the image, and can obtain better sparse representation than the common method, but the image block-based method can lead the characteristic representation not to have translation invariance, and the dictionary atom high redundancy can lead the boundary of the reconstructed image to generate blocky aggregation artifact.
The method has the advantages that the method is the same as the traditional dictionary learning, the convolution dictionary learning has clear physical meaning, the translation invariance is modeled in an objective function, the whole image is subjected to sparse decomposition by using a convolution filter and a sparse feature map, and the boundary aggregation artifact in the dictionary learning based on image segmentation can be rapidly and effectively solved.
Inspired by deep learning, some low-dose CT image reconstruction methods based on convolutional neural networks are proposed successively. The convolutional neural network minimizes errors between the reconstructed image and the label image through a training process, and the network model has strong feature extraction capability, but has the defects that the required data volume is large and the logic of internal parameter optimization is difficult to understand. Based on the method, the invention provides a low-dose CT reconstruction method combining convolutional neural network and convolutional dictionary learning, and solves the problem of poor quality of CT reconstructed images under low dose by virtue of strong feature extraction capability of the convolutional neural network and interpretability of the convolutional dictionary learning. The method can effectively remove noise and artifacts, and can better preserve image details.
The traditional low-dose CT image reconstruction method based on dictionary learning and sparse representation is to divide and process images block by block, which leads to boundary aggregation artifacts of reconstructed images, and most image reconstruction methods use manual prior (such as L0 prior), which also leads to limited expression capacity of the learned dictionary on image structures.
Disclosure of Invention
The invention aims to provide a low-dose CT image reconstruction method combining convolutional neural network and convolutional dictionary learning. The method utilizes the prior of the network self-adaptive learning model, so that the model can be better suitable for reconstructing an image. The convolution dictionary learning is based on the whole image, so that the problem of boundary aggregation artifact can be effectively solved, and the network optimization is more visual due to the interpretability. The combination of the two can better remove noise and artifacts in the low-dose image.
The invention provides a low-dose CT image reconstruction method combining convolutional neural network and convolutional dictionary learning, which comprises the following steps:
step one: selecting a certain number of normal dose CT data sets, wherein the data sets comprise training sets and test sets;
step two: data initialization, namely collecting projection data of a CT image to be reconstructed, simulating projection data of a low-dose CT image by adding noise to normal-dose CT projection data, performing filtering back projection processing on noise projection to obtain an initial reconstructed image, obtaining an initial convolution sparse feature map through a sparse feature map initialization network, and initializing convolution dictionary atoms corresponding to the convolution sparse feature map to be all zeros;
step three: model training, namely decomposing a total objective function into three sub-problems, and training a network model by alternately updating a reconstructed image, a convolution sparse feature map and a convolution dictionary in each iteration;
step four: repeating the third step until the set iteration times, namely the stage number, are reached;
step five: calculating loss of the reconstructed image, updating the model, and storing the model after the loss is stable;
step six: and inputting the test set into the trained model to obtain a reconstructed CT image.
The low-dose CT image reconstruction method combining the convolutional neural network and the convolutional dictionary learning provided by the invention utilizes the advantages of the convolutional neural network and the convolutional dictionary learning, effectively combines the strong characteristic extraction capability of the network with the interpretability of the convolutional dictionary learning, and adaptively learns the convolutional dictionary and the prior for each image through the network.
According to the method, the objective function is built by means of the convolution dictionary learning and CT reconstruction principle, and the network module is solved and built based on the mathematical optimization theory, so that the logicality is stronger during model performance maintenance, noise and artifacts in images can be removed in the aspect of reconstruction effect, and more image details can be reserved.
Drawings
FIG. 1 is a flow chart of a low dose CT image reconstruction method incorporating convolutional neural network and convolutional dictionary learning in accordance with the present invention.
FIG. 2 is a schematic diagram of the structure of updating the reconstructed image, updating the convolution dictionary, and sparse feature map for each iteration of the present invention.
Fig. 3 is a schematic diagram of the structure of each module and the network in the present invention.
Detailed Description
In order to better understand the technical scheme of the present invention, the following detailed description of the technical scheme of the present invention is provided with reference to the accompanying drawings.
Step one: an appropriate CT data set is selected.
