Image Reconstruction Method Based on Learnable Projection Operator and Iterative Optimization Framework

Abstract

This invention provides an image reconstruction method based on a learnable projection operator and an iterative optimization framework, belonging to the field of medical imaging technology. The method includes acquiring sparse projection data, recovering the processed data using a projection domain sub-network, and converting the projection data into image domain data using an inter-domain data transformation operator. Subsequently, the image domain sub-network optimizes the image domain data, and the optimized data is then converted back to the projection domain, iterating until convergence conditions are met. This invention also includes a consistency constraint framework to jointly optimize the two sub-network modules. Furthermore, the inter-domain data transformation operator module includes learnable position parameters and a reverse line integral calculation module to achieve efficient data domain transformation. By employing the above-mentioned image reconstruction method based on a learnable projection operator and an iterative optimization framework, this invention can provide high-quality CT images while reducing radiation dose.

Description

Technical Field

[0001] This invention relates to the field of medical imaging technology, and in particular to an image reconstruction method based on a learnable projection operator and an iterative optimization framework. Background Technology

[0002] Medical imaging plays a crucial role in clinical research and treatment planning. Computed tomography (CT), a widely used medical imaging technique, typically obtains images through sampling a certain number and dose of radiation signals. However, traditional CT scans require the use of high-intensity radiation to acquire detailed information about biological tissues, which may pose potential risks to human health. To reduce radiation dose and shorten scan time, researchers have proposed sparse projection sampling methods. Nevertheless, the data incompleteness caused by sparse sampling can produce stripe artifacts and speckle noise in CT images, affecting image quality.

[0003] The development of deep learning technology has provided a new approach to solving this problem. Data-driven methods can effectively recover undersampled CT data, thereby obtaining high-quality images while reducing radiation exposure. Filtered back projection (FBP) algorithms are widely used in CT image reconstruction due to their high computational efficiency; however, this method has high requirements for data completeness and radiation dose, and may amplify errors when processing noise, leading to a decrease in image quality. While iterative reconstruction methods can provide more accurate reconstruction results under low-dose conditions, their high computational resource consumption and slow reconstruction speed limit their application.

[0004] To overcome the limitations of existing technologies, this invention proposes a novel CT image reconstruction method. This method, through the design of a dedicated projection data transformation operator and the integration of a cross-domain collaborative optimization strategy, aims to reduce computational resource consumption during data transformation while improving image restoration quality. This approach is expected to improve reconstruction efficiency and reduce noise levels while preserving image structural characteristics, providing a more efficient and reliable solution for the field of medical imaging. Summary of the Invention

[0005] The purpose of this invention is to provide an image reconstruction method based on a learnable projection operator and an iterative optimization framework. This method achieves independent optimization of two data domains and joint alternating optimization, effectively improving the quality of CT reconstructed images under low radiation dose settings.

[0006] To achieve the above objectives, this invention provides an image reconstruction method based on a learnable projection operator and an iterative optimization framework, comprising the following steps:

[0007] Step S1: Obtain sparse projection sampling data;

[0008] Step S2: Use the projection domain subnetwork module to recover the sparse projection sampling data to obtain the recovered projection data;

[0009] Step S3: Convert the recovered projection data into image domain data using the inter-domain data conversion operator module;

[0010] Step S4: Optimize the image domain data using the image domain sub-network module to obtain optimized image domain data;

[0011] Step S5: Convert the optimized image domain data into projection data using the inter-domain data transformation operator module, and use it as the input for the next iteration;

[0012] Step S6: Repeat steps S2 to S5 until the preset number of iterations is reached or the convergence condition is met, and output the final reconstructed image.

[0013] Preferably, the method further includes a consistency constraint framework for jointly constraining the optimization process of the projection domain subnetwork module and the image domain subnetwork module.

[0014] Preferably, the projection domain subnetwork module includes:

[0015] The U-Net architecture serves as the backbone model. The U-Net architecture contains four dense encoding and decoding layers. Each encoding layer includes two 2D convolutional layers and one max pooling layer. Each decoding layer includes two 2D convolutional layers and one upsampling convolutional layer.

[0016] The sparse truth-guiding module transforms the image domain data into the projection domain through the forward projection operator in the last step of the iteration to guide sparse truth values, and then restores it back to the image domain through the backward projection operator.

[0017] The alignment loss enhancement module achieves projection domain data correction by estimating complete projection data from sparse projection data, and strengthens alignment loss based on mean square error design.

