CN116312983B - Hidden regularization low-dose CT image reconstruction method and system based on noise generation mechanism - Google Patents
Hidden regularization low-dose CT image reconstruction method and system based on noise generation mechanism Download PDFInfo
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Abstract
The invention discloses a hidden regularization low-dose CT image reconstruction method based on a noise generation mechanism, which expands the optimization problem of low-dose CT reconstruction based on the noise generation mechanism into a hidden regularization depth network NGMNet, trains parameters of the hidden regularization depth network NGMNet to obtain a depth network model of low-dose projection data reconstruction, and inputs low-dose projection data into the depth network model to optimize to obtain a reconstructed CT image; each operation unit of the hidden regularization depth network NGMNet comprises three network layers: a projection domain updating layer, a chord domain updating layer and an image domain updating layer; the projection domain updating layer, the chord domain updating layer and the image domain updating layer respectively correspond to updating rules of the projection domain Q, the chord domain Y and the image domain X when the framework of the low-dose CT reconstruction based on a noise generation mechanism is solved; according to the noise generation model solving process, the hidden regularization depth network from end to end is developed, and high-quality CT images can be recovered under the condition of extremely low dosage.
Description
Technical Field
The invention belongs to the field of image processing based on deep learning, and particularly relates to a hidden regularization low-dose CT image reconstruction method and system based on a noise generation mechanism.
Background
X-ray Computed Tomography (CT) is currently widely used in clinical examinations, but CT has ionizing radiation, which causes ionizing radiation damage to the human body after penetrating the human body. Therefore, reducing the scanning dose as much as possible under the premise of meeting clinical requirements is a hot spot problem of CT medical imaging research.
Generally, the simplest method of reducing the scan dose is to reduce the tube current [1], however, the dose reduction causes the image reconstruction to suffer from photon starvation effects and measurement noise, which can produce serious noise and artifacts. A number of CT reconstruction algorithms have been proposed to address this problem. The existing CT reconstruction method mainly comprises three types: (1) a projection recovery algorithm; (2) an image post-processing algorithm; (3) iterating a reconstruction algorithm;
the projection recovery algorithm is to recover projection data by combining the statistical characteristics of the measured noise and the priori knowledge model, and then reconstruct the recovered projection data by using the filtered back projection algorithm FBP. However, the loss of the original detail information of the image is inevitably caused in the process of denoising the projection data, so that the resolution of the corresponding CT image is reduced. The image post-processing algorithm directly processes the image after the low-dose reconstruction, can improve the signal to noise ratio of the low-dose CT image, and better retains the image edge information. In recent years, low-dose CT imaging technology based on deep learning is widely studied, and the core idea is to learn the nonlinear mapping from a low-dose CT image to a standard-dose CT image in a data-driven mode, and particularly, the introduction of a convolutional neural network brings technical support for training a deep learning model. However, the image post-processing method does not take into account the statistical properties of the projection domain data, and thus the algorithm performance is limited. The iterative reconstruction algorithm mainly utilizes noise statistical characteristics of measured data and prior information of an image domain to construct an objective function, and then solves a CT image with high quality through optimizing the objective function. However, the iterative reconstruction method needs to perform repeated iterative solution on the objective function for many times, the time cost and the calculation cost of CT image reconstruction are greatly increased, and the imaging of the method cannot meet the requirement of clinical CT real-time imaging.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a hidden regularization low-dose CT image reconstruction method based on a noise generation mechanism, which reconstructs images based on a deep learning model without a large amount of iterative computation work and solves the problems in the prior art.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: the hidden regularization low-dose CT image reconstruction method based on the noise generation mechanism is characterized by comprising the following steps of:
expanding the problem of low-dose CT reconstruction based on a noise generation mechanism into a hidden regularized depth network NGMNet, performing end-to-end training on the hidden regularized depth network NGMNet to obtain a depth network model of low-dose projection data reconstruction,
inputting low-dose projection data into the depth network model for optimization to obtain a reconstructed CT image;
wherein, each operation unit of the hidden regularization depth network NGMNet comprises three network layers: a projection domain updating layer, a chord domain updating layer and an image domain updating layer; the projection domain updating layer, the chord domain updating layer and the image domain updating layer respectively correspond to updating rules of the projection domain Q, the chord domain Y and the image domain X when the framework of the low-dose CT reconstruction based on a noise generation mechanism is solved;
the framework for low dose CT reconstruction based on noise generation mechanisms is as follows:
a is Ladong transformation, i is projection path, g 1(Y) and g2 (X) a priori terms representing chord domain Y and image domain X, respectively, lambda 1 ，λ 2 Is a regularized term parameter.
