CN109584324B - Positron Emission Tomography (PET) reconstruction method based on automatic encoder network - Google Patents
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Abstract
The invention provides a Positron Emission Tomography (PET) reconstruction method based on an automatic encoder network, which comprises the following steps: step A: establishing a Denoising Automatic Encoder (DAE) network model on the basis of a positron emission computed tomography (PET) image, and acquiring prior information of the image by using a trained Denoising Automatic Encoder (DAE); and B: the invention integrates a Denoising Automatic Encoder (DAE) network based on a Positron Emission Tomography (PET) reconstruction method, adopts the Denoising Automatic Encoder (DAE) network to learn the prior information of the PET image without supervision, then combines the DAE network with the image prior information with the traditional PET iterative reconstruction method, and alternately iterates the two to obtain the reconstructed image, thereby achieving good reconstruction effect.
Description
Technical Field
The invention relates to the technical field of medical image processing, which is mainly used in the fields of denoising, recovering, reconstructing and the like of electronic Computed Tomography (CT), positron emission computed tomography (PET), medical noisy images, and the like, in particular to a positron emission computed tomography (PET) reconstruction method based on an automatic encoder network.
Background
Positron Emission Tomography (PET) is currently the only new imaging technique that can display biomolecular metabolism, receptor and neuromediator activity in vivo, and is an important tool for tumor research and clinical diagnosis and treatment. PET reconstruction is a method of reconstructing a functional image acceptable to a clinician from low-tech-rate and noise-affected projection sinusoidal data. Due to the detector fuzzy effect, positron range and photon nonlinearity, the existing PET reconstructed image has the problems of poor resolution, unclear anatomical structure, inaccurate anatomical positioning, large Poisson noise and the like. At the same time, the limited number of photons in the PET data requires spatial smoothing to reduce noise.
In PET reconstruction, the measurement data y ∈ R M×1 Can be modeled as an independent Poisson randomSet of machine variables by affine transformation
And unknown image x ∈ R N×1 The relationship of (a) to (b) is as follows:
P∈R M×N is a detection probability matrix, P ij Representing the probability of detecting a photon originating from voxel j by detector i. s is formed by R M×1 And R ∈ R M×1 Respectively, representing scatter coincidence and random coincidence data. M is the number of lines of response (LOR) and N is the number of pixels in image space.
PET reconstruction methods include analytical methods and iterative methods. The analytic methods may be classified into a filtered back projection method (FBP), a back projection filtering method (BFP), a ρ -filter, a convolution back projection method, and the like, according to a specific calculation process. Most representative is a filtered back projection method, an algorithm of which is based on Radon (Radon) transform and fourier slice theorem, although an analysis method of which is fast, the noise immunity is poor, noise in original data is large, data is relatively undersampled, and a satisfactory reconstructed image is difficult to obtain.
Iterative reconstruction algorithms include Maximum Likelihood (MLEM), ordered subset maximum likelihood (OSEM), algebraic Reconstruction (ART), simultaneous Iterative Reconstruction (SIRT), conjugate Gradient (CGM), weighted Least Squares (WLS), maximum A Posteriori (MAP), etc. MLEM algorithms since the inverse problem of solving the emission distribution from the measurement data is an ill-defined problem, an iterative expectation-maximization algorithm that seeks a maximum likelihood solution can result in increased noise once the iteration reaches a certain point. The MAP algorithm, while eliminating divergence at higher iterations, the traditional smoothing priors or total variation previously resulted in excessive smoothing or artifacts in the reconstructed image.
The existing Positron Emission Tomography (PET) reconstruction method based on the automatic encoder network has the problems of high noise, excessive smoothness and artifacts.
How to design a Positron Emission Tomography (PET) reconstruction method based on an automatic encoder network to solve the problems proposed in the background art.
Disclosure of Invention
In view of the above-mentioned problems, the present invention aims to provide a Positron Emission Tomography (PET) reconstruction method based on an automatic encoder network, which is practical, excellent in performance and strong in environmental adaptability.