[0018] Preferably, the enhanced alignment loss module achieves projection domain data correction by estimating complete projection data from sparse projection sampling data, and designs enhanced alignment loss based on mean square error, with the following optimization objectives:

[0019]

[0020] Where MIN represents the optimization objective. This represents the full-view projection predicted by the projection domain subnetwork. represents the label of the full-view projection data, k represents the iteration round, μ represents the enhancement loss coefficient, and s represents the sparse parameter. for One of the views in the video. for One of the views in the array, where i represents the cardinality of the subscript and has an upper limit of v.

[0021] Preferably, the sparse truth-guided module, in the last iteration of the iterative framework, transforms the image domain iteration result into the projection domain using a learnable forward projection operator, performs sparse truth-guided operations, and then restores it back to the image domain using a back projection operator, i.e.:

[0022]

[0023] in, This represents projection data guided by sparse truth values. Ω represents the image data generated in the last iteration, Ω represents the set of indices corresponding to the sparsely sampled view in the original complete view, and N represents the total number of iterations. Indicates the forward projection operator. This represents the value in the j-th column of the projected data label, where j represents the cardinality of the subscript. Represents the back projection operator. This represents the final result image.

[0024] Preferably, the image domain sub-network module includes a bit-plane encoding / decoding module, which performs bit-plane decomposition encoding, optimization processing, and synthesis decoding on the image domain data.

[0025] Preferably, the encoding and decoding processes in the image domain sub-network module are as follows:

[0026] B = diag(b1, b2, ..., b m ),b m ∈{0,1};

[0027] P = diag(2) m-1 ,2 m-2 ,…,2 0 );

[0028]

[0029] Where B represents a matrix containing m channel decomposition elements of a single pixel, b m Let P represent the signal value on the m-th decomposed channel, where m represents the number of decomposed channels, and P represents the recovery matrix. Let d represent the decomposition of the pixel in the i-th row and j-th column of an image x in the k-th round on the m-th decomposition channel, where d represents the preset number of channels.

[0030] Preferably, the inter-domain data transformation operator module includes a learnable position parameter and a reverse line integral calculation module.

[0031] Preferably, the workflow of the inter-domain data transformation operator module is as follows:

[0032] Converting fan-shaped beam data into parallel beam data involves grouping all fan-shaped beam rays together, grouping mutually parallel rays into one group.

[0033] Data conversion is achieved through Radon's line integral transform, and its expression is as follows:

[0034]

[0035] Where L represents the imaginary straight-line radiation path between the X-ray source and the detector in the CT equipment; S represents the distance between the X-ray source and the detector; The set of angles relative to the origin of the radiation source during axial scanning; f(x,y) represents the attenuation coefficient of the radiation at position (x,y) on the tomography when it passes through the tissue being tested; R L This indicates the intensity of radiation after attenuation, which is captured by the detector;

[0036] When performing data conversion, it is assumed that the center of rotation of the radiation source in the axial scan is the origin, the L equation is a linear equation, and the direction of L away from the origin is... Assuming the distance between the origin and L is p, the theoretical expression for L is as follows:

[0037] x cosθ + y sinθ = p;

[0038] Where θ represents the angular direction, and p represents the radiation source at each point along the θ direction. The Radon transform theory is redefined under (θ, p) and double integral theory, and further derivations are shown in the formula:

[0039] R(θ,p)=∫∫f(x,y)δ(px cosθ-y sinθ)dxdy;

[0040] R(θ,p)=∫ x cosθ+y sinθ＝p f(x,y)dS;

[0041] Where R(θ,p) represents the pixel value of the pixel at a distance p in the direction of angle θ, and δ represents the Dirac function, which is used to filter specific points;

[0042] During parallel beam reconstruction, it is assumed that the detector rotates around the object at a constant speed and performs a strategy conversion from parallel beam to fan beam. Each ray of the fan beam corresponds to a ray of the parallel beam.

[0043] When the Radon line integral transform is satisfied, parallel beams and fan beams are equivalent, and their expression is:

[0044]

[0045] Where γ and β represent the two angular directions of the parallel beam, D represents the distance between the parallel beam detector and the object to be measured, and s' represents the distance between the fan-shaped beam detector and the object to be measured.