The CT noise generation model is as follows:
taking the negative logarithm of the above method, and solving and converting the negative logarithm into:
I 0 the intensity of the X-ray incident along the projection path is represented, i is the projection path, the image domain data X and the chord domain data Y are considered to be optimized, the prior knowledge is considered for the chord domain Y, and finally, the frame of the low-dose CT reconstruction based on the noise generation mechanism is obtained.
The network structure is as follows:
projection domain update layer Q (n) ：
Chord domain update layer Y (n) ：
Image domain update layer X (n) ：
wherein ,modeling a near-end operator by adopting a deep network architecture pro_net for the near-end operator, and further implicitly learning the regularization term; the pro_net adopts a U-Net network architecture to learn, the variance sigma of the electronic background noise is set as a learnable parameter, and the parameters to be learned include: pro_net network parameters, σ, η 1 、η 2 、η 3 ；η 1 、η 2 、η 3 To update step size, Y n-1 Is the updated result obtained by the (n-1) th iterative computation, X n-1 Is the updated result obtained by the (n-1) th iterative computation, Q n-1 The updating result obtained by the (n-1) th iterative computation is obtained, and C is the Euler constant.
And when the parameters of the hidden regularized depth network NGMNet are trained, performing end-to-end network training by adopting low-dose projection data and standard-dose image data, using MSELoss as a loss function, calculating the gradient of the loss function relative to the network parameters through back propagation, and optimizing the network parameters by adopting an Adam optimizer.
Constructing the noise generation model includes the steps of:
in an ideal clean/noiseless environment, the original projection data P scanned by CT has the following relationship with chord chart data Y:
wherein I0i A generation model representing the intensity of X-rays incident along projection path i to construct noisy projection data P is expressed in the form:
P＝Q+ε (2)
wherein Representing the quantum number received by the detector; />Representing electronic background noise, the first term representing an X-ray photon statistic; the second term represents electronic background noise; let the electronic background noise epsilon follow a non-stationary gaussian distribution of zero mean:
wherein σ2 Representing the variance of noise, obtained by imaging system parameters of modern CT equipment;
quantum noise approximately follows the poisson distribution law of polychromatic X-ray generation:
wherein Gi The ray intensity in an ideal environment is represented by Y, which is ideal "chord graph data", according to beer-lambert law:
combining formula (4) and formula (5) yields the following conditional distribution, i.e., a complex poisson distribution:
the following conditional distributions are obtained by combining the formula (2) and the formula (3):
to sum up, the posterior distribution of the complete data is obtained:
the maximum a posteriori estimation in the CT image denoising problem refers to: under the condition of knowing low-dose projection data P, searching the most possible 'chord graph data' Y without noise, and obtaining the complete posterior distribution of parameters Q and Y to be estimated according to the Bayesian theory:
and (3) obtaining a CT noise generation model according to the formula (9).
And during network training, a plurality of stages are adopted for iterative optimization, so that the denoising effect is improved.
In addition, the invention also provides a computer device, which comprises a processor and a memory, wherein the memory is used for storing a computer executable program, the processor reads the computer executable program from the memory and executes the computer executable program, and the processor can realize the hidden regularization low-dose CT image reconstruction method based on the noise generation mechanism when executing the computer executable program.
A computer readable storage medium may also be provided, in which a computer program is stored, which when executed by a processor, enables the implementation of the method for hidden regularization low-dose CT image reconstruction based on a noise generation mechanism described herein.
