A sparse helical CT reconstruction method, system, device, medium and program product based on back-projection tensor interpolation

Abstract

The application discloses a kind of based on the sparse helical CT reconstruction method, system, equipment, medium and program product of back projection tensor interpolation, belong to computer tomography (CT) imaging technical field, specifically includes the following steps: generating the back projection tensor data under sparse angle, the back projection tensor data indicates the intermediate data of back projection process in filter back projection algorithm;Interpolation is carried out to the back projection tensor data of the sparse angle by depth learning network, generates the back projection tensor data of full angle;Image reconstruction is carried out based on the back projection tensor data of full angle, and the final CT image is obtained.The reconstruction method of the application suppresses the generation of strip artifact from the source and directly repairs the key intermediate data for reconstruction, which can better retain and restore the true anatomical structure information than post-processing in the image domain, avoids excessive smoothing or filtering, and has generalization ability, suitable for different CT scanning geometry.

Description

Technical Field

[0001] This invention belongs to the field of computed tomography (CT) imaging technology, specifically relating to a sparse spiral CT reconstruction method, system, device, medium, and program product based on back projection tensor interpolation. Background Technology

[0002] Computed tomography (CT) is an important medical imaging technology that has been widely used in clinical settings such as disease diagnosis, surgical navigation, and radiotherapy planning. However, the X-ray radiation dose during CT scans may pose potential risks to patients, making the reduction of radiation dose a key requirement for the development of CT technology.

[0003] With the development of deep learning technology, data-driven sparse angle CT reconstruction methods have made significant progress. Existing methods can be divided into three categories: (1) Projection domain methods: using deep learning networks to directly interpolate missing projection data, but small errors in the projection domain can still cause artifacts in the reconstructed image; (2) Image domain methods: using convolutional neural networks to directly learn the mapping from sparse angle images to full-angle images, such as FBPConvNet, DD-Net, etc., but these methods ignore the physical process of CT imaging and are prone to loss of structural details; (3) Dual domain methods: combining projection domain and image domain information, such as DuDoNet, InDuDoNet, etc., but most methods have limited generalization ability of domain transformation and are difficult to adapt to different scanning geometries.

[0004] Although existing methods have improved the quality of sparse angle CT reconstruction to a certain extent, the following key problems still exist: (1) Amplification of projection interpolation error: In the chord graph interpolation method, even a small interpolation error will be amplified during the back projection process, resulting in global secondary artifacts in the reconstructed image and affecting the diagnostic accuracy; (2) Insufficient physical modeling: Existing deep learning methods mostly adopt "black box" learning, ignoring the modeling of the physical process of CT imaging, especially the insufficient modeling of sparse angle sampling geometry, resulting in unsatisfactory artifact correction effect; (3) Difficulty in encoding rotational structure: CT imaging is essentially a rotational scan. The intermediate data (such as the back projection tensor) in the back projection process has a radial structure that rotates with the angle. Traditional translational equal-variable convolutional neural networks have difficulty effectively encoding this rotational symmetry, resulting in the loss of details in the reconstructed image; Summary of the Invention To overcome the shortcomings of the prior art, the present invention aims to provide a sparse spiral CT reconstruction method, system, device, medium, and program product based on back-projection tensor interpolation. This addresses the technical problems in traditional sparse spiral CT reconstruction methods, where projection domain interpolation errors are amplified globally in the image domain, leading to stripe artifacts and loss of detail in the reconstructed image, as well as the easy filtering of structural information during image domain post-processing. This application, through back-projection tensor interpolation, localizes the error during the back-projection process, avoiding global error propagation and thus solving the problem of low reconstruction quality.

[0005] To achieve the above objectives, the present invention employs the following technical solution: This invention provides a sparse spiral CT reconstruction method based on back-projection tensor interpolation, comprising the following steps: Generate back-projection tensor data under sparse angles, wherein the back-projection tensor data represents the intermediate data of the back-projection process in the filtered back-projection algorithm; The sparse angle backprojection tensor data is interpolated using a deep learning network to generate full-angle backprojection tensor data. Image reconstruction is performed based on the full-angle backprojection tensor data to obtain the final CT image.