In order to achieve the purpose, the invention provides the following technical scheme: a Positron Emission Tomography (PET) reconstruction method based on an automatic encoder network comprises the following steps:
step A: establishing a Denoising Automatic Encoder (DAE) network model on the basis of a positron emission computed tomography (PET) image, and acquiring prior information of the image by using a trained Denoising Automatic Encoder (DAE);
PET reconstruction image mathematical model: measurement data y ∈ R M×1 Can be modeled as a set of independent Poisson random variables, transformed by affine
And unknown image x ∈ R N×1 The relationship of (a) to (b) is as follows:
wherein P ∈ R M×N Is a detection probability matrix, P ij Representing the probability of a photon originating from voxel j being detected by detector i, s ∈ R M×1 And R ∈ R M×1 Respectively representing scatter and random coincidence data, M is the number of lines of response (LOR), N is the number of pixels in image space, and the log-likelihood function is:
the maximum likelihood estimate of the unknown image x is:
and B, step B: combining a Denoising Automatic Encoder (DAE) network with image prior information with a traditional PET iterative reconstruction method, and alternately iterating the Denoising Automatic Encoder (DAE) network and the traditional PET iterative reconstruction method to obtain a reconstructed image.
Further, the step a specifically includes:
(1) The method comprises the following specific steps of establishing a DAE network model:
the DAE network consists of 20 convolution layers, wherein batch normalization is carried out between the layers except the 1 st layer and the 20 th layer, except the 20 th layer, the activation is carried out by using a linear rectification function (ReLU), the size of a convolution kernel is 3 multiplied by 3, the number of input and output channels is 3 (RGB), and the number of the other layers is 64;
the output of the optimal DAE network is the local mean of the true data density, and the denoised auto-encoder (DAE) error (the difference between the output and the input of the trained auto-encoder) is the average shift vector, the size of this average shift vector is used as the negative log-likelihood of the image prior, for image reconstruction, the probability of using the gradient descent is maximized by back-propagating the auto-encoder error, a ση (I) Representing the DAE network, the input image is I, the output of the DAE network is A ση (I)，
The DAE is trained by minimizing a cost function:
wherein the Gaussian noise η has a variance
A ση Indicating DAE as noise variance
Training, noise variance
And the degraded noise and its variance
Irrelevant, it is a specified parameter;
(2) Obtaining prior information of an image by using a DAE network, wherein L (I) = | | | A ση (I)-I|| 2 Measuring image I and local average value A thereof in true data density ση (I) The proximity of (a).
Further, the step B specifically includes:
(1) In the step B, the conventional iterative reconstruction method takes a maximum likelihood method (MLEM) as an example, and the corresponding steps are as follows:
and E: get the desired X by ML, construct alternate iterations:
and step M: will find Z ij Carry-in, let the partial derivative equal 0:
(2) Combining a Denoising Automatic Encoder (DAE) network with image prior information and an MLEM reconstruction method, and alternately iterating the two methods to obtain a reconstructed image;
wherein P ∈ R M×N Is a detection probability matrix, x is an unknown image, and gamma is a relative influence used for weighting the data item and the prior information; the DAE network iteration process is as follows: the first step is as follows: computing data items relative to an image
A gradient of (a); the second step is that: calculating the gradient of prior information, and averaging the moving vector | | | A ση (I)-I|| 2 The gradient of (A) is required fromDynamic encoder A ση (I) The gradient of (c), back-propagating the computation through the network; the final step updates the image I using a weighted sum of the two gradient terms.
Compared with the prior art, the invention has the beneficial effects that:
the invention integrates a de-noising automatic encoder (DAE) network on the basis of a positron emission computed tomography (PET) reconstruction method, unsupervised learning of prior information of a PET image is carried out by adopting the de-noising automatic encoder (DAE) network, then the DAE network with the image prior information is combined with a traditional PET iterative reconstruction method, and the two are alternately iterated to obtain a reconstructed image, thereby achieving good reconstruction effect.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a neural network framework constructed in accordance with the present invention;
FIG. 3 is a flowchart of a loop through the algorithmic process of the present invention;
FIG. 4 is a diagram of a test apparatus according to the present invention; (a) is a true emission image; (b) is an attenuation map; (c) is the sum of the mask and the true emission image; (d) a noise-free projection data map; (e) a noisy projection data map; (f) reconstructing an image for the FBP;
FIG. 5 is a graph of results of a conventional iterative algorithm; (a) is a result graph of a traditional MLEM algorithm; (b) is a result graph of a traditional OSEM algorithm; (c) is a result graph of the E-ML-INC-EM1 algorithm; (d) is a result graph of the E-ML-INC-EM3 algorithm; (e) is a PL-OS-EMDP algorithm result graph; (f) is a PL with point characteristics algorithm result graph;
FIG. 6 is a comparison of the results of a conventional iterative algorithm and the reconstruction of the present invention; (a) is an original image; (b) reconstructing a result graph for the traditional OSEM algorithm; (c) reconstructing a result graph by using a traditional MLEM algorithm; (d) is a reconstruction result graph of the E-ML-INC-EM-3 algorithm; (E) reconstructing a result graph by using an E-PL-OS-EMDP algorithm; (f) reconstructing a result graph according to the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. The embodiments described herein are only for explaining the technical solution of the present invention and are not limited to the present invention.