[0046] An efficient operator model is trained using multiple [R(θ,p),f(x,y)] datasets to achieve deep learning fitting of the parameters and weights of the Radon transform process, thereby obtaining accurate forward / backward projection operators.

[0047]

[0048] Therefore, the present invention employs the above-mentioned image reconstruction method based on a learnable projection operator and an iterative optimization framework, and the beneficial technical effects are as follows:

[0049] The method proposed in this invention improves the reconstruction quality of CT images under low radiation dose settings. This invention is based on improvements to iterative reconstruction algorithms and deep learning methods. In practical computer-aided medical diagnosis and treatment scenarios, the CT reconstruction images resulting from data acquisition using a lower-density CT projection sampling strategy contain numerous bar artifacts and star-shaped noise, which are optimized and resolved within the iterative reconstruction framework. Furthermore, the problem of model stalling at stage-specific or local optima due to alternating optimization across domains during actual model training and testing is effectively addressed using learnable projection operators and dual-domain feature consistency constraints.

[0050] This invention has wide applications in computed tomography (CT)-assisted medical diagnosis and treatment, enabling the reconstruction of medically significant images during CT sampling with lower radiation levels. This will provide a less harmful solution for patients who need CT scans. Attached Figure Description

[0051] Figure 1 This is a flowchart of an image reconstruction method based on a learnable projection operator and an iterative optimization framework according to the present invention;

[0052] Figure 2 A flowchart illustrating the specific process of a single-domain subnetwork module;

[0053] Figure 3 This is a schematic diagram of the inter-domain data conversion operator module;

[0054] Figure 4 Schematic diagram for enhancing alignment loss module;

[0055] Figure 5 This is a schematic diagram of a bit-plane encoding / decoding module;

[0056] Figure 6The dataset used in Example 1 contains images corresponding to three human tissues (from top to bottom: abdomen, head, and chest). It is divided into three downsampling strategies and full sampling (from left to right: 1 / 16 downsampling, 1 / 8 downsampling, 1 / 4 downsampling, and full sampling).

[0057] Figure 7 The image processing results of the method proposed in this invention are compared with the visualization results of the most advanced methods at home and abroad, corresponding to the imaging of three human tissues (from top to bottom: abdomen, chest, and head); among which, Figure 7 (a) in the text represents FBP; Figure 7 (b) in the text represents DoDuNet; Figure 7 (c) in the text represents NeumannNet; Figure 7 (d) in the text stands for MAGIC; Figure 7 (e) in the text represents NB-Ne; Figure 7 (f) in the text stands for RegFormer; Figure 7 (g) in the text refers to ADAM-Net; Figure 7 (h) in the text stands for DIOR; Figure 7 (i) in the figure represents the effect of the present invention; Figure 7 (j) in the diagram represents the reference visualization result;

[0058] Figure 8 A reference diagram is set for each iteration round, corresponding to three projection sampling settings, as shown in the figure with corresponding annotations;

[0059] Figure 9 To set the effects for the iteration rounds, three projection sampling settings and three tissue imaging of the human body are provided (each view corresponds to the abdomen, chest and head from left to right respectively);

[0060] Figure 10 To enhance the visualization of the impact of the alignment loss module on the pre-training process;

[0061] Figure 11 To visualize the accuracy of learnable operators and filtered back projection methods for data domain transformation, images are created for both dual-domain and three human tissues; among them, Figure 11 (a) shows the original projection data of the abdomen, chest, and head from top to bottom; Figure 11 In (b) from top to bottom, items 1, 3, and 5 are the original projection data of the abdomen, chest, and head, respectively, and items 2, 4, and 6 are the processing results of the FBP operator. Figure 11 In (c), from top to bottom, items 1, 3, and 5 are the original projection data of the abdomen, chest, and head, respectively, and items 2, 4, and 6 are the operator processing results in this invention. Figure 11 (d) in the image contains the original data of the abdomen, chest, and head images from top to bottom. Figure 11In (e), from top to bottom, items 1, 3, and 5 are the original data of the abdominal, chest, and head images, respectively, and items 2, 4, and 6 are the processing results of the FBP operator. Figure 11 In (f), from top to bottom, items 1, 3, and 5 are the original data of the abdominal, chest, and head images, respectively, and items 2, 4, and 6 are the operator processing results in this invention. Detailed Implementation

[0062] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0063] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0064] Example 1

[0065] An image reconstruction method based on learnable projection operators and an iterative optimization framework includes a projection domain sub-network module (PD-Net), an image domain sub-network module (ID-Net), an enhancement alignment loss module (EAL), a bit plane encoding / decoding module (BEM / BDM), inter-domain data transformation operator modules (forward and backward), and a consistency constraint framework. The overall process is illustrated in the diagram below. Figure 1 As shown, the single-domain sub-network modules (projection domain sub-network module, image domain sub-network module) are as follows: Figure 2 As shown, the inter-domain data transformation operator module is as follows: Figure 3 As shown, the enhanced alignment loss module is as follows: Figure 4 As shown, the bit-plane encoding / decoding module is as follows: Figure 5 .

