Low-dose CT reconstruction method and system based on global optimization iteration deep learning

Abstract

The invention discloses a low-dose CT reconstruction method and system based on global optimization iteration deep learning, and the method comprises the steps: collecting CT cross section data of a normal dose, and generating low-dose CT data; the method comprises the following steps: establishing a dual-domain analysis compression iteration model, constructing maximum posteriori estimation based on a CT projection chordal graph data composite Poisson noise generation mechanism, subdividing CT projection data into a projection domain and a chordal graph domain, sequentially updating the projection data, the chordal graph data and image data, and constructing an iteration algorithm to realize CT global optimization modeling. Expanding an iterative algorithm into a trained reconstruction network; inputting the paired data into the expanded network for training, and storing a model with the minimum output result loss; a sub-network and an attention mechanism are added for CT data features, jump connection weights are finely adjusted, middle layer neural network parameters are finely adjusted and updated through middle supervision, and a global optimization iteration deep learning model NGACI-Net is obtained. According to the method, the problems that the low-dose CT image quality is poor, the reconstruction efficiency is low, and generalization and interpretability are lacked are solved.

Description

Background Art

[0002] Low-dose CT is a technology that uses a lower X-ray dose for CT scanning, which can effectively reduce the radiation exposure received by patients while maintaining image quality similar to that of traditional CT, and is helpful for early cancer screening. However, low-dose CT scanning will lead to an increase in reconstructed image noise and artifacts, which will seriously affect the quality of the reconstructed image, and thus put forward higher requirements for the reconstruction algorithm. There are mainly three directions in the research on low-dose CT reconstruction algorithms: projection domain preprocessing, image postprocessing, and iterative reconstruction. Among them, projection domain preprocessing performs noise modeling and noise reduction at the projection data level to approximately restore the quality of the projection data to the normal dose. Image postprocessing performs noise reduction and enhancement processing on the reconstructed image level to improve the image quality, which can be understood as an extension of the natural image noise reduction algorithm. However, both of these methods only optimize the back-projection process of low-dose CT once, while iterative reconstruction incorporates prior knowledge into the optimization problem in the form of expectations, thus developing a series of regularization and Bayesian inversion methods, and solving the optimization problem by repeatedly performing forward projection and back-projection iterative operations. Traditional CT reconstruction usually uses iterative reconstruction algorithms, such as Siemens' SAFIRE algorithm, Philips' iDose algorithm, etc., but the repeated iteration requires high computational cost and slow execution speed.

[0003] In the research on low-dose CT image reconstruction, significant progress has been made in deep learning methods, but there are still certain limitations in relying solely on data-driven deep learning techniques. Therefore, combining deep learning with traditional CT reconstruction algorithms has become a research trend in recent years. Traditional CT reconstruction algorithms can usually comprehensively describe the physical laws in the CT reconstruction process, so they play a crucial role in constructing interpretable network structures, feature extraction, and cost function design. However, in low-dose CT reconstruction, traditional algorithms show obvious deficiencies when facing data undersampling. Traditional methods often rely on simple regularization priors, but these priors cannot effectively capture complex image features, resulting in poor quality of the reconstruction results. In contrast, deep learning algorithms have the ability to learn complex statistical priors from a large amount of data, which makes them show great potential in solving the deficiencies of traditional algorithms. By introducing deep learning, traditional reconstruction algorithms can automatically learn the latent information in the data without relying on explicit physical models, thereby improving the reconstruction effect and image quality.

[0004] Although significant progress has been made in low-dose CT image reconstruction using deep learning, there are still some challenges. First, the training process of deep learning models usually requires a large amount of labeled data, which may be limited by data acquisition in clinical practice. Second, deep learning methods lack explicit physical constraints, resulting in the reconstructed images they generate may lack physical interpretability, which may bring uncertainties in practical applications. In addition, the structure of deep learning networks is relatively complex, and the interpretability of the models is poor, and further optimization is still needed. Therefore, future research can focus on improvements in the following directions: First is the integration of model and data-driven methods, that is, how to combine traditional physical models with deep learning methods, which can not only make full use of the powerful feature expression ability of deep learning, but also maintain physical constraints and the interpretability of the models. Second is to improve the efficiency of existing computational algorithms and optimize the reconstruction speed to meet the clinical demand for rapid diagnosis. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a low-dose CT reconstruction method and system based on global optimization iterative deep learning in view of the deficiencies in the above-mentioned prior art. Based on the global modeling analysis compression iterative deep framework (NGACI-Net, Noise Generating Deep Analysis Compressed Iterative Network), it is used to solve the technical problems of noise, sparsity constraint and data consistency, insufficient feature extraction ability, information loss and gradient disappearance in low-dose CT image reconstruction.

[0006] The present invention adopts the following technical solutions:

[0007] A low-dose CT reconstruction method based on global optimization iterative deep learning, characterized by including the following steps:

[0008] S1. Construct a CT data set, generate corresponding chordogram data and projection data from the conventional-dose CT images in the CT data set through Radon transform and exponential transform, then inject compound Poisson noise into the undamaged projections to simulate low-dose CT scan data, and finally divide the data set into a training set, a validation set and a test set;

[0009] S2. Establish a dual-domain analysis compression iterative model based on CT projection domain and image domain data consistency constraints, sparsity constraints and residual error correction mechanism, and use the iterative threshold shrinkage algorithm and the joint algebraic reconstruction algorithm to achieve the solution. Then, based on the CT projection and chordogram data scanning mechanism and the projection domain compound Poisson noise generation model, construct a maximum a posteriori estimation model, and use the damped Newton method and the iterative threshold shrinkage algorithm to achieve the solution;

[0010] S3, combining the iterative algorithm of the chord diagram optimization model and the chord diagram image dual-domain model in step S2, iteratively updating the projection data, chord diagram data and image data in sequence through a progressive improvement strategy, and constructing an iterative algorithm to realize CT global optimization modeling;

[0011] S4. The iterative algorithm constructed in step S3 is converted into a trainable reconstruction network NGACI-Net by unfolding the network method. The corresponding sub-network and CBAM convolutional attention module are added for the CT chord diagram and image data features. The momentum method is used to accelerate the convergence of the overall algorithm. At the same time, residual learning, inter-level skip connections, and skip connection weight fine-tuning are used to correct the information loss problem of the deep unfolding network.

[0012] S5. Input the low-dose and conventional-dose CT paired data in the training set obtained in step S1 into the reconstruction network NGACI-Net obtained in step S4, and carry out the overall network and each layer operator training through intermediate supervision to obtain a low-dose CT reconstruction model.

[0013] Preferably, in step S1, according to the corresponding normal-dose CT image, corresponding low-dose CT data is generated based on the CT scanning and noise generation model, including projection data, chord diagram data and image data, and the CT data set is divided into a training set, a validation set and a test set at a ratio of 8:1:1.

[0014] Preferably, step S2 specifically includes:

[0015] S201, introducing a residual error correction mechanism in chord graph denoising, and realizing stable reconstruction based on a sparse prior module of compressed sensing, and obtaining the optimization target of a dual-domain analysis compression iterative model;

[0016] S202, constructing a maximum a posteriori estimation model based on the CT projection and chord diagram data scanning mechanism and the corresponding compound Poisson noise generation model to obtain the final optimization target of projection domain denoising.

[0017] Preferably, the optimization objectives of the dual-domain analysis compression iterative model are as follows:

[0018]

[0019] Among them, Φ is the reconstruction model, A is the Radon transform, and Y e is the chord diagram error, Y is the initial measurement value of the chord diagram, X is the image data, λ 1 ,λ 2 ,λ 3 They are weight parameters for balancing different items, and H is the sparse transformation regularization term.

[0020] Preferably, the final optimization goal of projection domain denoising is as follows:

[0021]

[0022] Among them, T represents the projection data in the ideal situation to be restored, Y represents the chordogram data in the ideal situation to be restored, N represents the total number of scanning rays, which can be calculated by the product of the total number of detectors and the number of projection views, and P i is the number of photons actually received by the i-th photosensitive unit of the detector, and T i is the number of photons received by the i-th photosensitive unit of the detector in the ideal situation, and I 0i is the initial number of photons of the CT of the i-th photosensitive unit of the detector, σ is the standard deviation of the CT electronic noise, and Y i is the ideal attenuation path sum of the i-th ray, and T i ! is the factorial of the number of photons received by the i-th photosensitive unit of the detector in the ideal situation, μ is the regularization weight parameter, and F is the sparse transformation operator.

[0023] Preferably, step S3 is specifically:

[0024] Based on the progressive improvement strategy, the projection data, chordogram data, and image data are iteratively updated in sequence, an iterative algorithm is constructed to achieve CT global optimization modeling, and a momentum term is introduced in the soft threshold iterative algorithm using the gradient acceleration strategy to improve it into an accelerated soft threshold iterative algorithm.

[0025] Preferably, step S4 is specifically:

[0026] S401. Based on the iterative algorithm obtained in step S3, replace the sparse transformation operator in the iterative threshold shrinkage algorithm with a deep network to achieve implicit regularization based on the deep neural network;

[0027] S402. Use the algorithm unfolding technology to map the calculation steps of each iteration in the iterative reconstruction algorithm to a single shallow neural network layer, and stack a limited number of neural network layers together to achieve global modeling analysis and compression of the iterative depth framework;

[0028] S403. For the NGACI-Net chordogram domain network, design a noise estimation sub-network for the CT chordogram domain data characteristics, and approximately calculate the noise variance level map according to the input noise chordogram and the CT noise model;

[0029] S404. For the NGACI-Net chordogram domain network, design an edge enhancement sub-network for the CT image domain data characteristics, implement an edge enhancement module based on the trainable Sobel Feldman operator, and extract edge information of different intensities of the image;

[0030] S405. Before the feature map extracted by the chordogram and image domain sub-networks and the original image are stacked in the channel dimension and input into the denoising sub-network, introduce the CBAM convolutional attention module, and through the attention mechanism, dynamically select important information of the image input to generate the final feature map;

[0031] S406. In the NGACI-Net, the skip connections in the UNet network connect the features of the corresponding layers in the encoder with the features of the corresponding layers in the decoder, and fine-tune the weights of the skip connections to further improve the network's feature extraction and denoising capabilities.