[0006] Preferably, the generation of back-projection tensor data under sparse angles is specifically achieved by: rearranging sparse spiral CT projection data into fan-beam projection data and then calculating it; or by directly calculating it under spiral scanning geometry based on a weighted filtering back-projection algorithm.

[0007] Preferably, the deep learning network is an encoder-decoder structure, used to take sparse backprojection tensor data of adjacent angles as input, extract multi-scale features and establish motion correlations to synthesize backprojection tensor data of missing intermediate angles.

[0008] Preferably, the image reconstruction based on the full-angle backprojection tensor data specifically involves: inputting multiple full-angle backprojection tensor data adjacent along the slice direction into a residual network, and outputting the final CT image from the residual network.

[0009] Preferably, the loss functions used when training the deep learning network include backprojection tensor loss, geometric consistency loss for constraining multi-scale features of the intermediate layers of the network, and image reconstruction loss.

[0010] The present invention also provides a sparse spiral CT reconstruction system for performing the method, comprising: The data generation module is used to perform the step of generating back-projection tensor data under sparse angles in the method; The tensor interpolation module is used to perform the step of interpolating the back-projection tensor data in the method. The image reconstruction module is used to perform the step of image reconstruction to obtain the final CT image in the method.

[0011] Preferably, the tensor interpolation module includes a deep learning network with an encoder-decoder structure; the image reconstruction module includes a residual network.

[0012] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method as described.

[0013] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described above.

[0014] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described above.

[0015] Compared with the prior art, the present invention has the following beneficial effects: This invention provides a sparse spiral CT reconstruction method based on backprojection tensor interpolation. By applying deep learning interpolation to the backprojection tensor—an intermediate data set rather than the original projection data or the final image—this method addresses the issue that the backprojection tensor is an intermediate result of the backprojection process in the Filtered Backprojection (FBP) algorithm. It contains complete information from the projection data and is closer to the image domain than the original projection data. Interpolating here offers two major advantages: First, interpolation errors are not amplified globally by subsequent backprojection operators as they would in the projection domain, thus suppressing the generation of stripe artifacts at their source. Second, it directly repairs the crucial intermediate data used for reconstruction, preserving and restoring more accurate anatomical structural information than post-processing in the image domain, avoiding over-smoothing or filtering. This solves the technical problems of stripe artifacts and detail loss in reconstructed images, as well as the tendency for image domain post-processing to filter out structural information.

[0016] Furthermore, two specific implementation paths for generating sparse backprojection tensor data were clarified, providing flexibility and an optimal data foundation in principle. Whether calculated by rearranging into a fan-shaped bundle or directly under helical geometry, it is ensured that the generated sparse tensor data mathematically corresponds accurately to the scanning information of sparse angles, providing high-quality, geometrically meaningful input for subsequent deep learning interpolation.

[0017] Furthermore, the deep learning network is constrained to employ an encoder-decoder structure, using adjacent angle data as input for motion correlation and multi-scale feature synthesis. This leverages the continuity and correlation of the back-projection tensor along the angular dimension. The encoder-decoder structure effectively extracts deep features; establishing motion correlations between adjacent angles allows the network to learn the patterns of object changes with angle, thus more accurately predicting data for missing angles; multi-scale feature extraction simultaneously captures global structure and local details, making the interpolated full-angle tensor data more realistic and continuous in both structure and texture.

[0018] Furthermore, a refined reconstruction backend was achieved by using a residual network to reconstruct the final image from full-angle backprojection tensor data. Residual networks excel at learning the residual mapping between input and output, effectively fusing multiple adjacent tensor data along the slice direction (providing 3D contextual information), and further eliminating minor inconsistencies or noise that may remain in the interpolation step. This results in a clearer and more detailed final CT image, fully transforming the advantages of high-quality intermediate data into high-quality image results.

[0019] Furthermore, the composite loss function used during network training was limited, and multi-level, multi-task supervision signals were constructed in principle to guide the network to learn better interpolation mappings. The backprojection tensor loss directly constrains the approximation output to the true full-angle tensor; the geometric consistency loss constrains the network's intermediate features to conform to the physical geometry of the scan, improving the physical reliability of the interpolation; and the image reconstruction loss performs end-to-end optimization to ensure the final image quality. The combination of these three factors ensures that the network not only interpolates data accurately but also leads to high-quality reconstruction.