The invention provides a technical scheme that: a Positron Emission Tomography (PET) reconstruction method based on an automatic encoder network comprises the following steps:
step A: establishing a Denoising Automatic Encoder (DAE) network model on the basis of a positron emission computed tomography (PET) image, and acquiring prior information of the image by using a trained Denoising Automatic Encoder (DAE);
PET reconstructed image mathematical model: measurement data y ∈ R M×1 Can be modeled as a set of independent Poisson random variables, transformed by affine
Unknown image x ∈ R N×1 The relationship of (a) to (b) is as follows:
wherein P ∈ R M×N Is a detection probability matrix, P ij Representing the probability of a photon originating from voxel j being detected by detector i, s ∈ R M×1 And R ∈ R M×1 Respectively representing scatter and random coincidence data, M is the number of lines of response (LOR), N is the number of pixels in image space, and the log-likelihood function is:
the maximum likelihood estimate of the unknown image x is:
and B, step B: combining a Denoising Automatic Encoder (DAE) network with image prior information with a traditional PET iterative reconstruction method, and alternately iterating the Denoising Automatic Encoder (DAE) network and the traditional PET iterative reconstruction method to obtain a reconstructed image.
Further, the step a specifically includes:
(1) The method comprises the following specific steps of establishing a DAE network model:
as shown in fig. 2, the DAE network consists of 20 convolutional layers, with the exception of layer 1 and layer 20, between which batch normalization is performed, with the exception of layer 20, activation using a linear rectification function (ReLU), the size of the convolutional kernel being 3 × 3, the number of input and output channels being 3 (RGB), and the remaining layers being 64;
the output of the optimal DAE network is the local mean of the true data density, and the denoised auto-encoder (DAE) error (the difference between the output and the input of the trained auto-encoder) is the average shift vector, the size of this average shift vector is used as the negative log-likelihood of the image prior, for image reconstruction, the probability of using the gradient descent is maximized by back-propagating the auto-encoder error, a ση (I) Representing the DAE network, the input image is I, the output of the DAE network is A ση (I)，
The DAE is trained by minimizing a cost function:
wherein the Gaussian noise η has a variance
A ση Indicating DAE as noise variance
Training, noise variance
And the variance of the degraded noise
Irrelevant, it is a specified parameter;
(2) Obtaining prior information of an image by using a DAE network, wherein L (I) = | | | A ση (I)-I|| 2 Measuring image I and local average value A thereof in true data density ση (I) The proximity of (a).
Further, the step B specifically includes:
(1) In the step B, the conventional iterative reconstruction method takes a maximum likelihood method (MLEM) as an example, and the corresponding steps are as follows:
and E: get the desired X through ML, construct alternate iterations:
and step M: will find Z ij Carry-in, let the partial derivative equal 0:
(2) Combining a Denoising Automatic Encoder (DAE) network with image prior information and an MLEM reconstruction method, and alternately iterating the two methods to obtain a reconstructed image;
wherein P ∈ R MxN Is a detection probability matrix, x is an unknown image, and gamma is a relative influence used for weighting the data item and the prior information; the DAE network iteration process is as follows: the first step is as follows: computing data items relative to an image
A gradient of (a); the second step: calculating the gradient of prior information, and averaging the moving vector | | | A ση (I)-I|| 2 The gradient of (2) requires an automatic encoder A ση (I) The gradient of (c), back-propagating the computation through the network; the last step uses two laddersThe weighted sum of the degree terms updates the image I.
| Algorithm | PSNR | SSIM |
| Traditional-FBP | 24.4681 | 0.6755 |
| Traditional-OSEM | 22.6343 | 0.7961 |
| Traditional-MLEM | 24.8795 | 0.8320 |
| E-ML-INC-EM-1 | 25.3645 | 0.8225 |
| E-PL-OS-EMDP | 21.8457 | 0.7873 |
| The invention | 30.3197 | 0.9275 |
The experimental results in the table show that the two indexes of the peak signal-to-noise ratio (PSNR) and the Structural Similarity (SSIM) of the image reconstructed by the optimized algorithm are higher than those of the image reconstructed by the traditional algorithm, so that a satisfactory effect is achieved.