[0032] S407. Design an inter-stage information path in the NGACI-Net framework and introduce residual connections in the deep residual network to correct information loss.

[0033] Preferably, step S5 is specifically as follows:

[0034] S501. The NGACI-Net model is trained using the Adam optimizer with (β 1 , β 2 ) = (0.5, 0.999). The initial learning rate is set to 0.0001. After 20 epochs, the learning rate is halved every 10 training times, and a total of 100 training times are performed. The data batch size used each time is 1.

[0035] S502. Construct a composite loss function for the NGACI-Net model.

[0036] S503. Incorporate the intermediate iteration results of the NGACI-Net model into the loss function for intermediate supervised training, and fine-tune the intermediate layer model to obtain a low-dose CT reconstruction model.

[0037] Preferably, the composite loss function of the NGACI-Net model is:

[0038] Loss = L MSE (X n , X * ) + αL MAE (X n , X * ) + βL SSIM (X n , X * ) + γL MAE (Y n , Y * )

[0039] where Y n , X n are the estimated chord diagrams and images in the last iteration, Y * , X * represent the corresponding reference chord diagrams and images, and α, β, and γ are hyperparameters that control the weights of different loss terms.

[0040] In a second aspect, an embodiment of the present invention provides a low-dose CT reconstruction system based on global optimization iterative deep learning, including:

[0041] Data module, constructs CT data set, generates corresponding chord data and projection data from conventional dose CT images in CT data set through Radon transform and exponential transform, then injects composite Poisson noise into undamaged projection to simulate low dose CT scan data, and finally divides the data set into training set, validation set and test set;

[0042] Solution module, based on the consistency constraints and sparsity constraints of CT projection domain and image domain data, a dual-domain analysis compression iterative model is established through the residual error correction mechanism, and the iterative threshold shrinkage algorithm and the joint algebraic reconstruction algorithm are used to achieve the solution. A maximum a posteriori estimation model is constructed based on the CT projection and chord diagram data scanning process and the corresponding composite Poisson noise generation mechanism, and the damped Newton method and the iterative threshold shrinkage algorithm are used to achieve the solution;

[0043] The iteration module combines the iterative algorithm of the chord diagram optimization model and the chord diagram image dual-domain model, and iteratively updates the projection data, chord diagram data, and image data in turn through a progressive improvement strategy, thus constructing an iterative algorithm to achieve CT full-domain optimization modeling.

[0044] The fine-tuning module converts the constructed iterative algorithm into a trainable reconstruction network NGACI-Net by unfolding the network method, adds corresponding sub-networks and CBAM convolutional attention modules for CT chordogram and image data features, uses momentum method to accelerate the convergence of the overall algorithm, and corrects the information loss problem of the deep unfolding network through residual learning, inter-level skip connections and skip connection weight fine-tuning;

[0045] The output module inputs the low-dose and conventional-dose CT paired data in the training set into the obtained reconstruction network NGACI-Net, and through intermediate supervision, the overall network and each layer operator training are carried out to obtain a low-dose CT reconstruction model.

[0046] In a third aspect, a computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the above-mentioned low-dose CT reconstruction method based on global optimization iterative deep learning are implemented.

[0047] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, comprising a computer program, which, when executed by a processor, implements the steps of the above-mentioned low-dose CT reconstruction method based on global optimization iterative deep learning.

[0048] Fifth aspect, a chip, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the above-mentioned low-dose CT reconstruction method based on global optimization iterative deep learning are implemented.

[0049] Sixth aspect, an embodiment of the present invention provides an electronic device, comprising a computer program, wherein when the computer program is executed by the electronic device, the steps of the above-mentioned low-dose CT reconstruction method based on global optimization iterative deep learning are implemented.

[0050] Compared with the prior art, the present invention has at least the following beneficial effects:

[0051] A low-dose CT reconstruction method based on global optimization iterative deep learning explores a global modeling analysis compression iterative framework that comprehensively considers noise generation and imaging mechanisms. This framework takes into account the statistical characteristics of X-ray photons and electronic noise background in the original measurement, the constraints of data consistency in the projection domain, chordogram domain, and image domain, and the prior information of sparse solutions in the sinogram and image domains. First, according to the noise generation mechanism corresponding to the CT scan measurement principle, the projection data contains the number of photons received by the detector obeying the Poisson distribution and electronic noise. At the same time, based on the Beer-Lambert law for maximum a posteriori estimation, a Bayesian inversion model for recovering clean and noise-free chordogram data under low-dose projection data conditions can be obtained. On this basis, combined with the CT dual-domain analysis compression iterative deep framework, a CT reconstruction model based on global optimization is finally formed.

[0052] Furthermore, by expanding the global modeling analysis compression iterative framework, a global modeling analysis compression iterative deep framework inspired by noise generation and imaging mechanisms (NGACI-Net) is proposed. One of the optimization steps of the proximal gradient iterative algorithm (proximal mapping) is replaced by a new mapping learned by a neural network, and the chordogram domain regularizer is implicitly learned through a deep neural network, thereby transforming an algorithm with an uncertain number of iterations into a trainable reconstruction network with a fixed number of layers. It realizes the fusion of the traditional sensor optimization model and the deep learning black box model, achieves the balance of model computational efficiency, robustness, and interpretability, and finds an ideal solution in the intersection of the data-driven solution space, sparse solution space, and data-constrained solution space.

[0053] Furthermore, considering the data characteristics of the chordogram domain, for the proximal mapping denoising network in the chordogram domain, Poisson-Gaussian noise distribution is approximated by heteroscedastic Gaussian noise, and a noise estimation sub-network is proposed to further extract noise features. For the proximal mapping denoising network in the image domain, a trainable Sobel operator is used as an edge enhancement sub-network to extract edge texture feature maps, so as to better restore the edge texture details of the reconstructed image. In addition, in order to better exert the effects of the noise estimation sub-network and the edge enhancement sub-network, a CBAM convolutional attention module is introduced, and through the attention mechanism, dynamic selection of important information in the input image is realized in both the channel and spatial dimensions. The network structure is optimized according to the CT data characteristics to maximally maintain the organizational structure of the non-artifact area and achieve a good reconstruction effect for low-dose CT images.

[0054] Furthermore, by fine-tuning the weights of the skip connections, and through the ideas of momentum, residual learning, intermediate supervision, and cross-stage information paths, the intermediate results in the iterative process are better utilized, the loss of intrinsic information is corrected, thereby slowing down the vanishing gradient phenomenon of the error of the output layer after multi-layer backpropagation, ensuring the normal update of the underlying parameters, and enhancing the learning efficiency of the model.

[0055] It can be understood that the beneficial effects of the second to sixth aspects above can be referred to the relevant descriptions in the first aspect above, and will not be elaborated here.

[0056] In summary, the present invention constructs a global modeling analysis compression iterative depth framework according to the CT scanning mechanism, and unfolds the iterative algorithm into a trainable reconstruction network; sub-networks and attention mechanisms are added according to the CT chordogram and image data characteristics to extract feature maps, and the feature extraction and denoising capabilities of the network are further improved by fine-tuning the skip connection weights; the ideas of momentum, residual learning, and cross-stage information paths are introduced, and the neural network parameters of the intermediate layer are fine-tuned and updated through intermediate supervision to better utilize the intermediate results in the iterative process and correct the loss of intrinsic information; the problems of poor quality, low reconstruction efficiency, lack of generalization and interpretability of low-dose CT images are improved.

[0057] The technical solutions of the present invention will be further described in detail below with reference to the drawings and embodiments. Description of the Drawings

[0058] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required to be used in the embodiments of the present application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0059] Figure 1Flowchart of a low-dose CT reconstruction method based on global modeling analysis compression iterative deep learning according to the present invention;

[0060] Figure 2 It is an explanatory diagram of CT global data provided by the present invention;

[0061] Figure 3 It is a schematic diagram of the low-dose CT data simulation process provided by the present invention;

[0062] Figure 4 It is an example diagram of normal-dose chordogram data and CT images and low-dose chordogram data and CT images provided by the present invention;

[0063] Figure 5 It is a schematic diagram of the overall unfolded network structure of NGACI-Net provided by the present invention;

[0064] Figure 6 It is a schematic diagram of the chordogram domain network structure of NGACI-Net provided by the present invention;

[0065] Figure 7 It is a schematic diagram of the image domain network structure of NGACI-Net provided by the present invention;

[0066] Figure 8 It is a comparison diagram of the low-dose CT reconstruction results of six model simulation test sets in Example 1 of the present invention;

[0067] Figure 9 It is a comparison diagram of the low-dose CT reconstruction results of six model simulation test sets in Example 2 of the present invention;

[0068] Figure 10 It is a comparison diagram of the low-dose CT reconstruction structure and residuals before and after network optimization of the NGACI-Net model of the present invention;

[0069] Figure 11 It is a comparison diagram of the low-dose CT reconstruction windowing details before and after network optimization of the NGACI-Net model of the present invention;

[0070] Figure 12 It is a comparison diagram of the low-dose CT reconstruction results of six model clinical data in Example 1 of the present invention;

[0071] Figure 13 Schematic diagram of a computer device provided by an embodiment of the present invention;

[0072] Figure 14 Block diagram of an electronic device provided by an embodiment of the present invention according to the present invention.