[0020] This invention also provides a sparse spiral CT reconstruction system for executing the method, which modularizes and materializes the method process from the perspective of system implementation principles. The three modules of data generation, tensor interpolation, and image reconstruction clearly correspond to the core steps of the method, ensuring that this innovative method can be implemented as a complete, efficient, and executable system, facilitating integration and application.

[0021] Furthermore, the specific implementations of the encoder-decoder network and residual network in the system were clarified, ensuring the advanced nature and effectiveness of the core components, thereby guaranteeing that the entire system achieves the performance expected by the patented method. (See attached figures for details.) Figure 1 This is a structural diagram of the sparse spiral CT reconstruction algorithm for back projection tensor interpolation provided in an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the process of rearranging spiral data into fan-shaped bundle data using the algorithm of the present invention, as provided in an embodiment of the present invention. Figure 3This is a schematic diagram illustrating the direct processing of spiral CT data by the algorithm of the present invention provided in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the reconstruction result of the helical data rearranged into fan-shaped bundle data using the algorithm of the present invention provided in an embodiment of the present invention; Figure 5 A schematic diagram of the direct reconstruction result of spiral CT data using the algorithm of the present invention, provided in an embodiment of the present invention. Detailed Implementation

[0022] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0023] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0024] The core of this invention is a sparse spiral CT reconstruction model based on back-projection tensor interpolation. It proposes an interpolation framework with back-projection tensors as the intermediate domain. This framework divides the reconstruction process into three key stages: back-projection tensor generation based on spiral data; back-projection tensor interpolation network; and image reconstruction module.

[0025] (1) Generation of backprojection tensors based on spiral data: Backprojection tensors can be generated from spiral projection data in two ways: rearranged into fan-shaped bundle data and directly processed. If rearranged into fan-shaped bundle data, the implementation of FBP can be roughly divided into three steps: filtering, backprojection, and summation. Among them, the backprojection tensor data is the intermediate data in the backprojection process of the FBP reconstruction algorithm, which is expressed as: (1) Where i and j are the two-dimensional spatial indices of voxels (or pixels) in the reconstructed image; i represents the row index, j represents the column index; and k is the angular index of the sparsely sampled projection data, k = 1, 2, ..., K. sv K sv β represents the total number of sparse angles; u represents the channel direction index of the detector element; β u θk is the ray angle corresponding to detector unit u; θk is the exposure angle of the k-th projection view. This is the back-projection tensor data under sparse angles; This is sparse angular CT projection data rearranged into a fan-shaped beam, where the detector unit index... Corresponding ray angle Angular index Corresponding exposure angle ; Indicates the reconstruction filter kernel; "" indicates a one-dimensional convolution operation; "INT" indicates an interpolation operation in the back projection process, which satisfies spatial geometric relations. ,in The distance from the ray source to the center of rotation; This represents the weighting factor for back projection, i.e., at the exposure angle. From the source point to the image point The distance.

[0026] If processed directly, this study uses WFBP for reconstruction of multi-slice spiral CT data and implements back-projection tensor interpolation within the WFBP framework. In the WFBP algorithm, sparse spiral CT projection data is first geometrically reconstructed into pseudo-parallel beam data. Then, a filter kernel is used. right Perform filtering: (2) The filtering operation actually filters the pseudo-parallel data along the helical tangent. Finally, sparse angular helical CT backprojection tensor data is obtained by performing backprojection as follows: for each voxel... and each projection angle For all conjugate half-circles Perform the following summation: (3) in, It is a weighting function used to reduce the weight of the data in the rows before and after the detector in order to reduce image artifacts in spiral CT reconstruction; It is the normalized weight sum, and each Calculate for each voxel separately; These are the detector grid coordinates where the rays pass through the voxels.

[0027] It should be noted that H_(i,j,z,k) in the above formula (3) is defined as However, the summation index k is inconsistent with the variable v in the weighting function W(v). According to the conventional understanding of the weighted filter back projection (WFBP) algorithm, this parameter should be the normalized weight sum, which should be calculated by summing the detector row orientation indices v, i.e., H = ∑W(v), used to normalize the back projection contribution.