A certain number of normal dose CT data sets are selected, and the total number of the data sets selected in the experiment is 800, the size is 512×512, 765 data sets are used as training sets, and 35 data sets are used as test sets.
Step two: data initialization: projection data of an image to be reconstructed is acquired. The low-dose projection data is simulated by adding noise to the normal-dose projection data, and then the projection data after noise addition is subjected to filtering back projection processing, so that an initial reconstructed image is obtained. And obtaining an initial convolution sparse feature map through a sparse feature map initialization network, and initializing a convolution dictionary to be all zero.
Step 201): studies have shown that two major sources of CT projection data noise generation are X-ray quantum noise and system electronic noise. The projection of the log-pre-change received by the detector can be described by a statistically independent poisson distribution plus a statistically independent gaussian distribution, i.e.:
thus, the low dose projection data P is simulated by adding noise to the normal dose projections that follows a poisson distribution plus a gaussian distribution. Where λ is the expected value of the number of photons, m e Is a measure of the intensity of radiation collected by the detector, is an average of electronic noise (typically m e 0),
is the variance of the electronic noise.
Step 202): and initializing data. Obtaining an initialized reconstructed image Y by a Filtered Back Projection (FBP) algorithm 0 . Will initiate image Y 0 And estimated noise variance sigma i (namely, after two types of noise are added into the image, the integral noise variance) is brought into an initial module of convolution sparse coding (corresponding to a convolution sparse feature map initialization network in fig. 3), and m initial convolution sparse feature maps X= { X with the size of N multiplied by N are obtained 1 ,X 2 ,…,X m X is }, X i And corresponding convolution dictionary atom D i Initializing with all 0 s typically convolutionally dictionary atoms are much smaller in size than sparse feature maps. Wherein the noise variance sigma i Can be defined as:
wherein I is 0 For the number of incident photons (representing the intensity of the radiation before the ray reaches the body),
for the expected value of projection data on the ith detector (by adjusting I 0 And->
Can simulate the dose. )
Step three: and (5) model training. The overall objective function is decomposed into three sub-problems, and the network model is trained by updating the reconstructed image Y, the convolutional sparse feature map X, and the convolutional dictionary D alternately in each iteration.
Since the overall objective function is a problem that includes minimization of three variables (i.e., the image to be reconstructed Y, the convolution dictionary D, and the convolution sparse feature map X), for ease of solution, the overall objective function is decomposed into three sub-problems and these sub-problems are minimized alternately by means of separable parabolic agents and a semi-quadratic splitting algorithm, and the network model is trained by updating the reconstructed image Y, the convolution sparse feature map X, and the convolution dictionary D alternately in each iteration. The objective function may be expressed as:
wherein A is a system matrix, P is projection data, Y is an image to be reconstructed, Σ is a diagonal matrix, and matrix elements thereof are sigma i 2 ，D i Representing the ith convolution dictionary atom, X i For a sparse feature map corresponding to dictionary atoms, phi (X) represents the prior of the sparse feature map X,
representing regularized terms, beta, on dictionary D X And beta D Regularization parameters of X and D, respectively. Fig. 2 is a schematic structural diagram of the t-th alternate iterative update process.
Step 301) reconstructing an image with an iterative reconstruction algorithm
The time interval between the t (t=1, 2, during M) iterations, the result after the last iteration, namely the image Y (t-1) Convolving sparse feature map Y (t-1) And convolutional sparse coding D (t-1) Inputting into an image reconstruction module, and processing the image by adopting a certain reconstruction method (gradient descent algorithm, conjugate gradient descent algorithm, separable parabolic proxy method, etc.) to obtain a reconstructed image Y (t) 。
Step 302): and calculating a noise standard deviation according to the noise variance in the step 202, and inputting the standard deviation into a super-parameter prediction network (corresponding to the super-parameter prediction network in fig. 3) to obtain an initial value of a super-parameter required by the follow-up.
Taking the noise standard deviation (shown in formula 3) in the projection data as input, adding the noise standard deviation into a designed super-parameter prediction module to obtain super-parameter alpha required by each iteration in the reconstruction process X(t) 、α D(t) 、λ X(t) And lambda (lambda) D(t) (4 super-parameters needed to update the convolution dictionary D and the convolution sparse feature map X, which correspond to the coefficient parameters in the solution algorithm).