[0073] Among them, 60. computer device; 61. processor; 62. memory; 63. computer program; 600. electronic device; 610. processing unit; 620. storage unit; 6201. random access storage unit; 6202. cache storage unit; 6203. read-only storage unit; 6204. program / utilities; 6205. program module; 630. bus; 640. display unit; 650. input / output interface; 660. network adapter; 700. external device. Detailed implementation manners

[0074] The present invention provides a low-dose CT reconstruction method based on global optimization iterative deep learning. First, a dual-domain analysis compression iterative model is established based on the consistency constraint and sparsity constraint of CT projection domain and image domain data. On this basis, a maximum a posteriori estimation problem is constructed based on the CT projection and chordogram data scanning process and the corresponding compound Poisson noise generation mechanism, and a better initial solution of chordogram data is calculated through an iterative algorithm. Finally, based on the progressive improvement strategy, the projection data, chordogram data, and image data are updated in sequence, an iterative algorithm is constructed to realize CT global optimization modeling, and the iterative algorithm is transformed into a trainable reconstruction network through the unfolding network method. On this basis, a noise estimation sub-network is added based on the CT noise model according to the characteristics of chordogram data, an edge enhancement sub-network is added based on the trainable sobel operator according to the characteristics of image data, and the dynamic selection of important information in the features extracted by the sub-network is realized through the CBAM convolutional attention module, further optimizing the feature extraction ability of the deep learning model. At the same time, the information loss problem existing in the deep unfolding network is corrected through the momentum method and the inter-level skip connection, the feature extraction and denoising ability of the network is further improved through residual learning and skip connection weight fine-tuning, and the gradient disappearance phenomenon of the error of the output layer passing through multiple layers of backpropagation is slowed down through intermediate supervision, ensuring the normal training of the model.

[0075] Embodiment 1

[0076] Please refer to Figure 1 , a low-dose CT reconstruction method based on global optimization iterative deep learning of the present invention, includes the following steps:

[0077] S1. Construct a CT data set based on the "2016 NIH-AAPM-Mayo Clinic Low-Dose CT Challenge" data set, generate corresponding chordogram data and projection data for the conventional-dose CT images in the CT data set through Radon transform and exponential transform, and then inject compound Poisson noise into the undamaged projection to simulate low-dose CT scan data; finally, divide the preprocessed data set into a training set, a validation set, and a test set;

[0078] S101. Data set acquisition

[0079] The present invention obtains the AAPM public dataset and selects the conventional-dose CT scan data therefrom to construct a CT dataset. It is sourced from the "2016-NIH-AAPM-Mayo Low-Dose CT Grand Challenge" and is authorized by Mayo Clinics. The experimental dataset includes 2378 DICOM-format CT images of 10 different patients scanned from the chest to the abdomen at a normal radiation dose (120 kVp voltage and 200 mAs effective current), with a size of 512×512.

[0080] S102. Simulation of paired low-dose CT data

[0081] The training of deep learning models usually relies on a large number of paired datasets, which is particularly difficult for the training of low-dose CT images. Because even if two scans are performed at conventional and low doses, due to reasons such as respiratory motion, it is impossible to obtain truly paired low-dose CT data, and scanning a phantom will cause overfitting due to its overly simple structure. Therefore, in order to effectively support the training of deep learning models, it is particularly important to use a simulation method to generate low-dose CT reconstruction images and chordogram data corresponding to conventional-dose CT images based on the CT scanning mechanism. By simulating the physical process of CT scanning, the simulation method can generate representative low-dose CT images and simulate different scanning parameters, detector responses, and noise characteristics, thereby obtaining realistic image data.

[0082] The low-dose CT data simulation generates corresponding low-dose CT data from CT images of normal dose, including projection data, chordogram data, and image data. The CT scan global data is as Figure 2 shown. The specific process of the low-dose CT data simulation is as Figure 3 shown;

[0083] In CT tomography, the attenuation distribution of the pixels and voxels of the human body slice image is consistent. In practice, the Hounsfield unit (HU) is generally used as the dimensionless unit for CT tomography, so as to express the pixel values of CT images in a standard and convenient way. The Hounsfield unit is obtained by linearly transforming the measured attenuation coefficient. This conversion is based on the density of air and water, where pure water is defined as 0 Hounsfield units and air is defined as -1000 Hounsfield units. The greater the tissue density, the stronger the X-ray absorption, and its value is positive, showing a bright signal; for tissues with lower density, less X-ray is absorbed, showing a negative value and a dark signal. Therefore, the conversion relationship between the CT image pixel value HU and the voxel linear attenuation value μ is as follows:

[0084]

[0085] Therefore, after the inverse quantization of the integer Hounsfield unit (HU) values obtained from conventional-dose CT images, the attenuation distribution f(x, y) corresponding to the human tissue slice can be calculated based on the inverse-quantized HU values. Next, it is necessary to simulate the CT scanning process to convert the attenuation function f(x, y) into the corresponding chordogram data. The chordogram data obtained from conventional-dose CT scans can be calculated using the Radon transform, that is, the attenuation line integral of the CT scan. The attenuation of X-rays in an object follows the Beer-Lambert Law, that is, the attenuation process satisfies the exponential attenuation law. Based on the initial number of emitted photons I of the X-ray 0 and the attenuation line integral, the expected value of the number of emitted photons I received by the detector in the ideal state can be calculated. In actual situations, the original projection data obtained from CT scans is usually mixed with various noises. Research shows that the original projection data approximately satisfies the compound Poisson distribution model. Assume that the number of photons collected by the i-th photosensitive unit of the detector is I i , then I i The relationship with the chordogram data can be expressed by the following mathematical formula:

[0086]

[0087] where is the mean of the Poisson distribution, and ε i is the electronic background noise of the i-th photosensitive unit of the detector. Usually, the electronic noise is modeled as a Gaussian distribution with zero mean. The Poisson-Gaussian noise model is used in many experimental algorithms for simulating low-dose CT images, injecting compound Gaussian and Poisson noises into the undamaged projections. The variance of the Gaussian noise is 11, and the number of incident photons simulating the low-dose level is 5000. After simulating the low-dose CT scan projection data based on the CT scanning mechanism, it can be converted into low-dose chordogram data using logarithmic transformation. Next, the filtered back-projection (FBP) algorithm can be used to reconstruct the low-dose CT image. Figure 4 shows the conventional-dose CT data (left column) and the low-dose CT data with added noise (right column). The speckle noise and streak artifacts in the low-dose CT image do not have strict mathematical statistical characteristics in the image domain, but some perceptual information can be obtained by observing many noise images and residual images. For example, there are a large number of streaks of different lengths in the low-dose CT image, which often show a divergent shape. The noise in the lung CT image is often low, and both speckle noise and streak artifacts often exist in the parts of the human body with higher density.

[0088] S103. Dataset Division

[0089] The CT dataset consists of the experimental dataset of the "2016-NIH-AAPM-Mayo Low-dose CT Contest". Based on the corresponding normal-dose CT images, the corresponding low-dose CT data, including projection data, chordogram data, and image data, are generated according to the CT scan and noise generation model. The preprocessed CT dataset paired dataset is divided into a training set, a validation set, and a test set in a ratio of 8:1:1.

[0090] Considering that the CT dataset basically evenly covers 3mm-thick human body slices from the chest to the abdomen of ten patients, the data of eight patients (1943 slices) are divided according to the ratio of 8:1:1 for training, the data of one patient (211 slices) are used for validation, and the data of one patient (224 slices) are used for testing. The CT projection data, chordogram data, and image data are converted into the Tensor data type applicable to the Pytorch framework.

[0091] S2. A dual-domain analysis compression iterative model is established through a residual error correction mechanism based on the data consistency constraint and sparsity constraint in the CT projection domain and image domain, and the iterative threshold shrinkage algorithm (ISTA) and the simultaneous algebraic reconstruction technique (SART) are used to achieve the solution. A maximum a posteriori estimation model is constructed based on the CT projection and chordogram data scanning process and the corresponding compound Poisson noise generation mechanism, and the damped Newton method and the iterative threshold shrinkage algorithm are used to achieve the solution;

[0092] S201. Dual-domain analysis compression iterative model

[0093] In the field of image reconstruction, a continuous imaging system can be discretized into a linear inverse problem model

[0094] y = Ax

[0095] In this model, the goal is to invert the unknown image x through the known observation data y, and A is the forward measurement operator. The purpose of image reconstruction is to find an x that can not only fit the observation data y well but also find a better x according to the prior properties of the image. When the system matrix A is the discrete Radon transform, this inverse problem is CT image reconstruction.

[0096] Ideally, the inverse of the forward operator A can be directly solved for this inverse problem. In fact, the FBP algorithm can be regarded as an approximate inverse of A. However, due to the existence of noise, the projection data is damaged and amplified countless times during the inversion process, and finally, the reconstructed CT image has strip artifacts. The purpose of the low-dose CT reconstruction task is to remove the artifacts that affect the image quality and normal tissues. If the noise distribution is known, the following maximum likelihood (ML) estimation problem can be solved to reconstruct the image x:

[0097]

[0098] where \(p(y|x)\) is the likelihood of observing data \(y\) for the ideal CT reconstructed image \(x\) (knowledge of the system matrix \(A\) is implicit in this formula). However, the maximum likelihood method has some obvious drawbacks. Since the inverse problem of noise perturbation is underdetermined, that is, there are potentially non-unique solutions and it is highly sensitive to noise. Therefore, additional prior knowledge must be introduced to uniquely and stably recover the reconstructed image. Encode the prior knowledge into the prior distribution of \(x\) to obtain the maximum a posteriori (MAP) estimate:

[0099]

[0100] In the optimization problem of CT reconstruction, the goal is to estimate the reconstructed image closest to the actual image from the projection data through an iterative reconstruction algorithm. To achieve this goal, the difference between the reprojection data of the reconstructed image and the actually acquired projection data is usually used as a constraint term of the objective function, also known as the data fidelity term. The role of this term is to measure the fitting degree between the reconstructed image and the actual projection data. At the same time, for the inverse imaging problem of CT that needs to reconstruct an image from incomplete data, in order to overcome the ill-posedness of the problems caused by noise or undersampling, the usual strategy is to incorporate prior knowledge in the desired form into the optimization problem as a constraint term of the objective function, also known as the regularization term. Then the objective function of iterative reconstruction is expressed as the following formula, from which a series of regularization and Bayesian inversion methods are developed.