[0028] (2) Back-projection tensor interpolation network: The core of this invention lies in using a deep learning network to perform high-precision interpolation of sparse angle back-projection tensor data to generate full-angle back-projection tensor data. This network is designed to effectively learn and utilize the geometric prior information contained in the back-projection tensor data, especially its structural characteristics related to rotational scanning in CT systems. As a preferred implementation, this deep learning network can employ an encoder-decoder structure. The network takes sparse back-projection tensor slices of adjacent angles as input (e.g., ...). and The goal is to synthesize backprojection tensor data for the intermediate missing angle (t). The network extracts multi-scale features and establishes motion correlations between input data, ultimately generating data with missing angles accurately through a synthesis mechanism based on feature flow and occlusion masks. This design enables the network to adapt to any intermediate representation domain (such as backprojection tensors under fan-shaped bundles or spiral geometry) generated from spiral data.

[0029] (3) Image Reconstruction Module: This invention uses a residual network to replace a simple summation operator, thereby improving the overall reconstruction performance of the backprojection tensor network. Therefore, the final reconstructed CT image can be calculated using the following formula: (11) in, This represents the residual network.

[0030] (4) Loss function: In order to accurately interpolate the missing projection data of the sparse angular back projection tensor, this invention uses network output and tags The mean absolute error between them is used as the loss function: (12) Where K is the total number of projection angles of the full-angle projection data; K sv represents the number of projected angles after sparse sampling; t is the index of the missing angles traversed, t = 1, 2, ..., (K - K sv ); This indicates the number of missing projection angles. Furthermore, this invention constrains the reconstructed pyramid features to ensure that the interpolated backprojection tensor data maintains geometric consistency with the label data. Therefore, a geometric consistency loss is used for progressive supervised learning in the multi-scale feature space: (13) Where n is the level index of the pyramid feature map, for example, n=1, 2, 3 represent feature maps of different scales from coarse to fine, respectively; It is an encoder with the same parameters. From label data Pyramid features extracted from; The loss is a Census loss, which calculates the soft Hamming distance between the corresponding feature maps after the Census transform on a channel-by-channel basis. On the other hand, this invention introduces a residual DNN to replace the simple summation operator, which further reduces the interpolation error generated by the backprojection interpolation network and improves the overall reconstruction performance. Therefore, the reconstructed image loss can be calculated as follows: (14) in, Represents the reconstructed image; The image represents the labeled image. Therefore, the final loss function formula of this invention is: (15) Among them, weight parameters and Set them to 1 and 0.01 respectively.

[0031] Using the above technical solutions, this invention provides a sparse spiral CT reconstruction algorithm and system based on back projection tensor interpolation, which has the following beneficial effects: (1) By using back projection tensor domain interpolation, the error is limited to the local range, avoiding the problem of global error amplification in traditional methods; (2) By using an encoder-decoder network design, the geometric characteristics of CT rotation scanning are effectively encoded, improving the reconstruction quality; (3) The framework has good generalization ability and is suitable for different CT scan geometry and parameter settings; (4) While significantly reducing radiation dose, it can achieve diagnostic-grade image quality.