[0066] Projection Domain Subnetwork Module: For undersampled sparse CT projection data, a lightweight and efficient U-Net subnetwork is used as the backbone model to recover the projection domain data. During the recovery process, a sparse ground truth guidance module enhances the data recovery capabilities of the backbone model. In the case of missing projection samples, an enhanced alignment loss module strengthens the guiding role of the remaining ground truth data in the data recovery process.

[0067] The projection domain sub-network module comprises a backbone model, a sparse truth-guided module, and an enhanced alignment loss module. Training of the backbone model is completed under the constraints of the enhanced alignment loss module, with a sparse truth-guided operation used in the final iteration.

[0068] The backbone network employs a lightweight U-Net architecture, comprising four dense encoder-decoder layers. Each encoder layer consists of two 2D convolutional layers and a max-pooling layer for feature extraction and downsampling; each decoder layer contains two 2D convolutional layers and an upsampling convolutional layer for feature reconstruction and upsampling. The network reconstructs incompletely sampled CT projection data through end-to-end learning. During iteration, if the current iteration is the last, a sparse ground truth guidance module is activated to enhance the accuracy of data reconstruction. The U-Net architecture, due to its efficient parameter learning and memorization capabilities, becomes a scalable and replaceable key component in the model.

[0069] The sparse truth-guided module, in the final iteration of the iterative framework, transforms the image domain iteration results into the projection domain using a learnable forward projection operator, performs sparse truth-guided analysis, and then restores the image domain using a back projection operator. That is:

[0070]

[0071] in, This represents projection data guided by sparse truth values. Ω represents the image data generated in the last iteration, Ω represents the set of indices corresponding to the sparsely sampled view in the original complete view, and N represents the total number of iterations. Indicates the forward projection operator. This represents the value in the j-th column of the projected data label, where j represents the cardinality of the subscript. Represents the back projection operator. This represents the final result image.

[0072] An enhanced alignment loss module is implemented in sparse view CT iterative reconstruction to achieve projection domain data correction by estimating complete projection data from sparse projection data. The optimization objective MIN L2 of the projection domain subnetwork is as follows:

[0073]

[0074] in, This represents the full-view projection predicted by the projection domain subnetwork. The label represents the full-view projection data, and k represents the iteration round. Since sparse projection is itself part of complete projection, in addition to using complete and sparse projection to calculate the loss in the projection domain sub-network, an enhanced alignment loss is designed based on MSE to drive the generation of better quality unknown data through sparse projection. The optimization objective is:

[0075]

[0076] in for One of the views in the video. for One of the views in the diagram, where s represents sparse parameters (4, 8, 16) and the upper bound of i is v (128, 64, 32). By fusing the two formulas above and adding a weight μ, a complete projection domain alignment loss is designed as follows:

[0077]

[0078] Here, MIN represents the optimization objective.

[0079] Image Domain Sub-Network Module: CT image data reconstructed from incompletely recovered projection data still requires further optimization. Using a lightweight and efficient image domain sub-network to perform image domain data optimization is crucial. During image domain data optimization, a bit-plane encoding / decoding module is first used to decompose the image at the pixel level. Next, the decomposed coded data is restored to its decomposed domain. Finally, the restored data is synthesized and decoded to obtain the optimized CT image.

[0080] The image domain sub-network module contains a bit-plane encoding / decoding module (same as the projection domain sub-network module). First, the CT projection data that has been partially restored is converted into CT image data and bit-plane decomposition is performed for initial encoding. The initial encoding result is input into the dense encoding / decoding network model for end-to-end restoration enhancement. Finally, the output data is processed by bit-plane synthesis decoding.