[0101]

[0102] Meanwhile, in the CT reconstruction task, it is also desirable for the model to be robust to small perturbations of the input. For the reconstruction model \(\varPhi\) that continuously maps the measurement data to an image, although the reconstruction model \(\varPhi\) is designed to solve the inverse problem from the measurement \(y = Ax\) and reconstruct the image \(x\), it can only approximately make This is because the system matrix \(A\) is underdetermined, and the reconstruction model \(\varPhi\) may also generate artifacts. Therefore, \(\varPhi\) has the risk of instability. The instability can be calculated by the following formula

[0103]

[0104] Therefore, a residual error correction mechanism is introduced in the projection domain, and a sparsity prior module based on compressive sensing is used to achieve stable reconstruction. Let the residual error be \(Y\) e , then the optimization objective can be determined according to the CT dual-domain analysis compressive iteration depth framework:

[0105]

[0106] Among them, Φ satisfies the bounded relative error norm property and can map the chordogram data back to the image domain. Different from the traditional convex optimization scheme, the present invention uses the FBP algorithm to replace the unfiltered backprojection operator, which can improve the smoothness of the unfiltered backprojection and generate an image with correct proportional pixel values. A is the Radon transform, Y e is the chordogram error, Y is the initial chordogram measurement value, X is the image data, λ 1 , λ 2 , λ 3 are the weight parameters for balancing different terms respectively, and H is the sparse transform operator. The first term of the optimization objective is the difference between the reconstruction model and the output of the sparsity prior module based on compressive sensing, the second term is the noise perturbation of the measurement, the third term is also the residual error in the projection domain, and the last term is used to enforce the sparsity of the output image by the compressive sensing module.

[0107] The block coordinate descent method is used to optimize the objective as follows:

[0108]

[0109] Among them, for the update of Y e , the following problem needs to be solved:

[0110]

[0111] This optimization objective is differentiable, and the simultaneous algebraic reconstruction technique SART is used to solve it as shown in the following formula

[0112]

[0113] Similarly, for the update of X, the following problem needs to be solved:

[0114]

[0115] This optimization objective belongs to the LASSO problem, including the non-differentiable l 1 norm regularization term, and the iterative soft thresholding algorithm ISTA is used to solve it as shown in the following formula

[0116]

[0117] Among them, H * is the adjoint function of H, S θ (·) is the soft thresholding function, and γ t is the iteration step size.

[0118] In the above analysis, it is assumed that the initial chordogram measurement value Y of the reconstruction model is noise-free, that is, Y = AX. When there is noise perturbation in the projection data, the noise e can be decomposed into e 1 and e 2 , where e1 Satisfy e 1 = An * , where n * is an observable image corresponding to noise artifacts. Therefore, X + n * still conforms to the data-driven prior and the sparsity prior. And e 2 = e - e 1 is the complement of e 1 . Since the noise artifacts n * can be incorporated into a part of the image X, e 1 can be ignored and only e 2 is considered. Since e 2 lies outside the intersection of the three spaces of the data-driven prior, the sparsity prior, and the measurement data constraint, it has no contribution to the final image. Only the system tolerance level ε needs to be modified accordingly to accommodate the influence of the noise e, without affecting the final convergence of the algorithm.

[0119] S202. CT Projection Domain Denoising Model

[0120] Although the noise in the initial measurement value Y of the chordogram does not affect the algorithm convergence, it is obviously more helpful to accelerate the algorithm convergence by modeling and solving the chordogram data preprocessing to obtain an ideal initial solution. To estimate an ideal noise-free chordogram from the noisy sinogram data, the current research mainly divides into two major directions: the pre-log method and the post-log method. The pre-log method is based on the Beer-Lambert law, directly constructs a forward model, and uses the assumption of the Poisson distribution to recover the CT projection data without performing a logarithmic transformation. Many pre-log methods are based on the Poisson noise model, such as the Maximum Likelihood (ML) method based on Expectation Maximization (EM), and the Penalized-likelihood (PL) method, etc. In contrast, the post-log method uses the sinogram data obtained by taking the logarithm of the original projection data and adopts a statistical iterative method to recover the ideal "chordogram" data. These methods usually assume that the noise in the measured chordogram data is Gaussian noise and use Penalized Weighted Least Squares (PWLS) for processing. This paper adopts the hybrid Poisson noise model widely used in the CT field, which synthesizes the noise characteristics of photon statistics and the background characteristics of electronic noise and can more accurately describe the reconstruction process of the chordogram data, thus achieving a higher quality reconstruction effect.

[0121] In actual situations, the original projection data P obtained by CT scanning is usually mixed with various noises. Therefore, it is necessary to more precisely reconstruct the generation model of the projection data, and its mathematical expression is

[0122] P = T + ε

[0123] Where T represents the number of photons received by the detector, and ε represents the electronic noise. Both of these will transfer the uncertainty of the noise source to the projection data.

[0124] The electronic noise is caused by many potential factors and usually has a not very large amplitude. Its mean and variance respectively reflect the dark current and readout noise of the electrons. According to the assumptions in the traditional method, it can be reasonably assumed that it follows a stationary Gaussian distribution with zero mean:

[0125]

[0126] The number of photons T received by the CT detector is the result of quantum fluctuations. The independence of the arrival of random individual photons will lead to quantum noise, and photon counting is a classical Poisson process. Existing research results show that the quantum noise of low-dose CT approximately follows the Poisson distribution law:

[0127]

[0128] Where I i represents the ray intensity in the ideal environment and is also the mean value of the number of photons.

[0129] Use Y to represent the ideal chordogram data, which is also the ultimate goal of the projection domain denoising model. According to the Beer-Lambert law, I i satisfies:

[0130]

[0131] Then, combining the Poisson distribution formula and the Beer-Lambert law, the following conditional distribution can be obtained:

[0132]

[0133] Since the electronic noise follows a Gaussian distribution, it can be obtained:

[0134]

[0135] Combining the above two conditional distributions, it can be deduced that the CT projection domain data noise generation model follows the following conditional distribution:

[0136]

[0137] According to the MAP (Maximum A Posteriori Estimation) theory, the MAP of CT projection domain denoising is to solve the noise-free chordogram data Y in the ideal case under the condition of known low-dose projection data S. Therefore, the posterior distribution of the generation model can be obtained as:

[0138]

[0139] To simplify the maximum a posteriori estimation of the above formula, which is equivalent to minimizing its negative logarithm, and for the chordogram data Y sparse transformation regularization term F, a maximum a posteriori estimation model is constructed based on the CT projection and the chordogram data scanning process and the corresponding compound Poisson noise generation mechanism. The final optimization objective for projection domain denoising is as follows:

[0140]

[0141] Using the block coordinate descent method to optimize the objective, for the update of T, the following problem needs to be solved:

[0142]

[0143] To solve the above formula, the integer variable detector received photon number T is relaxed to a continuous variable, and then the differentiable generalized factorial Γ(T i +1) can be used to replace Ti!, and the solution is realized by the damped Newton method. The specific expression is as follows:

[0144]

[0145] For the update of Y, the following problem needs to be solved:

[0146]

[0147] Similarly, the soft threshold iterative algorithm ISTA algorithm is used to solve the following formula

[0148]

[0149] where F * is the adjoint function of F, and S θ (·) is the soft threshold function, and ρ t is the iteration step size.

[0150] S3. Combining the iterative algorithm of the chordogram optimization model and the chordogram image dual-domain model in step S2, the projection data, chordogram data, and image data are iteratively updated in sequence through a progressive improvement strategy, and an iterative algorithm is constructed to realize CT global optimization modeling;

[0151] In summary, the CT global iterative framework first iteratively solves the ideal initial chordogram measurement value Y based on the projection domain denoising model, and then the initial chordogram measurement value can be iteratively solved using the dual-domain analysis compression iterative model to obtain the reconstructed image.

[0152] Furthermore, through the progressive improvement strategy for the two dual-domain models of the projection chordogram domain and the chordogram image domain, the projection data, chordogram data, and image data are iteratively updated in sequence, and finally the CT global optimization iterative framework (NGACI) is realized as follows:

[0153] Table 1 CT global iterative framework algorithm

[0154]

[0155] In order to accelerate convergence, the gradient acceleration strategy Nesterov acceleration technology is used in the soft threshold iteration algorithm to introduce the momentum term to become the accelerated soft threshold iteration algorithm (FISTA). The momentum term is usually calculated as the weighted average of the previous update direction, which can be expressed by the following formula:

[0156] V t =X k-1 +λ k (X k-1 -X k-2 )

[0157]

[0158] Due to the bounded relative error norm (BREN) property, the NGACI algorithm is a contraction mapping, in other words, the new observable error during the iteration is smaller than the previous observable error. Repeating this process can make the observable error decrease exponentially quickly, so the NGACI algorithm can iteratively eliminate the observable error. In this process, the NGACI algorithm integrates data-driven, sparsity priors, and measurement data consistency to achieve stable reconstruction.

[0159] S4. The iterative algorithm is converted into a trainable reconstruction network NGACI-Net by unfolding the network method. The corresponding sub-network and CBAM convolutional attention module are added for the CT chord diagram and image data features. The momentum method is used to accelerate the convergence of the overall algorithm. At the same time, residual learning, inter-level skip connections and skip connection weight fine-tuning are used to correct the information loss problem of the deep unfolding network. The overall unfolding network and the training of operators at each layer are taken into account through intermediate supervision.