Step 303): updating convolution dictionary and convolution sparse feature map
Using the reconstruction result Y in step three (t) Updating a convolved sparse feature map X by introducing two auxiliary variables X' and D (t) Convolution dictionary D (t) 。
Step 303-1): the sparse feature map is updated (corresponding to "solving the convolutional sparse feature map X network" in map three). Will exceed the parameter alpha X(t) Reconstructing an image Y by current iteration (t) X from the previous iteration (t-1) And (3) carrying out a ' solving auxiliary variable X ' module '. To obtain the corresponding closed-form solution, X 'is obtained by adopting a method based on fast Fourier transform' (t) . X 'is to' (t) And super parameter lambda X(t) Splicing to obtain X 'with channel number added with 1' (t) (the multiple channel is lambda) X(t) ). Then inputting the spliced result into the module, and learning to obtain more information by utilizing the strong characteristic extraction capability of the convolutional neural networkNew convolution sparse feature map X (t) 。
Step 303-2): the convolution dictionary is updated (corresponding to the "solve convolution dictionary network" in fig. 3). X is to be (t) 、D (t-1) Current reconstructed image Y (t) Super parameter alpha D(t) Input into a ' solving auxiliary variable D ' module ', and the obtained result D ( ' t) And super parameter lambda D(t) Splicing, and then obtaining a convolution dictionary D after the iteration by utilizing a convolution dictionary solving network to the splicing result (t) . At update D ( ' t) In the module (c), a corresponding closed-form solution is obtained using a least squares method.
Step four: repeating the third step until the set iteration times are reached
Step five: and calculating loss of the reconstructed image, updating the model, and storing the model after the loss is stable.
And calculating loss of the final iteration result and the normal dose image by using an L1 norm, and carrying out back propagation according to the obtained loss to update the network parameters, the convolution dictionary D and the convolution sparse feature map X, and storing the trained model after the model is stable. Wherein the learning rate in the back propagation is dynamically changed according to the epoch in the training, for example: the learning rate was halved at 50 th and 100 th epochs. Wherein, the complete traversal of all image reconstructions of the training set is recorded as one epoch.
Step six: and inputting the test set into the trained model to obtain a reconstructed CT image.
The test image is read and subjected to the same data initialization step as the training set (adding noise to its projections to simulate low dose projection data). And reconstructing the low-dose projection data of the test image by using the model obtained by training to obtain a low-dose CT reconstructed image with higher quality.
Claims (10)
1. A low-dose CT image reconstruction method combining convolutional neural network and convolutional dictionary learning comprises the following steps:
step one: selecting a certain number of normal dose CT data sets, wherein the data sets comprise training sets and test sets;
step two: data initialization, namely collecting projection data of a CT image to be reconstructed, simulating projection data of a low-dose CT image by adding noise to normal-dose CT projection data, performing filtering back projection processing on noise projection to obtain an initial reconstructed image, obtaining an initial convolution sparse feature map through a sparse feature map initialization network, and initializing convolution dictionary atoms corresponding to the convolution sparse feature map to be all zeros;
step three: model training, namely decomposing a total objective function into three sub-problems, and training a network model by alternately updating a reconstructed image Y, a convolution sparse feature map X and a convolution dictionary D in each iteration;
step four: repeating the third step until the set iteration times, namely the stage number, are reached;
step five: calculating loss of the reconstructed image, updating the model, and storing the model after the loss is stable;
step six: and inputting the test set into the trained model to obtain a reconstructed CT image.
2. The method of claim 1, wherein the two main sources of CT projection data noise are X-ray quantum noise and system electronic noise, and the projections received by the detector before logarithmic change can be described by a statistically independent poisson distribution plus a statistically independent gaussian distribution, namely:
modeling low dose projection data P by adding to the normal dose projection a poisson distribution-compliant plus gaussian noise, where λ is the desired value of the number of photons, a measure of the intensity of radiation collected by the detector, m e Is the mean value of the electronic noise (typically m e 0),
is the variance of the electronic noise.