[0081] The bit-plane encoding / decoding module converts CT image pixels within a certain grayscale range into m-bit channels in binary. Noise in the CT image also enters multiple channels during the encoding process. Therefore, the work performed by the image domain sub-network is not a direct end-to-end image operation, but rather an end-to-end channel operation, followed by decoding into a CT image. The channel encoding and decoding process is shown in the following formulas (sets). That is:

[0082] B = diag(b1, b2, ..., b m ),b i ∈{0,1};

[0083] P = diag(2) m-1 ,2 m-2 ,…,2 0 );

[0084]

[0085] Where B represents a matrix containing m channel decomposition elements of a single pixel, b m Let P represent the signal value on the m-th decomposed channel, where m represents the number of decomposed channels, and P represents the recovery matrix. Let d represent the decomposition of the pixel in the i-th row and j-th column of an image x in the k-th round on the m-th decomposition channel, where d represents the preset number of channels. The encoding / decoding process, which takes the form of a formula (or set of formulas), can be simply represented as the encoding operator ε(·) and the decoding operator.

[0086] Inter-domain data conversion operator module: The traditional process of reconstructing CT projection data into CT image data consumes a lot of computing resources. The inter-domain operator module sets 130 projection position parameters as learnable parameters, uses the model to solve for and memorize the position parameters of a large amount of data, and forms a data conversion operator that can be used immediately.

[0087] The inter-domain data transformation operator module includes a learnable position parameter and a reverse line integral calculation module. The data obtained from the projection domain sub-network is processed by an inter-domain data transformation operator to obtain the corresponding CT image data in real time.

[0088] The inter-domain data transformation operator module, based on the dual-domain interaction operator of industrial CT, learns the bidirectional mapping between sparse sinusoidal data in the projection domain and labels in the image domain. The operator is a transformation operator between complete projection data and complete view CT images, designed based on Radon transform and medical CT, and is implemented by making some parameters in the Radon transform learnable. Specifically, it transforms fan-beam data into parallel-beam data. All fan-beam rays are grouped together, and parallel rays are grouped together to convert to parallel-beam imaging. The data restructuring is replaced by transforming the variables of the algorithm. Therefore, the Radon line integral transform is as follows:

[0089]

[0090] Where L represents the imaginary straight-line radiation path between the X-ray source and the detector in the CT equipment; S represents the distance between the X-ray source and the detector; The set of angles relative to the origin of the radiation source during axial scanning; f(x,y) represents the attenuation coefficient of the radiation at position (x,y) on the tomography when it passes through the tissue being tested; R L This represents the intensity of the attenuated radiation, captured by the detector. Assuming the center of rotation of the radiation source in the axial scan is the origin, and assuming the L equation in the formula is a linear equation, the direction of L away from the origin is... Assuming the distance between the origin and L is p, then the expression for is as follows:

[0091] x cosθ + y sinθ = p;

[0092] Where θ represents the angular direction, and p is a point radiation source in the direction θ. Under (θ,p) and double integral theory, the Radon transform theory is redefined and further derived as shown in the formula:

[0093] R(θ,p)=∫∫f(x,y)δ(px cosθ-y sinθ)dxdy;

[0094] R(θ,p)=∫ x cosθ+y sinθ＝p f(x,y)dS;

[0095] To achieve dual-domain data conversion, it is always assumed that the detector rotates around the object at a uniform speed during parallel beam reconstruction. Under this assumption, a strategy conversion from parallel beam to sector beam is performed. Each ray of the sector beam corresponds to a ray of the parallel beam; that is, the data g(γ,β) of each sector beam corresponds exactly to the data p(s',θ) of a parallel beam. When the Radon line integral transform is satisfied, the parallel beam and the sector beam are equivalent.

[0096]

[0097] Under the requirements of the above further derivation formula, s' and All angles and directions θ are assumed to be unknowns. A sufficiently large amount of [R(θ,p),f(x,y)] data is used to train an efficient operator model to enable deep learning to memorize the parameters and weights of the Radon transform process. In fact, this is a pre-trained network solving for the assumed unknowns using Radon transform theory on a large dataset; for powerful deep learning, this is a simple task. This yields an accurate forward / backward projection operator, denoted as...

[0098]

[0099] Consistency constraint framework: Traditional deep learning-based CT reconstruction methods are performed in the same data domain. The consistency constraint framework will interact with the frequency domain and image domain to fuse information from both domains, and use frequency domain features to constrain the image domain data recovery work to maintain positive directionality.