[0160] S401, based on the NGACI algorithm obtained in S3, the sparse transformation operator in the ISTA algorithm is replaced by a deep network, thereby avoiding the complex process of manually designing and adjusting the regularization term and realizing implicit regularization based on a deep neural network;

[0161] In addition to the shortcomings of traditional regularization methods, implicit regularization techniques based on deep neural networks have shown superior performance. This method no longer relies on explicit regularization expressions, but instead implicitly obtains sparsity prior regularization effects through deep network learning.

[0162] S402. Based on step S401, the algorithm unfolding technique is used to map the calculation steps of each iteration in the iterative reconstruction algorithm into a single shallow neural network layer, and a finite number of neural network layers are stacked together to implement the global modeling analysis compressed iterative depth framework (NGACI-Net) algorithm as follows:

[0163] Although deep neural networks perform excellently in end-to-end mapping, the problems of their dependence on a large amount of high-quality training data and lack of interpretability still exist. To solve these problems, Gregor and LeCun proposed the algorithm unfolding method, which transforms traditional iterative algorithms into deep neural networks. Each iteration corresponds to a layer of the network, and the network parameters are optimized through backpropagation. This method not only retains the interpretability of iterative algorithms but also improves the parameter efficiency and generalization ability of the network. The algorithm unfolding method has multiple advantages. First, it inherits the domain knowledge of traditional iterative algorithms and reduces the dependence on large-scale training data. Second, by embedding physical processes and prior knowledge into the network structure, the number of parameters is significantly reduced, thereby improving the computational efficiency and storage efficiency. In practical applications, due to the optimization of convolution operations on modern computing platforms, the inference process of the unfolded network is more efficient. In addition, the number of layers of the unfolded network is much less than the number of iterations of traditional iterative algorithms, thus significantly reducing the computational amount. In summary, the NGACI-Net framework proposed in this study combines the advantages of deep learning and traditional iterative algorithms to achieve efficient denoising and reconstruction of low-dose CT images.

[0164] Table 2 CT global iterative depth framework algorithm

[0165]

[0166] Each iteration of the unfolded NGACI-Net contains four cascaded modules: the projection chord Figure 1 consistency module (Y-PSC), the image chord Figure 1 consistency module (Y-SIC), the image residual perception module (X-RA), and the image refinement module (X-IR). The projection chord diagram and the image chord Figure 1 consistency module incorporate the potential CT physical imaging process and the sparsity prior in the chord diagram domain, and ensure the consistency between the reconstructed image and the observed data. The image residual perception module attempts to further estimate the residual image features after mapping the chord diagram error to the image domain. Finally, the image refinement module learns the sparsity prior in the image domain based on deep learning to further fine-tune the reconstructed image. NGACI-Net minimizes the residual error through the above iterative process to achieve stable CT reconstruction. The complete NGACI-Net network structure diagram is as Figure 4 shown.

[0167] S403. For the NGACI-Net chordogram domain network, a noise estimation sub-network is designed for the CT chordogram domain data features, so as to approximately calculate the noise variance level map according to the input noisy chordogram and the CT noise model, and further enhance the chordogram denoising ability of the network.

[0168] Existing CNN denoisers usually perform poorly on real noisy images, mainly because they may overfit Gaussian white noise, while the real noise distribution is very different from the Gaussian distribution. Real image noise is usually more complex and more dependent on the signal. In fact, the noise generated by photon induction in the CT chordogram domain can be modeled as a Poisson distribution, and the remaining stationary perturbations can be modeled as a Gaussian distribution. Since the incident photon count follows a Poisson distribution, it has the property that its variance is equal to its expectation, which indicates that photon noise is related to the signal intensity and its standard deviation increases with the square root of the signal. Therefore, the Poisson-Gaussian model can be further approximated by heteroscedastic Gaussian noise.

[0169] According to the Beer-Lambert law, the number of photons I received by the detector under ideal conditions satisfies:

[0170]

[0171] However, due to the perturbation of Poisson-Gaussian noise, the actual number of photons received by the detector is P, then the chordogram domain data satisfies

[0172]

[0173] Approximating the Taylor expansion of the log function gives

[0174]

[0175] After linearly approximating the projection data and detector counts, since the Poisson noise variance is equal to the expectation I, plus the electronic noise with a standard deviation of σ n the chordogram noise variance estimate can be obtained as follows:

[0176]

[0177] Therefore, for the projection chord Figure 1 consistency module and image chord Figure 1 consistency module of the chordogram domain denoising network, the noise variance level map can be approximately calculated according to the input noisy chordogram and the CT noise model. The input noise estimation sub-network further extracts features, and at the same time, total variation (TV) regularization is introduced to constrain the smoothness of the noise estimation feature map. Due to the existence of the noise estimation sub-network, the denoising performance and generalization ability can be further enhanced. The complete structure diagram of the NGACI-Net chordogram domain network is as Figure 5 shown.

[0178] S404. For the NGACI-Net chord diagram domain network, an edge enhancement sub-network is designed for the data features in the CT image domain, so as to implement an edge enhancement module based on the trainable Sobel Feldman operator, extract edge information of different intensities in the image, and protect the details of human organs in the reconstructed image.

[0179] For the image domain denoising network, an edge enhancement sub-network is added to better retain edge texture details. In this study, an edge enhancement module is designed based on the trainable Sobel Feldman operator. The operators in the four directions of vertical, horizontal, and two diagonals are defined as a group, and multiple groups of trainable sobel operators are used on the input image. Each group of operators performs a convolution operation to obtain a feature map for extracting edge information. Then the module stacks it with the input image in the channel dimension to obtain the final feature output of the module. Different from the traditional fixed-value Sobel operator, a learnable parameter α, called the Sobel factor, is defined in the trainable Sobel operator. The value of this parameter can be adaptively optimized during the training process to extract edge information of different intensities. The complete structural diagram of the NGACI-Net image domain network is as Figure 6 shown.

[0180] S405. Before the feature maps extracted by the chord diagram and image domain sub-networks are stacked with the original image in the channel dimension and input into the denoising sub-network, a CBAM convolutional attention module is introduced to dynamically select important information of the image input through the attention mechanism, generating the final feature map.

[0181] In the classic denoising method, the network treats the mapping of the features of each channel in the image equally, resulting in over-focusing on the low-feature regions and insufficient attention to the high-information regions. Since the NGACI-Net chord diagram domain network introduces a noise estimation sub-network to extract noise estimation feature maps based on the CT noise model, and the image domain network introduces an edge enhancement module based on the trainable sobel operator to extract edge texture feature maps. Before the feature maps are stacked with the original image in the channel dimension and input into the denoising sub-network, a CBAM convolutional attention module is introduced to dynamically select important information of the image input through the attention mechanism. The CBAM module can sequentially generate attention feature map information in both the channel and spatial dimensions, and then multiply the attention feature map information with the original input feature map to achieve adaptive feature correction, generating the final feature map.

[0182] S406. The skip connections in the UNet network in NGACI-Net connect the features of the corresponding layers in the encoder with the features of the corresponding layers in the decoder to help retain more spatial information and detailed features. Make a certain fine-tuning of the weights of the skip connections to further improve the feature extraction and denoising capabilities of the network.

[0183] The neural network in NGACI-Net improves the lightweight UNet architecture according to the characteristics of CT data. Among them, the skip connections in the UNet network connect the features of the corresponding layers in the encoder with the features of the corresponding layers in the decoder to help retain more spatial information and detailed features. Its essence is to encourage the model to preferentially use the simplest (i.e., closer to linear) prediction logic. And the accelerated proximal gradient algorithm also reduces the non-linear ability of the entire reconstruction mapping to a certain extent. Therefore, by making certain fine-tuning of the weights of the skip connections, the feature extraction and denoising capabilities of the network can be further improved.

[0184] S407. An inter-stage information path is designed in the NGACI-Net framework to correct the inherent information loss in most unfolded network methods. And the residual connections in the deep residual network (ResNet) are introduced to protect the image detail information and avoid gradient disappearance.

[0185] S5. Input the paired low-dose and conventional-dose CT data in the training set obtained in step S1 into the global modeling analysis compression iterative depth framework NGACI-Net obtained in step S4, and through intermediate supervision, take into account the training of the overall unfolded network and each layer operator to obtain a low-dose CT reconstruction model. Finally, the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and root mean square error (RMSE) are used on the test set to comprehensively evaluate the reconstruction performance of NGACI-Net.

[0186] S501. The Adam optimizer with (β 1 ,β 2 )=(0.5, 0.999) is used for the training of the NGACI-Net model, and the initial learning rate is set to 0.0001. To effectively adjust the learning rate, after 20 epochs, the learning rate is halved every 10 training times. A total of 100 trainings are carried out, and the data batch size used each time is 1.

[0187] S502. An appropriate loss function can improve the performance of the deep neural network. Therefore, a composite loss function is designed for the proposed NGACI-Net. First, the MAE (mean absolute error) loss is assigned to the chord diagram data to prevent the processed chord diagram data from being overly smoothed, because the l 1 norm tends to produce sharp edges. Then, the MSE and MAE losses are used to solve the distance between the reconstructed image and the reference image. Finally, the SSIM (structural similarity) loss is adopted to improve the structural fidelity; the composite loss function designed for NGACI-Net is defined as:

[0188] Loss = L MSE (X n ,X* ) + αL MAE (X n , X * ) + βL SSIM (X n , X * ) + γL MAE (Y n , Y * )

[0189] where Y n , X n are the chord diagram and the image estimated in the last iteration, Y * , X * represent the corresponding reference chord diagram and image, and α, β, and γ are hyperparameters that control the weights of different loss terms.