[0032] The present invention will now be described in further detail with reference to the accompanying drawings: Example 1 Example 1 illustrates a specific implementation of the present invention by processing helical projection data rearranged into sector beam data. (See reference...) Figure 1 and Figure 2 The process includes the following steps: In step S1, as Figure 2As shown, the spiral projection data of a real clinical scan (dimension is...) is obtained. ,in Indicates the detector array dimension. (This represents the number of scanning angles in one rotation). The first step is to uniformly and sparsely sample the full-angle spiral CT projection data to obtain the corresponding sparse spiral CT projection data (the sparse spiral CT projection data dimension is...). , (Representing the sparse sampling factor); through a rearrangement algorithm, the sparse spiral projection data is rearranged into fan-beam CT projection data to obtain sparse angular fan-beam CT projection data (the dimension of the fan-beam CT projection data is...). ); In step S2, a filtered backprojection operation is performed on the sparse spiral CT projection data from step S1 to generate the corresponding backprojection tensor data at sparse angles, which can be represented as: (1) Where i and j are the two-dimensional spatial indices of voxels (or pixels) in the reconstructed image; i represents the row index, and j represents the column index; k is the angular index of the sparsely sampled projection data, k = 1, 2, ..., K sv K sv β represents the total number of sparse angles; u represents the channel direction index of the detector element; β u θk is the ray angle corresponding to detector unit u; θk is the exposure angle of the k-th projection view. This is the back-projection tensor data under sparse angles; This is sparse angular CT projection data, where the detector unit index is... Corresponding ray angle Angular index Corresponding exposure angle ; Indicates the reconstruction filter kernel; "" indicates a one-dimensional convolution operation; "INT" indicates an interpolation operation in the back projection process, which satisfies spatial geometric relations. ,in The distance from the ray source to the center of rotation; This represents the weighting factor for back projection, i.e., at the exposure angle. From the source point to the image point The distance; In step S3, a deep learning network is used in the backprojection tensor domain to interpolate the missing angle data from the sparse angle backprojection tensor data in step S2, generating full-angle backprojection tensor data. Specifically, for the backprojection tensor interpolation network, as a preferred network architecture, this embodiment employs a deep learning network based on an encoder-decoder structure. The encoder input of this network is the backprojection tensor data of adjacent angles, such as... and ,in, This represents the missing projection angles in sparse spiral CT. Utilizing an encoder... Extracting features from a 4-layer pyramid, and gradually reducing the spatial size while increasing the feature channels to 32, 48, 72, and 96, can be represented as: . (2) Next, multiple decoders were used to reverse-distort the pyramid features. Refine the intermediate flow field based on the bidirectional flow field. Generate separately Furthermore, this invention enables each decoder to... It also outputs a higher-level reconstruction intermediate feature. This can fill in missing reference information to facilitate motion estimation. Therefore, the features between decoders can be calculated as follows: (3) (4) (5) (6) in, This indicates a join operation. This is a single-channel conditional input used for interpolation of arbitrary projection angles. This is the estimated occlusion mask, with values ​​ranging from 0 to 1. Therefore, the required intermediate backprojection tensor slices can be synthesized using the following formula: (7) in, This indicates the reverse deformation operation. This represents element-wise multiplication. Through training with large datasets, the backprojection interpolation network can accurately extract backprojection tensor data from sparse angles. Synthesize high-quality full-angle backprojection tensor data .

[0033] To effectively capture and utilize the inherent geometric prior information (i.e., rotational radial structure) in backprojection tensor data related to the rotational scanning of the CT system, the embodiment specifically designs the convolutional operations in the network to make it sensitive and adaptable to changes in the rotation of the input data. For example, rotational isovariant convolution based on Fourier series expansion can be used to encode the rotational radial structure of backprojection tensor data at different angles, which is defined as: (8) in, Represents the rotation matrix; Indicates the first One rotation angle, It is the number of rotation angles; , Two-dimensional spatial coordinates; Indicates the angle The first A parameterized convolutional kernel is used to encode the radial structure and rotational prior patterns of the backprojection tensor; , These are the coefficients of the basis functions; , Represents two-dimensional basis functions.

[0034] In step S4, image reconstruction is performed on the full-angle backprojection tensor data generated in step S3 to obtain the final CT image. This invention uses a residual network to replace a simple summation operator, thereby improving the overall reconstruction performance of the backprojection tensor network. Therefore, the final reconstructed CT image can be calculated using the following formula: (9) in, This represents a residual network consisting of 6 residual blocks. For the loss function used in model training, in order to accurately interpolate the missing projection data of the sparse angular backprojection tensor, this invention employs network output... and tags The mean absolute error between them is used as the loss function: (10) in, This indicates the number of missing projection angles. Furthermore, this invention constrains the reconstructed pyramid features to ensure that the interpolated backprojection tensor data maintains geometric consistency with the label data. Therefore, a geometric consistency loss is used for progressive supervised learning in the multi-scale feature space: (11) in, It is an encoder with the same parameters. From label data Pyramid features extracted from; The loss is a Census loss, which calculates the soft Hamming distance between the corresponding feature maps after the Census transform on a channel-by-channel basis. On the other hand, this invention introduces a residual DNN to replace the simple summation operator, which further reduces the interpolation error generated by the backprojection interpolation network and improves the overall reconstruction performance. Therefore, the reconstructed image loss can be calculated as follows: (14) in, Represents the reconstructed image; The image represents the labeled image. Therefore, the final loss function formula of this invention is: (15) Among them, weight parameters and Set them to 1 and 0.01 respectively. The reconstruction results are as follows: Figure 4 As shown.