Compared with the prior art, the invention has at least the following beneficial effects: the hidden regularization low-dose CT image reconstruction method based on the noise generation mechanism traces the source noise generated by low dose, and expands the source noise into an end-to-end hidden regularization depth network according to the solving process of the noise generation model, so that a high-quality CT image can be recovered under the condition of extremely low dose, and clinical application can be better served; aiming at the problem of low optimization speed in the traditional iterative algorithm, the hidden regularization low-dose CT image reconstruction method based on the noise generation mechanism can quickly reconstruct images after training the high-quality CT training data pair, so that the problems of low optimization speed and the like of the iterative algorithm are effectively solved; the end-to-end training model provided by the hidden regularization low-dose CT image reconstruction method based on the noise generation mechanism effectively solves the problem that the gap between the noise generation and the CT reconstruction images in the prior art is overcome, the hidden regularization term can fully learn chord graph priori and image priori in the optimization process by the end-to-end mode, errors accumulated by superposition optimization of different modules in the prior art can be effectively reduced, and the defect that the end-to-end method cannot be realized in the prior art is overcome.
Drawings
Fig. 1 (a) NGMNet rebuild network framework, (b) pro_net network architecture.
Fig. 2 (a) shows the images as low dose images, (b) reconstructed images for FBP, (c) reconstructed images for NGMNet.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention provides a hidden regularization low-dose CT image reconstruction method based on a noise generation mechanism, which comprises the following steps:
constructing a noise generation model
According to the beer-lambert law, under an ideal clean/noiseless environment, the original projection data P scanned by CT has the following relationship with chord chart data Y:
wherein I0i Representing edgesThe intensity of the X-rays incident on projection path i.
However, various noises are often mixed in the original projection data P during the actual CT scan, and thus a generation model of the noisy projection data P is constructed, which is expressed as follows
P=q+ε (2) whereRepresenting the quantum number received by the detector; />Representing electronic background noise, the first term representing an X-ray photon statistic; the second term represents electronic background noise.
The electronic background noise epsilon is caused by a number of potential factors, the mean and variance of which reflect the dark current and readout noise of the electrons, respectively. According to conventional assumptions, it can be reasonably assumed that the electronic background noise ε follows a non-stationary Gaussian distribution of zero mean:
wherein σ2 The variance representing the noise can be obtained from imaging system parameters of modern CT devices.
Q is the quantum number of CT measurement, which generates unavoidable quantum fluctuation due to the influence of quantum fluctuation in X-rays, and generally, quantum noise approximately follows poisson distribution law generated by polychromatic X-rays
wherein Gi Represents the intensity of the radiation in an ideal environment and is also the mean value of the number of photons.
The ideal "chord graph data" is denoted by Y, which satisfies, according to the beer-lambert law:
by combining equations (4) and (5), the following conditional distribution, i.e., the complex poisson distribution, can be obtained:
by combining equations (2) and (3), the following condition distribution can be obtained:
to sum up, the posterior distribution of the complete data is obtained:
according to the maximum posterior estimation theory, the maximum posterior estimation in the CT image denoising problem is as follows: under the knowledge of the low dose projection data P, the most likely "chordal image data" Y without noise is found. Therefore, according to the bayesian theory, the complete posterior distribution of the parameters q and Y to be estimated can be obtained:
to sum up, the CT noise generation model is:
for easy solution, taking the negative logarithm of equation (10), then the solution translates into the solution:
meanwhile, the image domain data X and the chord graph domain Y are considered to be optimized, priori knowledge is considered for Y (chord graph domain), and the general framework for finally obtaining the low-dose CT reconstruction based on the noise generation mechanism is as follows:
a is Ladong transformation, i.e. front projection operation, g 1(Y) and g2 (X) a priori terms representing chord domain Y and image domain X, respectively, lambda 1 ，λ 2 Is a regularized term parameter.