[0190] S503. Incorporate the intermediate iteration results of NGACI-Net into the loss function for intermediate supervision training to further fine-tune the intermediate layer model. The fine-tuning loss calculation formula is:

[0191]

[0192] where n represents the number of unfolded network iteration layers, ω i represents the loss weight for training the i-th layer model, output i represents the output CT image of the i-th layer model, and target is the normal-dose CT image.

[0193] Since the network is unfolded by an iterative algorithm, the overall network architecture is actually obtained by cascading a series of denoising networks. In each iteration, the output result of the previous network is input into the next network, which provides the network with a mechanism for repetitive top-down and bottom-up reasoning, allowing the initial estimates of the entire image and features to be re-evaluated while also increasing the overall structural complexity and training difficulty of the network. Incorporating the reconstructed images of the network intermediate layer into the loss calculation through intermediate supervision can mitigate the vanishing gradient phenomenon of the error of the output layer after multi-layer backpropagation and ensure the normal update of the underlying parameters. In the weight parameter setting of the fine-tuning loss calculation formula, the output closer to the final output result of the unfolded network has a larger proportion in the training loss because the loss values of the output results of the earlier networks are larger and more difficult to train. The selection of pre-training plus fine-tuning operations is also due to the fact that it is challenging to directly train after coupling the unfolded network algorithm with the neural network.

[0194] S504. For the simulation data, this study adopted the Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Mean Squared Error (MSE) as quantitative evaluation indicators.

[0195] PSNR is an important indicator for evaluating image quality and is widely used in the fields of image processing and computer vision. The calculation formula of PSNR is:

[0196]

[0197] where MAX I represents the maximum value of image pixels, which is 255 in 8-bit images and 1 in normalized images.

[0198] MSE represents the mean squared error between the original image and the processed image. For an image of size m×n, the calculation formula of SSIM is:

[0199]

[0200] where I o (i,j) is the (i,j)-th pixel value of the original image, and I p (i,j) is the (i,j)-th pixel value of the processed image. MSE measures the deviation between the two by calculating the average of the squares of the differences between the processed image and the original image.

[0201] PSNR is an index expressed on a logarithmic scale and is used to measure the similarity between the original image and the image processed through the network. The higher its value, the better the restored quality of the image. Usually, the unit of PSNR is expressed in decibels (dB).

[0202] SSIM: SSIM is an index widely used in the field of image processing to evaluate the similarity between two images. Compared with traditional pixel-level comparisons, SSIM comprehensively considers three aspects of the image: brightness, contrast, and structure, and captures the structural information of the image more comprehensively. Compared with some traditional pixel difference measurement methods, it more effectively retains the structural features of the image, making the generated image closer to the real image in quality. The specific calculation method of SSIM is introduced as follows.

[0203] The calculation of SSIM is based on three key factors: Luminance, Contrast, and Structure.

[0204] 1) Brightness

[0205] The luminance part calculation in SSIM mainly involves the means of two images. Specifically, the luminance is calculated as follows:

[0206]

[0207] where x and y represent the two images being compared, μ x and μ y are the means of the images respectively, and c 1 is a constant introduced to stabilize the calculation. The luminance calculation mainly compares the overall gray level of the images to evaluate the similarity in luminance between the two images. This part takes into account the overall luminance of the images and helps to capture the global features in the images.

[0208] 2) Contrast

[0209] Different from the luminance calculation, the contrast part calculation in SSIM involves the standard deviations of two images. For two images x and y, their standard deviations are σ x and σ y respectively, and the formula for calculating the contrast is:

[0210]

[0211] c 2 has the same function as c 1 in the luminance part calculation formula, and is also a smoothing term introduced to prevent the denominator from being too small. The contrast calculation mainly compares the pixel intensity distributions of the images to evaluate the similarity in contrast between the two images. This part takes into account the local contrast of the images and helps to capture the detailed information in the images.

[0212] 3) Structure

[0213] The structure calculation in SSIM considers the covariance of two images. Let the two images be x and y, and the covariance be σ xy , then the formula for calculating the structure part is:

[0214]

[0215] Similar to c 1 and c 2 , c 3 is a constant introduced to stabilize the calculation. The structure calculation mainly focuses on the structural information of the images, and evaluates the similarity in structure between the two images by comparing the correlation between pixels in the images. This part helps to capture the texture and minute structural differences in the images.

[0216] Combining the luminance, contrast, and structure calculation formulas, the expression of SSIM can be obtained as follows:

[0217] SSIM(x,y) = [L(x,y)] α [C(x,y)] β [S(x,y)] γ .

[0218] Where α, β, γ > 0 are parameters that adjust the importance of the corresponding model parts. By adjusting their values, we can more precisely express the importance of each part in the model. Here, it is assumed that α, β, γ are all 1, and c 3 = c 2 / 2, then:

[0219]

[0220] For the constants c 1 and c 2 , they are usually set as follows:

[0221]

[0222] In the above formula, L represents the dynamic range of pixel values, and k 1 and k 2 are adjustable constants. In this article, k 1 = 0.01, k 2 = 0.03. Such settings can ensure that the values of c 1 and c 2 adapt to different image dynamic range situations. The value range of SSIM is usually between [-1, 1]. Specifically, the closer the SSIM value is to 1, the higher the similarity and the better the quality of the two images; while the closer the value is to -1, the lower the similarity and the worse the quality of the two images; when the SSIM value is 0, it means there is no structural similarity between the two images.

[0223] Those skilled in the art of the relevant technical field can understand that various aspects of the present invention can be implemented as a system, method, or program product. Therefore, various aspects of the present invention can be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or an implementation combining hardware and software aspects, which can be collectively referred to as "circuit", "module", or "platform" here.

[0224] Embodiment 2

[0225] The present invention provides a low-dose CT reconstruction system based on global optimization iterative deep learning. This system can be used to implement the above-mentioned low-dose CT reconstruction method based on global optimization iterative deep learning. Specifically, this low-dose CT reconstruction system based on global optimization iterative deep learning includes a data module, a solution module, an iteration module, a fine-tuning module, and an output module.

[0226] in,

[0227] Data module, constructs CT data set, generates corresponding chord data and projection data from conventional dose CT images in CT data set through Radon transform and exponential transform, then injects composite Poisson noise into undamaged projection to simulate low dose CT scan data, and finally divides the data set into training set, validation set and test set;

[0228] The solution module establishes a dual-domain analysis compression iterative model based on the data consistency constraints, sparsity constraints and residual error correction mechanism of the CT projection domain and image domain, and uses the iterative threshold shrinkage algorithm and the joint algebraic reconstruction algorithm to achieve the solution. Then, based on the CT projection and chord diagram data scanning mechanism and the projection domain composite Poisson noise generation model, the maximum a posteriori estimation model is constructed, and the damped Newton method and the iterative threshold shrinkage algorithm are used to achieve the solution.

[0229] The iteration module combines the iterative algorithm of the chord diagram optimization model and the chord diagram image dual-domain model, and iteratively updates the projection data, chord diagram data, and image data in turn through a progressive improvement strategy, thus constructing an iterative algorithm to achieve CT full-domain optimization modeling.

[0230] The fine-tuning module converts the constructed iterative algorithm into a trainable reconstruction network NGACI-Net by unfolding the network method, adds corresponding sub-networks and CBAM convolutional attention modules for CT chordogram and image data features, uses momentum method to accelerate the convergence of the overall algorithm, and corrects the information loss problem of the deep unfolding network through residual learning, inter-level skip connections and skip connection weight fine-tuning;

[0231] The output module inputs the low-dose and conventional-dose CT paired data in the training set into the obtained reconstruction network NGACI-Net, and through intermediate supervision, the overall network and each layer operator training are carried out to obtain a low-dose CT reconstruction model.

[0232] Example 3

[0233] The present invention provides a terminal device, which includes a processor and a memory. The memory is used to store a computer program, and the computer program includes program instructions. The processor is used to execute the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Graphics Processing Unit (GPU), Tensor Processing Unit (TPU), Digital Signal Processor (DSP), Application Specific Integrated Circuit (ASIC), Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function. The processor described in the embodiments of the present invention can be used for the operation of a low-dose CT reconstruction method based on global optimization iterative deep learning, including:

[0234] A CT data set was constructed, and the corresponding chord diagram data and projection data were generated from the conventional dose CT images in the CT data set through Radon transform and exponential transform. Then, the compound Poisson noise was injected into the undamaged projection to simulate the low dose CT scanning data. Finally, the data set was divided into training set, validation set and test set. A dual-domain analysis compression iterative model was established based on the consistency constraints, sparsity constraints and residual error correction mechanism of CT projection domain and image domain data, and the solution was achieved using the iterative threshold shrinkage algorithm and the joint algebraic reconstruction algorithm. Then, a maximum a posteriori estimation model was constructed based on the scanning mechanism of CT projection and chord diagram data and the composite Poisson noise generation model in the projection domain, and the solution was achieved using the damped Newton method and the iterative threshold shrinkage algorithm. The chord diagram optimization model and the chord diagram image dual-domain model were combined to obtain the maximum a posteriori estimation model. The iterative algorithm of the type is used to iteratively update the projection data, chord diagram data and image data in turn through a progressive improvement strategy, and an iterative algorithm is constructed to realize the global optimization modeling of CT. The constructed iterative algorithm is converted into a trainable reconstruction network NGACI-Net through the unfolding network method, and corresponding sub-networks and CBAM convolutional attention modules are added according to the characteristics of CT chord diagram and image data. The momentum method is used to accelerate the convergence of the overall algorithm. At the same time, residual learning, inter-level skip connections and skip connection weight fine-tuning are used to correct the information loss problem of the deep unfolding network. The low-dose and conventional-dose CT paired data in the training set are input into the reconstruction network NGACI-Net, and the overall unfolding network and the operator training of each layer are taken into account through intermediate supervision to obtain a low-dose CT reconstruction model.