[0035] Example 2 In this embodiment, other features are the same as in Embodiment 1, except that it directly processes the helical projection data. In this embodiment, step S1, as follows: Figure 3 As shown, the spiral projection data of the acquired real clinical scans (the projection data dimension is...) ,in Indicates the detector array dimension. (This represents the number of scanning angles in one rotation). The first step is to perform uniformly sparse sampling of the spiral projection data at equal intervals along the scanning angle direction to simulate sparse angle spiral CT projection data (the dimension of sparse angle spiral CT projection data is...). , (representing the sparse sampling factor). In step S2, rearrangement, filtering, and backprojection operations are performed on the sparse angle spiral CT projection data from step S1 to generate the corresponding backprojection tensor data under the sparse angle, which can be represented as: In the WFBP algorithm, sparse spiral CT projection data is first geometrically rearranged into pseudo-parallel beam data. Then, a filter kernel is used. right Perform filtering: (16) in, This represents pseudo-parallel bundle data generated by geometric rearrangement; This represents the filter kernel; the filtering operation actually filters pseudo-parallel data along the helical tangent. Finally, backprojection tensor data of sparse angled helical CT is obtained by performing backprojection for each voxel. and each projection angle For all conjugate half-circles Perform the following summation: (17) in, It is a weighting function used to reduce the weight of the data in the rows before and after the detector in order to reduce image artifacts in spiral CT reconstruction; It is the normalized weight sum, and each Calculate for each voxel separately; These are the detector grid coordinates where the rays pass through the voxels.

[0036] In step S3, the encoder input is the back-projection tensor data of adjacent angles, such as... and ,in, This indicates the missing projection angle in sparse angle CT. The image slice (image layer) index represents the volume of the 3D image reconstructed by multi-slice spiral CT; the rest is the same as in Example 1; In step S4, this example uses a 2.5D residual network to reconstruct the 3D image. The reconstruction result is as follows. Figure 5 As shown.

[0037] The beneficial effects of the above technical solution are as follows: (1) By using back projection tensor domain interpolation, the error is limited to the local range, avoiding the problem of global error amplification in traditional methods; (2) By using an encoder-decoder network design, the geometric characteristics of CT rotation scanning are effectively encoded, improving the reconstruction quality; (3) The framework has good generalization ability and is suitable for different CT scan geometry and parameter settings; (4) While significantly reducing radiation dose, it can achieve diagnostic-grade image quality.

[0038] Although the embodiments in this specification are only for depth reconstruction of sparse spiral data with a fixed geometry, the method described in this specification can also be used for depth reconstruction of other geometric data.

[0039] Example 3 This embodiment provides a sparse spiral CT reconstruction system for performing the method described in Embodiment 1 above. Figure 1 As shown, the system mainly includes a data generation module, a tensor interpolation module, and an image reconstruction module. These modules work collaboratively under the scheduling and control of the processor, and their specific implementation is as follows: 1. Data Generation Module This module receives raw sparse helical projection data acquired by a CT scan and generates backprojection tensor data at sparse angles. This module supports two parallel implementation paths, the one used being determined by system configuration or input parameters: Path 1 (based on rearranged sector bundle geometry): Rearrangement submodule: First, it processes the input raw spiral projection data. The data is rearranged into a fan-beam projection using a spiral interpolation algorithm. The data dimension is... ,in This represents the number of detector channels. The number of projection angles after sparse sampling.

[0040] Filtering and backprojection tensor module: Subsequently, the backprojection tensor T(i,j,k) is calculated according to the following formula (1): (1) The specific operations of this submodule include: 1) Using the reconstruction filter kernel right Perform one-dimensional convolution filtering; 2) Based on the distance from the ray source to the center of rotation and geometric relations The filtered data is interpolated (INT operation) to the image grid points through which each ray passes. Above; 3) Multiply by the cosine term and back projection weights (ω_(i,j,k)) From the X-ray source to the voxel (Distance weighting factor). The final output is a three-dimensional tensor. , where I and J are the row and column sizes of the reconstructed image grid.