[0100] The consistency constraint framework unites the dual-domain subnetworks and incorporates a joint loss function supported by inter-domain data transformation operators. During operation, the image domain subnetwork module is constrained by the joint loss function, training and memorizing in the correct direction of data recovery.

[0101] Figure 6Examples of images from the dataset used in Example 1 are provided by the Mayo Clinic and are official public datasets from the 2016 and 2020 AAPM Low-Dose CT Challenge. The datasets correspond to imaging of three human tissues (from top to bottom: abdomen, head, and chest), and are divided into three downsampling strategies and full sampling (from left to right: 1 / 16 downsampling, 1 / 8 downsampling, 1 / 4 downsampling, and full sampling). The experimental results and visualizations are based on this dataset.

[0102] Figure 7 The image processing results of the method proposed in this invention are compared with the visualization results of the most advanced methods at home and abroad, corresponding to the imaging of three human tissues (from top to bottom: abdomen, chest, and head); among which, Figure 7 (a) in the text represents FBP; Figure 7 (b) in the text represents DoDuNet; Figure 7 (c) in the text represents NeumannNet; Figure 7 (d) in the text stands for MAGIC; Figure 7 (e) in the text represents NB-Ne; Figure 7 (f) in the text stands for RegFormer; Figure 7 (g) in the text refers to ADAM-Net; Figure 7 (h) in the text stands for DIOR; Figure 7 (i) in the figure represents the effect of the present invention; Figure 7 (j) in the diagram represents the reference visualization result;

[0103] Figure 8 A reference diagram is set for each iteration round, corresponding to three projection sampling settings, as shown in the figure with corresponding annotations;

[0104] Figure 9 To set the effects for the iteration rounds, three projection sampling settings and three tissue imaging of the human body are provided (each view corresponds to the abdomen, chest and head from left to right respectively);

[0105] Figure 10 To enhance the visualization of the impact of the alignment loss module on the pre-training process;

[0106] Figure 11 To visualize the accuracy of learnable operators and filtered back projection methods for data domain transformation, images are created for both dual-domain and three human tissues; among them, Figure 11 (a) shows the original projection data of the abdomen, chest, and head from top to bottom; Figure 11 In (b) from top to bottom, items 1, 3, and 5 are the original projection data of the abdomen, chest, and head, respectively, and items 2, 4, and 6 are the processing results of the FBP operator. Figure 11In (c), from top to bottom, items 1, 3, and 5 are the original projection data of the abdomen, chest, and head, respectively, and items 2, 4, and 6 are the operator processing results in this invention. Figure 11 (d) in the image contains the original data of the abdomen, chest, and head images from top to bottom. Figure 11 In (e), from top to bottom, items 1, 3, and 5 are the original data of the abdominal, chest, and head images, respectively, and items 2, 4, and 6 are the processing results of the FBP operator. Figure 11 In (f), from top to bottom, items 1, 3, and 5 are the original data of the abdominal, chest, and head images, respectively, and items 2, 4, and 6 are the operator processing results in this invention.