Solving optimization problem of low-dose CT reconstruction based on noise generation mechanism
To facilitate the construction of deep expansion networks, the near-end gradient technique is used to update alternately Q, Y, X. The method comprises the following steps:
update Q: in the nth iteration, the update of Q is achieved by solving a gradient approximation of the problem (12) with respect to Q, the approximation problem being:
wherein ,Qn-1 Is the updated result obtained by the (n-1) th iterative computation, eta 1 To update the step size.
The updating method of Q is as follows:
will beSubstituting formula (14), C is an euler constant, and the update rule for Q is:
updating Y: the update of Y is accomplished by solving a quadratic approximation of the problem (12) about Y, the approximation problem being:
wherein ,Yn-1 Is the updated result obtained by the (n-1) th iterative computation, eta 2 In order to update the step size,
the solution of formula (16) is:
will beSubstituting the update rule of Y into equation (17) is:
wherein ,is composed of regular term g 1 The determined near-end operator is adaptively learned by adopting a neural network pro_net, and the regularization term is further implicitly learned.
Updating X: similarly, the update of X is accomplished by solving a quadratic approximation of the problem (12) with respect to X, the approximation problem being:
wherein ,Xn-1 Is the updated result obtained by the (n-1) th iterative calculation, eta 3 In order to update the step size,
the solution of formula (19) is:
will beSubstituting the update rule into formula (20) to obtain X is:
wherein ,is composed of regular term g 2 (-) the determined near-end operator, also adaptively learning the near-end operator by using a neural network pro_net, and further implicitly learning the regularization term.
Expanding an optimization algorithm into a depth network according to a solving process
According to the above solving process, the whole optimizing process is expanded into a network form to form a hidden regularization depth network NGMNet (Noise Generating Mechinism Net) with resolvability, and each operation unit of NGMNet comprises three network layers: the projection domain updating layer, the chord domain updating layer and the image domain updating layer have the following network structure:
projection domain update layer (Q) (n) )：
Chord domain updating layer (Y) (n) )：
Image domain update layer (X) (n) )：
wherein ,for the near-end operator, the depth network architecture pro_net is employed to model the near-end operator, further implicitly learning the regularization term. The pro_net adopts a U-Net network architecture to learn, the variance sigma of the electronic background noise is set as a learnable parameter, and the parameters to be learned include: pro_net network parameters, σ, η 1 、η 2 、η 3 ；η 1 、η 2 、η 3 To update step size, Y n-1 Is the updated result obtained by the (n-1) th iterative computation, X n-1 Is the updated result obtained by the (n-1) th iterative computation, Q n-1 The updating result obtained by the (n-1) th iterative computation is obtained, and C is the Euler constant. In fig. 1, (a) rebuilds the network framework for NGMNet and (b) is pro_net network architecture.
End-to-end network training is performed using the low dose projection data and the standard dose image data, MSELoss is used as a loss function, gradients of the loss function relative to network parameters are calculated through back propagation, and an Adam optimizer is used to optimize the network parameters.
In numerical experiments, the invention uses lodopab dataset for experiments. The lodopab data included 35820 low dose chordal image data and normal dose image data pairs, 3522 validation data pairs and 3553 test data pairs. And (3) carrying out low-dose projection data reconstruction by using the trained NGMNet network: the input is low-dose projection data, the output is a reconstructed CT image, and in fig. 2, (a) is a low-dose image, (b) is an FBP reconstructed image, and (c) is an NGMNet reconstructed image, as can be seen from fig. 2, the NGMNet hidden regularized depth network can effectively remove complex noise caused by dose reduction, and a high-quality CT image is reconstructed.
In addition, the invention also provides a computer device, which comprises a processor and a memory, wherein the memory is used for storing a computer executable program, the processor reads part or all of the computer executable program from the memory and executes the computer executable program, and the processor can realize the hidden regularization low-dose CT image reconstruction method based on the noise generation mechanism when executing part or all of the computer executable program.
In another aspect, the present invention provides a computer readable storage medium, where a computer program is stored, where the computer program, when executed by a processor, can implement the method for hidden regularization low-dose CT image reconstruction based on a noise generation mechanism according to the present invention.