The foregoing merely represents preferred embodiments of the invention, which are described in some detail and detail, and therefore should not be construed as limiting the scope of the invention. It should be noted that, for those skilled in the art, various changes, modifications and substitutions can be made without departing from the spirit of the present invention, and these are all within the scope of the present invention. Therefore, the protection scope of the present patent should be subject to the appended claims.
Claims (1)
1. A Positron Emission Tomography (PET) reconstruction method based on an automatic encoder network is characterized by comprising the following steps: the method comprises the following steps:
step A: establishing a Denoising Automatic Encoder (DAE) network model on the basis of a Positron Emission Tomography (PET) image, and acquiring prior information of the image by using a trained Denoising Automatic Encoder (DAE);
PET reconstructed image mathematical model: measurement data
Can be modeled as a set of independent Poisson random variables, transformed by affine
And unknown images
The relationship of (a) to (b) is as follows:
wherein,
is a matrix of the probability of detection,
is represented by a detector
Detecting origin of voxels
The probability of a photon of (a) is,
and
respectively representing scatter coincidence and random coincidence data,
is the number of lines of response (LOR),
is the number of pixels in image space, and the log-likelihood function is:
unknown image
The maximum likelihood estimate of (c) is:
and B: combining a Denoising Automatic Encoder (DAE) network with image prior information with a traditional PET iterative reconstruction method, and alternately iterating the Denoising Automatic Encoder (DAE) network and the traditional PET iterative reconstruction method to obtain a reconstructed image;
the step A specifically comprises the following steps:
(1) The method comprises the following specific steps of establishing a DAE network model:
the DAE network consists of 20 convolutional layers, with the exception of layer 1 and layer 20, between which batch normalization is performed, with the exception of layer 20, which is activated using a linear rectification function (ReLU), with the size of the convolutional kernel being
The number of input and output channels is 3 (RGB), and the remaining layers are 64;
the output of the optimal DAE network is the local mean of the true data density and the denoised auto-encoder (DAE) error is the mean shift vector, the size of this mean shift vector is used as the negative log-likelihood of the image prior, for image reconstruction, the probability of using the gradient descent is maximized by back-propagating the auto-encoder error,
representing a DAE network, the input image is I, the output of the DAE network is
，
Then the DAE is trained by minimizing a cost function:
wherein, gaussian noise
Having a variance
，
Indicating DAE as noise variance
Training, noise variance
And the variance of the degraded noise
Irrelevant, it is a specified parameter;
(2) Obtaining a priori information about the image using the DAE network
Measuring image I and its local average value in real data density
The proximity of (a);
the step B specifically comprises the following steps:
(1) In the step B, the conventional iterative reconstruction method takes a maximum likelihood method (MLEM) as an example, and the corresponding steps are as follows:
and E: get the desired X through ML, construct alternate iterations:
and step M: will find out
Carry-in, let the partial derivative equal 0:
(2) Combining a Denoising Automatic Encoder (DAE) network with image prior information and an MLEM reconstruction method, and alternately iterating the two methods to obtain a reconstructed image;
wherein,
is a matrix of the probability of detection,
in order to be an unknown image,
is used to weight the relative influence of the data item and the prior information; the DAE network iteration process is as follows: the first step is as follows: computing data items against an image
A gradient of (a); second step, calculating the gradient of prior information and averaging the moving vector
Gradient of (2) requires an automatic encoder
The gradient of (c), back-propagating the computation through the network; the final step updates the image I using a weighted sum of the two gradient terms.
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| CN111627082B (en) * | 2020-05-21 | 2022-06-21 | 浙江大学 | PET image reconstruction method based on filtering back projection algorithm and neural network |
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