3. A low dose CT image reconstruction method as claimed in claim 1 or 2, wherein the initialized reconstructed image Y is obtained by a Filtered Back Projection (FBP) algorithm 0 Will initiate image Y 0 And estimated noise variance sigma i The initial convolution sparse feature images X= { X with m pieces of size of N multiplied by N are obtained by being carried into an initial module of convolution sparse coding 1 ,X 2 ,…,X m Initializing the corresponding convolution dictionary atoms with all 0 s, typically the convolution dictionary atoms are much smaller in size than the sparse feature map. Wherein the noise variance may be defined as:
wherein I is 0 In order to be able to count the number of incident photons,
is the expected value of the projection data on the i-th detector.
4. The low dose CT image reconstruction method according to claim 1, wherein the sub-problems are alternately minimized by means of separable parabolic proxy and a semi-quadratic splitting algorithm, the network model is trained by alternately updating the reconstructed image Y, the convolved sparse feature map X and the convolved dictionary D in each iteration, the objective function being representable as:
wherein A is a system matrix, P is projection data, Y is an image to be reconstructed, Σ is a diagonal matrix, and matrix elements thereof are
D i Representing the ith convolution dictionary atom, X i For the sparse feature map corresponding to dictionary atom, phi (X) represents the prior,/-for the sparse feature map X>
Representing regularized terms, beta, on dictionary D X And beta D Regularization parameters of X and D, respectively.
5. A method of reconstructing a low dose CT image as claimed in claim 1 or 4, wherein the image is reconstructed by an iterative reconstruction algorithm, the time interval between the t (t=1, 2, during M) iterations, the result after the last iteration, namely the image Y (t-1) Convolution sparse feature map X (t-1) And convolutional sparse coding D (t-1) Inputting into an image reconstruction module, and processing the image by adopting a certain reconstruction method to obtain a reconstructed image Y (t) 。
6. The method of reconstructing a low dose CT image as recited in claim 5, wherein a convolution dictionary and a convolution sparse feature map are updated and the reconstruction result Y in step three is utilized (t) Updating a convolved sparse feature map X by introducing two auxiliary variables X' and D (t) Convolution dictionary D (t) 。
7. The method of low-dose CT image reconstruction as recited in claim 6, wherein the sparse feature map is updated by adding the standard deviation of noise in the projection data of claim 3 as input to a designed super-parametric prediction module to obtain 4 super-parameters α required for iteratively updating the convolution dictionary D and the convolution sparse feature map X during reconstruction X(t) 、α D(t) 、λ X(t) And lambda (lambda) D(t) These super-parameters correspond to the coefficient parameters in the solution algorithm. Will exceed the parameter alpha X(t) Reconstructing an image Y by current iteration (t) X from the previous iteration (t-1) The solution auxiliary variable module is carried in, and in order to obtain the corresponding closed solution, the solution is adoptedMethod for obtaining X 'based on fast Fourier transform' (t) . X 'is to' (t) And super parameter lambda X(t) Splicing to obtain X 'with channel number added with 1' (t) The multiple channel is lambda X(t) Then inputting the spliced result into the module, and learning to obtain an updated convolution sparse feature graph X by utilizing the strong feature extraction capability of the convolution neural network (t) 。
8. The method of low dose CT image reconstruction as recited in claim 7 wherein the convolution dictionary is updated to X (t) 、D (t-1) Current reconstructed image Y (t) Super parameter alpha D(t) Input into a solving auxiliary variable module, and obtain a result D ( ' t) And super parameter lambda D(t) Splicing, and then obtaining a convolution dictionary D after the iteration by utilizing a convolution dictionary solving network to the splicing result (t) . At update D ( ' t) In the module (c), a corresponding closed-form solution is obtained using a least squares method.
9. The method for reconstructing a low dose CT image according to claim 1, wherein the loss is calculated by using L1 norm for the result of the last iteration and the normal dose image, and back propagation is performed according to the obtained loss, so as to update the network parameters, the convolution dictionary D and the convolution sparse feature map X, and after the model is stabilized, the trained model is saved.
10. The method for reconstructing a low dose CT image according to claim 1, wherein the test image is read, and the same data initialization step as the training set is performed, noise is added to the projections thereof to simulate the low dose projection data, and the low dose projection data of the test image is reconstructed by using the model obtained by training to obtain a high quality low dose CT reconstructed image.
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| CN116844734B (en) * | 2023-09-01 | 2024-01-16 | 福建自贸试验区厦门片区Manteia数据科技有限公司 | Method and device for generating dose prediction model, electronic equipment and storage medium |
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