The computer device may be a notebook computer, a desktop computer, or a workstation.
The processor may be a Central Processing Unit (CPU), a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).
The memory can be an internal memory unit of a notebook computer, a desktop computer or a workstation, such as a memory and a hard disk; external storage units such as removable hard disks, flash memory cards may also be used.
Computer readable storage media may include computer storage media and communication media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. The computer readable storage medium may include: read Only Memory (ROM), random access Memory (RAM, random Access Memory), solid state disk (SSD, solid State Drives), or optical disk, etc. The random access memory may include resistive random access memory (ReRAM, resistance Random Access Memory) and dynamic random access memory (DRAM, dynamic Random Access Memory), among others.
Claims (8)
1. A hidden regularization low-dose CT image reconstruction method based on a noise generation mechanism is characterized in that,
expanding the problem of low-dose CT reconstruction based on a noise generation mechanism into a hidden regularized depth network NGMNet, performing end-to-end training on the hidden regularized depth network NGMNet to obtain a depth network model of low-dose projection data reconstruction,
inputting low-dose projection data into the depth network model for optimization to obtain a reconstructed CT image;
wherein, each operation unit of the hidden regularization depth network NGMNet comprises three network layers: a projection domain updating layer, a chord domain updating layer and an image domain updating layer; the projection domain updating layer, the chord domain updating layer and the image domain updating layer respectively correspond to updating rules of the projection domain Q, the chord domain Y and the image domain X when the framework of the low-dose CT reconstruction based on a noise generation mechanism is solved;
the framework for low dose CT reconstruction based on noise generation mechanisms is as follows:
a is Ladong transformation, i is projection path, g 1(Y) and g2 (X) a priori terms representing chord domain Y and image domain X, respectively, lambda 1 ，λ 2 Is a regularized item parameter; i 0 Representing the intensity of the X-rays incident along the projection path, P i Is noise projection data; the network structure is as follows:
projection domain update layer Q (n) ：
Chord chart domainUpdate layer Y (n) ：
Image domain update layer X (n) ：
wherein ,modeling a near-end operator by adopting a deep network architecture pro_net for the near-end operator, and further implicitly learning the regularization term; the pro_net adopts a U-Net network architecture to learn, the variance sigma of the electronic background noise is set as a learnable parameter, and the parameters to be learned include: pro_net network parameters, σ, η 1 、η 2 、η 3 ；η 1 、η 2 、η 3 To update step size, Y n-1 Is the updated result obtained by the (n-1) th iterative computation, X n-1 Is the updated result obtained by the (n-1) th iterative computation, Q n-1 The updating result obtained by the (n-1) th iterative computation is obtained, and C is the Euler constant.
2. The hidden regularization low-dose CT image reconstruction method based on a noise generation mechanism of claim 1, wherein the CT noise generation model is:
taking the negative logarithm of the above method, and solving and converting the negative logarithm into:
I 0 the intensity of the X-ray incident along the projection path is represented, i is the projection path, the image domain data X and the chord domain data Y are considered to be optimized, the prior knowledge is considered for the chord domain Y, and finally, the frame of the low-dose CT reconstruction based on the noise generation mechanism is obtained.
3. The hidden regularization low-dose CT image reconstruction method based on a noise generation mechanism of claim 1, wherein the end-to-end network training is performed using low-dose projection data and standard dose image data while training parameters of the hidden regularization depth network NGMNet, using MSELoss as a loss function, calculating gradients of the loss function relative to network parameters by back propagation, and optimizing the network parameters using Adam optimizers.