[0235] See also Figure 13 , the terminal device is a computer device. The computer device 60 of this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, the low-dose CT reconstruction method based on global optimization iterative deep learning in the embodiment is implemented. To avoid repetition, it is not described one by one here. Alternatively, when the computer program 63 is executed by the processor 61, the functions of each model / unit in the low-dose CT reconstruction system based on global optimization iterative deep learning in the embodiment are implemented. To avoid repetition, it is not described one by one here.

[0236] The computer device 60 may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will appreciate that Figure 13 This is only an example of the computer device 60 and does not constitute a limitation of the computer device 60. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0237] The so-called processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, Graphics Processing Unit (GPU), Tensor Processing Unit (TPU), Digital Signal Processor (DSP), Application Specific Integrated Circuit (ASIC), Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0238] The memory 62 may be an internal storage unit of the computer device 60, such as the hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk equipped on the computer device 60, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc.

[0239] Furthermore, the memory 62 may also include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or will be output.

[0240] Please refer to Figure 14 , the terminal device is an electronic device 600, and the electronic device 600 is presented in the form of a general computing device. The components of the electronic device may include but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including the storage unit 620 and the processing unit 610), a display unit 640, etc.

[0241] Among them, the storage unit stores program code, and the program code can be executed by the processing unit 610, so that the processing unit 610 executes the steps according to various exemplary embodiments of the present invention described in the above method part of this specification. For example, the processing unit 610 can execute steps as shown in Figure 1 .

[0242] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access storage unit (RAM) 6201 and / or a cache storage unit 6202, and may further include a read-only storage unit (ROM) 6203.

[0243] The storage unit 620 may also include a program / utilities 6204 having a set (at least one) of program modules 6205. Such program modules 6205 include, but are not limited to: an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment.

[0244] The bus 630 may represent one or more of several types of bus structures, including a storage unit bus or storage unit controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of a variety of bus structures.

[0245] The electronic device 600 may also communicate with one or more external devices 700 (such as a keyboard, a pointing device, a Bluetooth device, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 600, and / or may communicate with any device that enables the electronic device 600 to communicate with one or more other computing devices (such as a router, a modem). Such communication may be carried out through the input / output interface 650. Moreover, the electronic device 600 may also communicate with one or more networks (such as a local area network, a wide area network, and / or a public network, such as the Internet) through the network adapter 660. The network adapter 660 may communicate with other modules of the electronic device 600 through the bus 630. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms, etc.

[0246] Embodiment 4

[0247] The present invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and, of course, the expandable storage medium supported by the terminal device. It can be any tangible medium that contains or stores a program, and this program can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides a storage space that stores the operating system of the terminal. And, in this storage space, there are also stored one or more instructions suitable for being loaded and executed by a processor, and these instructions can be one or more computer programs (including program codes). It should be noted that more specific examples of the computer-readable storage medium here include: an electrical connection having one or more wires, a portable disk, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0248] The computer-readable storage medium also includes data signals propagated in a baseband or as part of a carrier wave, in which the readable program code is carried. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium can also be any readable medium other than the readable storage medium, and this readable medium can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted by any suitable medium, including but not limited to wireless, wired, optical cable, radio frequency, etc., or any suitable combination of the above.

[0249] The program code for performing the operations of the present invention can be written in any combination of one or more programming languages. The programming languages include object-oriented programming languages - such as Java, C++, etc., and also include conventional procedural programming languages - such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, executed as an independent software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user's computing device through any type of network, including a local area network or a wide area network, or can be connected to an external computing device (for example, by using an Internet service provider to connect through the Internet).

[0250] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the low-dose CT reconstruction method related to global optimization iterative deep learning in the above embodiments; the one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps:

[0251] Construct a CT data set, generate corresponding chordogram data and projection data from the conventional-dose CT images in the CT data set through Radon transform and exponential transform, then inject compound Poisson noise into the undamaged projections to simulate low-dose CT scan data, and finally divide the data set into a training set, a validation set, and a test set; establish a dual-domain analysis compression iteration model based on the data consistency constraint, sparsity constraint, and residual error correction mechanism in the CT projection domain and image domain data, and use the iterative threshold shrinkage algorithm and the joint algebraic reconstruction algorithm to achieve the solution. Then, construct a maximum a posteriori estimation model based on the CT projection and chordogram data scanning mechanism and the projection domain compound Poisson noise generation model, and use the damped Newton method and the iterative threshold shrinkage algorithm to achieve the solution; combine the iterative algorithms of the chordogram optimization model and the chordogram image dual-domain model, and sequentially iterate and update the projection data, chordogram data, and image data through a progressive improvement strategy to construct an iterative algorithm to achieve CT global optimization modeling; transform the constructed iterative algorithm into a trainable reconstruction network NGACI-Net through the unfolded network method, add corresponding sub-networks and CBAM convolutional attention modules for the CT chordogram and image data features, use the momentum method to accelerate the convergence of the overall algorithm, and at the same time correct the information loss problem of the deep unfolded network through residual learning, inter-level skip connections, and skip connection weight fine-tuning; input the paired low-dose and conventional-dose CT data in the obtained training set into the reconstruction network NGACI-Net, and train the overall unfolded network and each layer operator through intermediate supervision to obtain a low-dose CT reconstruction model.

[0252] The databases involved in the embodiments provided in the present application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., and is not limited thereto. The processors involved in the embodiments provided in the present application may be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., and is not limited thereto.

[0253] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Components in the description and shown in the accompanying drawings here of the embodiments of the present invention can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0254] Use the training set in step S1 to train five typical reconstruction models, namely EDCNN, REDCNN, NGIM-IRL, UNet, and FBPConvNet, and also use the above three evaluation metrics to evaluate their reconstruction effects on the test set, so as to conduct a comparative analysis with the performance of the NGACI-Net model provided by the present invention. The results are shown in the following table:

[0255] Table 3 Performance comparison of six models on the test set

[0256]

[0257] The calculated results of the evaluation metrics for the reconstruction results of the NGACI-Net model provided by the present invention on the test set are: PSNR = 44.8344, SSIM = 0.9801, MSE = 15.0551. In terms of the mean and variance of the three metrics, it is superior to the other five models. Compared with the advanced medical image reconstruction model FBPconvNet, the NGACI-Net model has increased by 4.41% in PSNR and 0.52% in SSIM, and the model size is also relatively better. The present invention has reached the advanced level of low-dose CT image reconstruction.

[0258] To verify the rationality of the network optimization part and their roles and contributions, this article conducts a quantitative comparison of PSNR and SSIM before and after optimization. The results are shown in the following table. By comparing the evaluation metrics before and after replacing the network structure, it can be clearly observed that after optimizing the network, both PSNR and SSIM have been significantly improved, fully demonstrating the rationality of this part.

[0259] Table 4 Performance comparison of ablation experiments

[0260]

[0261] To visually compare the reconstruction effects of six models on low-dose CT images, two CT images were selected from the test set in this study, and the corresponding low-dose CT images, conventional-dose CT images, and reconstruction images of the six models were visualized, as Figure 8 and Figure 9 shown. It can be seen that for CT images with relatively simple tissue and organ structures, there is no obvious difference between the reconstruction images of the NGACI-Net model and the normal-dose CT images, and a good reconstruction effect is achieved by the low-dose CT reconstruction method based on global iterative deep learning provided by the present invention; for CT images with relatively complex tissue and organs, compared with the input images, the artifacts in the output images of the NGACI-Net model are basically removed, and the visual effect is greatly improved. In addition, the network still well preserves the original tissue and organ structures during the reconstruction process, further verifying the quantitative results shown in Table 3.

[0262] To visually compare the effect of network optimization, in this study, the corresponding CT images were visualized and compared from two perspectives: residual maps and windowed detail maps, as Figure 10 and Figure 11 shown. It can be seen from the residual images output by the network that the optimized NGACI-Net learns more residuals, that is, the noise artifacts in the original images are removed more thoroughly. The residual maps also further confirm that this method of removing noise artifacts by residual learning well preserves the original tissue and organ structures. And from the windowed CT reconstruction images, it can be more intuitively seen that the optimized unfolded network restores the details of the organ edges better. Therefore, this algorithm can, to a certain extent, solve the problem that it is difficult to remove noise artifacts in low-dose reconstruction.

[0263] In the model testing stage, to verify the effectiveness of the low-dose CT reconstruction algorithm, this study not only used simulation data but also collected 760 clinical low-dose CT data from multiple patients in the hospital. For real clinical data, due to the lack of corresponding conventional-dose paired images, quantitative evaluation cannot be carried out. Therefore, we provided the effect diagrams after artifact removal for visual comparison, as Figure 12 shown. It can be seen that the NGACI-Net removes the noise artifacts in the low-dose CT images more thoroughly and reconstructs the details better.

[0264] Compared with the advanced medical image reconstruction model FBPconvNet, the NGACI-Net model has an increase of 4.41% in PSNR and an increase of 0.52% in SSIM, and the model size is also relatively more optimal. The present invention has reached an advanced level in low-dose CT image reconstruction. On this basis, the ability of the NGACI-Net model to remove noise artifacts and restore organ details is further improved compared with the FBPconvNet model, and the model size is also relatively more optimal.