[0107] Therefore, the present invention adopts the above-mentioned image reconstruction method based on a learnable projection operator and an iterative optimization framework. This method realizes independent optimization of two data domains and joint alternating optimization, which effectively improves the quality of CT reconstructed images under low radiation dose settings.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An image reconstruction method based on a learnable projection operator and an iterative optimization framework, characterized in that, The method comprises the following steps: Step S1, acquiring sparse projection sampling data; Step S2, recovering the sparse projection sampling data by using a projection domain sub-network module to obtain recovered projection data; Step S3, converting the recovered projection data into image domain data by using an inter-domain data conversion operator module; Step S4, optimizing the image domain data by using an image domain sub-network module to obtain optimized image domain data; Step S5, converting the optimized image domain data into projection data by using the inter-domain data conversion operator module, serving as input of the next round of iteration; Step S6, repeating steps S2 to S5 until a preset number of iterations is reached or a convergence condition is met, and outputting a final reconstructed image; The inter-domain data conversion operator module comprises a position parameter learning and a reverse line integral calculation module; The workflow of the inter-domain data conversion operator module is as follows: The fan beam data is converted into parallel beam data by grouping all fan beam rays, and rays parallel to each other are grouped in a group; The data conversion is realized by Radon line integral transformation, and the expression is as follows: ； in, This represents the imaginary straight-line radiation path between the X-ray source and the detector in a CT scanner. Indicates the distance between the radiation source and the detector; This represents the set of angles formed by the radioactive source relative to the starting point during a tomographic axial scan; This indicates that the X-ray is in the fracture zone when it passes through the tissue being tested. Attenuation coefficient at location; This indicates the intensity of radiation after attenuation, which is captured by the detector; When data conversion is performed, it is assumed that the center of rotation of the radiation source in the axial scan is the origin, The equation is a linear equation of the first order, The direction away from the origin is , it is assumed that the distance between the origin and is , then The theoretical expression of is as follows: ； wherein, denotes the angular direction, and , denotes a point source of radiation in the direction and under the theory of double integration transformation theory and further derivation as in the formula: ； ； wherein, represents angular direction, the distance is pixel value of a pixel point at a distance of represents a Dirac function, used to filter a specific point; In parallel beam reconstruction, it is assumed that the detector rotates uniformly around the object, and the strategy conversion from parallel beam to fan beam is performed, and each ray of the fan beam corresponds to a ray of the parallel beam; When the Radon line integral transformation is satisfied, the parallel beam and the fan beam are equivalent, and the expression is as follows: ； wherein, and denote two angular directions of the parallel light beam, denotes the distance of the parallel light beam detector from the object to be measured, denotes the distance of the fan light beam detector from the object to be measured; Using multiple Data pairs are used to train an efficient operator model to implement the fitting of the Radon transform process by deep learning to the parameters and weights, obtaining accurate forward / backward projection operators / : ； 。 2. The image reconstruction method based on a learnable projection operator and an iterative optimization framework according to claim 1, characterized in that, The method further comprises a consistency constraint framework for jointly constraining the optimization process of the projection domain sub-network module and the image domain sub-network module.

3. The image reconstruction method based on a learnable projection operator and an iterative optimization framework according to claim 1, characterized in that, The projection domain sub-network module comprises: The U-Net structure is used as a backbone model, and the U-Net structure comprises four dense coding and decoding layers, each coding layer comprises two two-dimensional convolution layers and one maximum pooling layer, and each decoding layer comprises two two-dimensional convolution layers and one up-sampling convolution layer; The sparse true value guiding module converts the image domain data to the projection domain through a forward projection operator for sparse true value guiding in the last step of iteration, and restores the image domain through a back projection operator; The enhanced alignment loss module realizes projection domain data correction by estimating complete projection data from sparse projection data, and designs enhanced alignment loss based on mean square error.

4. The image reconstruction method based on a learnable projection operator and an iterative optimization framework of claim 3, wherein, The enhanced alignment loss module realizes projection domain data correction by estimating complete projection data from sparse projection data, and designs enhanced alignment loss based on mean square error, and the optimization target is as follows: ； wherein, denotes an optimization objective, denotes a full view projection predicted generated by the projection domain subnetwork, denotes a full view projection data label, denotes an iteration round, denotes a boosting loss coefficient, denotes a sparse parameter, is one of the views in is one of the views in is one of the views in is one of the views in denotes an index base with an upper limit of .

5. The image reconstruction method based on a learnable projection operator and an iterative optimization framework of claim 3, wherein, The sparse true value guiding module converts the image domain iteration result to the projection domain through a learnable forward projection operator for sparse true value guiding in the last iteration of the iteration framework, and restores the image domain through a back projection operator, that is: ； ； ； wherein, denotes the projection data based on the sparse truth-guided, denotes the image data generated at the last iteration, denotes the corresponding index set of the sparse sampling view in the original complete view, N denotes the total iteration round, denotes the forward projection operator, denotes the projection data label the column value, denotes the index base, denotes the back projection operator, denotes the final result image.

6. The image reconstruction method based on a learnable projection operator and an iterative optimization framework of claim 1, wherein, The image domain sub-network module comprises a bit plane coding / decoding module, and the bit plane coding / decoding module performs bit plane decomposition coding, optimization processing and synthesis decoding on the image domain data.

7. The image reconstruction method based on a learnable projection operator and an iterative optimization framework of claim 6, wherein, The coding and decoding process in the image domain sub-network module is as follows: ； ； ； ； in, Indicates a point containing one pixel A matrix of channel decomposition elements, Signal value, Indicates the number of decomposed channels. Represents the recovery matrix. Indicates the first A picture of the round The line, number The number of pixels in the column at the 1st indivual Decomposition on the channel Indicates the preset number of channels.

Images