4. The method of hidden regularization low-dose CT image reconstruction based on a noise generation mechanism of claim 1, wherein constructing the noise generation model includes the steps of:
in an ideal clean/noiseless environment, the original projection data P scanned by CT has the following relationship with chord chart data Y:
wherein I0i A generation model representing the intensity of X-rays incident along projection path i to construct noisy projection data P is expressed in the form:
P＝Q+ε (2)
wherein Representing the quantum number received by the detector; />Representing electronic background noise, first generationTable X-ray photon statistics; the second term represents electronic background noise; let the electronic background noise epsilon follow a non-stationary gaussian distribution of zero mean:
wherein σ2 Representing the variance of noise, obtained by imaging system parameters of modern CT equipment;
quantum noise approximately follows the poisson distribution law of polychromatic X-ray generation:
wherein Gi The ray intensity in an ideal environment is represented by Y, which is ideal "chord graph data", according to beer-lambert law:
combining formula (4) and formula (5) yields the following conditional distribution, i.e., a complex poisson distribution:
the following conditional distributions are obtained by combining the formula (2) and the formula (3):
to sum up, the posterior distribution of the complete data is obtained:
the maximum a posteriori estimation in the CT image denoising problem refers to: under the condition of knowing low-dose projection data P, searching the most possible 'chord graph data' Y without noise, and obtaining the complete posterior distribution of parameters Q and Y to be estimated according to the Bayesian theory:
and (3) obtaining a CT noise generation model according to the formula (9).
5. The hidden regularization low-dose CT image reconstruction method based on a noise generation mechanism of claim 1, wherein a plurality of stages are employed for iterative optimization during network training.
6. The hidden regularization low-dose CT image reconstruction system based on the noise generation mechanism is characterized by comprising a network model training module, a network model optimizing module and a network model unit;
the network model training module expands the optimization problem of low-dose CT reconstruction based on a noise generation mechanism into a hidden regularized depth network NGMNet, trains parameters of the hidden regularized depth network NGMNet, and obtains a depth network model reconstructed by low-dose projection data;
the network model optimization module inputs the low-dose projection data into the depth network model for optimization to obtain a reconstructed CT image;
the hidden regularization depth network NGMNet is used for training, and each operation unit of the hidden regularization depth network NGMNet comprises three network layers: a projection domain updating layer, a chord domain updating layer and an image domain updating layer; the projection domain updating layer, the chord domain updating layer and the image domain updating layer respectively correspond to updating rules of the projection domain Q, the chord domain Y and the image domain X when solving a framework of low-dose CT reconstruction based on a noise generation mechanism, and the framework of low-dose CT reconstruction based on the noise generation mechanism is as follows:
a is Ladong transformation, i is projection path, g 1(Y) and g2 (X) a priori terms representing chord domain Y and image domain X, respectively, lambda 1 ，λ 2 Is a regularized item parameter; i 0 Representing the intensity of the X-rays incident along the projection path, P i Is noise projection data; the network structure is as follows:
projection domain update layer Q (n) ：
Chord domain update layer Y (n) ：
Image domain update layer X (n) ：
wherein ,modeling a near-end operator by adopting a deep network architecture pro_net for the near-end operator, and further implicitly learning the regularization term; the pro_net adopts a U-Net network architecture to learn, the variance sigma of the electronic background noise is set as a learnable parameter, and the parameters to be learned include: pro_net network parameters, σ, η 1 、η 2 、η 3 ；η 1 、η 2 、η 3 To update step size, Y n-1 Is the updated result obtained by the (n-1) th iterative computation, X n-1 Is the updated result obtained by the (n-1) th iterative computation, Q n-1 Is the firstAnd (3) updating the result obtained by (n-1) iterative calculation, wherein C is an Euler constant.
7. A computer device comprising a processor and a memory, the memory storing a computer executable program, the processor reading the computer executable program from the memory and executing the computer executable program, the processor executing the computer executable program to implement the noise generation mechanism-based hidden regularization low dose CT image reconstruction method of any one of claims 1-5.
8. A computer readable storage medium, wherein a computer program is stored in the computer readable storage medium, and when the computer program is executed by a processor, the computer program can implement the hidden regularization low-dose CT image reconstruction method based on a noise generation mechanism of any one of claims 1-5.
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| CN110009613A (en) * | 2019-03-28 | 2019-07-12 | 东南大学 | Low-dose CT imaging method, apparatus and system based on the dense network of depth |
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