[0265] In summary, for a low-dose CT reconstruction method and system based on global optimization iterative deep learning according to the present invention, CT cross-sectional data of normal dose is collected, Gaussian noise and Poisson noise are added to generate low-dose CT data, and the data is randomly divided into a training set and a test set; a dual-domain analysis compression iterative model is established based on the consistency constraint and sparsity constraint of CT projection domain and image domain data, and a maximum a posteriori estimation problem is constructed based on the composite Poisson noise generation mechanism of CT projection and chord diagram data. Finally, the CT projection data is further divided into a projection domain and a chord diagram domain, and the projection data, chord diagram data and image data are sequentially updated based on a progressive improvement strategy to construct an iterative algorithm to realize CT global optimization modeling, and the iterative algorithm is expanded into a trainable reconstruction network; paired data (normal dose and corresponding low-dose CT data) is input into the expanded network for training, and the model with the smallest output result loss is saved; a sub-network and an attention mechanism are added according to the CT data characteristics, and by fine-tuning the skip connection weights, the idea of momentum, residual learning and cross-stage information channels are introduced, and the intermediate layer neural network parameters are updated by fine-tuning through intermediate supervision; finally, the performance of the low-dose CT reconstruction of the expanded network model is evaluated on the test set. The present invention reaches the advanced level of low-dose CT reconstruction, and improves the problems of poor low-dose CT image quality, low reconstruction efficiency, lack of generalization and interpretability.

[0266] The above content is only to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A low-dose CT reconstruction method based on global optimization iterative deep learning, characterized in that: The following steps are involved: S1. Construct a CT data set, generate corresponding chord data and projection data from the conventional dose CT images in the CT data set through Radon transform and exponential transform, then inject compound Poisson noise into the undamaged projection to simulate low dose CT scan data, and finally divide the data set into training set, validation set and test set; S2. Based on the data consistency constraints, sparsity constraints and residual error correction mechanism of CT projection domain and image domain, a dual-domain analysis compression iterative model is established, and the iterative threshold shrinkage algorithm and joint algebraic reconstruction algorithm are used to achieve the solution. Then, based on the CT projection and chord diagram data scanning mechanism and the projection domain composite Poisson noise generation model, a maximum a posteriori estimation model is constructed, and the damped Newton method and iterative threshold shrinkage algorithm are used to achieve the solution. S3, combining the iterative algorithm of the chord diagram optimization model and the chord diagram image dual-domain model in step S2, iteratively updating the projection data, chord diagram data and image data in sequence through a progressive improvement strategy, and constructing an iterative algorithm to realize CT global optimization modeling; S4. The iterative algorithm constructed in step S3 is converted into a trainable reconstruction network NGACI-Net by unfolding the network method. The corresponding sub-network and CBAM convolutional attention module are added for the CT chord diagram and image data features. The momentum method is used to accelerate the convergence of the overall algorithm. At the same time, residual learning, inter-level skip connections, and skip connection weight fine-tuning are used to correct the information loss problem of the deep unfolding network. S5. Input the low-dose and conventional-dose CT paired data in the training set obtained in step S1 into the reconstruction network NGACI-Net obtained in step S4, and carry out the overall network and each layer operator training through intermediate supervision to obtain a low-dose CT reconstruction model.

2. The low-dose CT reconstruction method based on global optimization iterative deep learning according to claim 1, characterized in that: In step S1, according to the corresponding normal-dose CT image, corresponding low-dose CT data are generated based on the CT scanning and noise generation model, including projection data, chord data and image data, and the CT data set is divided into a training set, a validation set and a test set at a ratio of 8:1:

1.

3. The low-dose CT reconstruction method based on global optimization iterative deep learning according to claim 1, characterized in that: Step S2 is specifically as follows: S201, introducing a residual error correction mechanism in chord graph denoising, and realizing stable reconstruction based on a sparse prior module of compressed sensing, and obtaining the optimization target of a dual-domain analysis compression iterative model; S202, constructing a maximum a posteriori estimation model based on the CT projection and chord diagram data scanning mechanism and the corresponding compound Poisson noise generation model to obtain the final optimization target of projection domain denoising.

4. The low-dose CT reconstruction method based on global optimization iterative deep learning according to claim 3, characterized in that: The optimization objectives of the dual-domain analysis compression iterative model are as follows: Among them, Φ is the reconstruction model, A is the Radon transform, and Y e is the chord diagram error, Y is the initial measurement value of the chord diagram, X is the image data, λ1, λ2, λ3 are the weight parameters for balancing different terms, and H is the sparse transformation regularization term.

5. The low-dose CT reconstruction method based on global optimization iterative deep learning according to claim 3, characterized in that: The final optimization goal of projection domain denoising is as follows: Where T represents the projection data under ideal conditions that need to be restored, Y represents the chord diagram data under ideal conditions that need to be restored, and N represents the total number of scanning rays, which can be calculated by multiplying the total number of detectors by the number of projection views. i is the number of photons actually received by the i-th photosensitive unit of the detector, T i is the number of photons received by the i-th photosensitive unit of the detector under ideal conditions, I 0i is the initial photon number of the CT of the i-th photosensitive unit of the detector, σ is the standard deviation of the CT electronic noise, and Y i is the ideal attenuation path and T of the ith ray. i ! is the factorial of the number of photons received by the i-th photosensitive unit of the detector under ideal conditions, μ is the regularization weight parameter, and F is the sparse transformation operator.

6. The low-dose CT reconstruction method based on global optimization iterative deep learning according to claim 1, characterized in that: Step S3 is specifically as follows: Based on the progressive improvement strategy, the projection data, chord diagram data and image data are iteratively updated in sequence, and an iterative algorithm is constructed to realize the global optimization modeling of CT. The momentum term is introduced into the soft threshold iterative algorithm using the gradient acceleration strategy to improve it into an accelerated soft threshold iterative algorithm.

7. The low-dose CT reconstruction method based on global optimization iterative deep learning according to claim 1, characterized in that: Step S4 is specifically as follows: S401, based on the iterative algorithm obtained in step S3, replacing the sparse transformation operator in the iterative threshold shrinkage algorithm with a deep network to implement implicit regularization based on the deep neural network; S402, using algorithm unfolding technology to map the computational steps of each iteration in the iterative reconstruction algorithm into a single shallow neural network layer, and stacking a limited number of neural network layers together to achieve a global modeling analysis compressed iterative deep framework; S403, for the NGACI-Net chord diagram domain network, a noise estimation subnetwork is designed according to the CT chord diagram domain data characteristics, and a noise variance level map is approximately calculated according to the input noise chord diagram and the CT noise model; S404. For the NGACI-Net chord domain network, an edge enhancement subnetwork is designed based on the data features of the CT image domain, and an edge enhancement module is implemented based on the trainable Sobel Feldman operator to extract edge information of different intensities of the image; S405, before the feature map extracted by the chord diagram and the image domain sub-network and the original image are superimposed on the channel dimension and input into the denoising sub-network, a CBAM convolutional attention module is introduced to realize dynamic selection of important information of the image input through the attention mechanism to generate the final feature map; S406, the jump connection in the UNet network in NGACI-Net connects the features of the corresponding layer in the encoder with the features of the corresponding layer in the decoder, and fine-tunes the weights of the jump connection to further improve the network feature extraction and denoising capabilities; S407. Design cross-stage information pathways in the NGACI-Net framework and introduce residual connections in the deep residual network to correct information loss.

8. The low-dose CT reconstruction method based on global optimization iterative deep learning according to claim 1, characterized in that: Step S5 is specifically as follows: The S501 and NGACI-Net models were trained using the Adam optimizer with (β1, β2) = (0.5, 0.999). The initial learning rate was set to 0.0001. After 20 epochs, the learning rate was halved every 10 trainings. A total of 100 trainings were performed, and the data batch size used each time was 1. S502, constructing a composite loss function of the NGACI-Net model; S503, incorporating the intermediate iteration results of the NGACI-Net model into the loss function for intermediate supervised training, fine-tuning the intermediate layer model, and obtaining a low-dose CT reconstruction model.

9. The low-dose CT reconstruction method based on global optimization iterative deep learning according to claim 8, characterized in that: The composite loss function of the NGACI-Net model is: Loss=L MSE (X n ,X * )+αL MAE (X n ,X * )+βL SSIM (X n ,X * )+γL MAE (Y n ,Y * ) Among them, Y n , X n is the chord diagram and image estimated in the last iteration, Y * , X * denotes the corresponding reference chord diagram and image, α, β, and γ are hyperparameters that control the weights of different loss terms.

10. A low-dose CT reconstruction system based on global optimization iterative deep learning, characterized in that: include: Data module, constructs CT data set, generates corresponding chord data and projection data from conventional dose CT images in CT data set through Radon transform and exponential transform, then injects composite Poisson noise into undamaged projection to simulate low dose CT scan data, and finally divides the data set into training set, validation set and test set; The solution module establishes a dual-domain analysis compression iterative model based on the data consistency constraints, sparsity constraints and residual error correction mechanism of the CT projection domain and image domain, and uses the iterative threshold shrinkage algorithm and the joint algebraic reconstruction algorithm to achieve the solution. Then, based on the CT projection and chord diagram data scanning mechanism and the projection domain composite Poisson noise generation model, the maximum a posteriori estimation model is constructed, and the damped Newton method and the iterative threshold shrinkage algorithm are used to achieve the solution. The iteration module combines the iterative algorithm of the chord diagram optimization model and the chord diagram image dual-domain model, and iteratively updates the projection data, chord diagram data, and image data in turn through a progressive improvement strategy, thus constructing an iterative algorithm to achieve CT full-domain optimization modeling. The fine-tuning module converts the constructed iterative algorithm into a trainable reconstruction network NGACI-Net by unfolding the network method, adds corresponding sub-networks and CBAM convolutional attention modules for CT chordogram and image data features, uses momentum method to accelerate the convergence of the overall algorithm, and corrects the information loss problem of the deep unfolding network through residual learning, inter-level skip connections and skip connection weight fine-tuning; The output module inputs the low-dose and conventional-dose CT paired data in the training set into the obtained reconstruction network NGACI-Net, and through intermediate supervision, the overall network and each layer operator training are carried out to obtain a low-dose CT reconstruction model.

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