[0041] Path 2 (WFBP based on spiral geometry): The reconstruction and filtering submodule directly processes the original sparse spiral projection data. First, it reconstructs it into pseudo-parallel beam data. Where v is the detector row direction index. Next, filtering is performed along the channel direction u using a filter kernel h to obtain... As shown in formula (2) below.

[0042] Backprojection Tensor Quantum Module: Then, within the framework of Weighted Filtered Backprojection (WFBP), backprojection calculations are performed according to formula (3): Formula (2) This submodule iterates over each voxel (i, j, z) and each sparse angle. Calculate the sum of contributions from all conjugate semicircles (index n). These are the coordinates of the ray passing through the voxel on the detector. It is a weighting function used to mitigate spiral artifacts. It is the normalized weight sum. The final output is a four-dimensional back-projection tensor. , where Z is the number of slices in the reconstructed image.

[0043] 2. Tensor Interpolation Module This module receives sparse backprojection tensors from the data generation module. Its core is to use deep learning networks to complete the data for missing angles and output back-projection tensor data for all angles. .

[0044] Network Structure: The core of this module is a deep learning network with an encoder-decoder structure (such as an improved U-Net). This network is designed to learn the motion field and appearance changes of the backprojection tensor data between adjacent projection angles.

[0045] Input and Output: For any missing angle t to be interpolated, the network slices the backprojection tensors corresponding to two adjacent known sparse angles (e.g., k and k+1). and As input, the network's training objective is to directly synthesize a complete backprojection tensor slice with a missing intermediate angle t. .

[0046] Internal mechanisms: Feature extraction and motion estimation: The encoder extracts multi-scale pyramid features from the input tensor. Internally, the network models the motion by learning a bidirectional motion field. arrive And from arrive Pixel-level (or voxel-level) displacement.

[0047] Feature alignment and synthesis: Using the learned motion field, the features (and image content) of the input tensor are warped towards the intermediate angle t. The decoder is then responsible for fusing these aligned features.

[0048] Occlusion handling: The network also learns to generate occlusion masks to handle areas that are not visible in the input view due to occlusion, and generates reasonable content by combining contextual information.

[0049] Training supervision: This module needs to be trained offline before deployment. During training, the loss function is shown in formulas (12)-(15), including: 1) Output Tensor With real full-angle tensor labels Between Loss; 2) Multi-scale features of the output of the n=1, 2, and 3rd layers of the network encoder. The geometric consistency loss applied to _(z,t)^n (using Census transform to calculate the Soft Hamming distance) ensures the structural consistency of the feature space; 3) The final image reconstruction loss. The total loss is... , where η and λ are hyperparameters, for example, they can be set to 1 and 0.01 respectively.

[0050] 3. Image Reconstruction Module This module receives the full-angle back-projection tensor output by the tensor interpolation module. Its task is to perform the final image reconstruction to obtain high-quality CT images.

[0051] Reconstruction Network: This module uses a Residual Network (ResNet) to replace the simple summation along the angular dimension operation in traditional FBP. This design can further learn and eliminate residual errors that may be introduced by the interpolation module, and enhance image details.

[0052] Input and Processing: For the target slice z, the residual network takes the full-angle backprojection tensor data of all angles K corresponding to the preceding and following adjacent slices (e.g., z-1, z, z+1) as input, i.e., the input is... This utilizes the spatial continuity information between adjacent slices.

[0053] Output: The residual network R(·) performs nonlinear mapping and fusion on the input, directly outputting the final reconstructed, high-quality CT image slices. As shown in formula (11): .

[0054] System workflow: In clinical or experimental applications, the system's workflow is as follows: Sparse scanning helical projection data is input into the system → The data generation module calculates the sparse backprojection tensor → The tensor interpolation module interpolates the sparse tensor into a complete full-angle backprojection tensor using a pre-trained deep learning network → The residual network of the image reconstruction module fuses and finely reconstructs the full-angle tensor, outputting the final high-quality CT image volume. This entire process achieves the goal of obtaining diagnostic-grade image quality while significantly reducing the projection sampling rate (radiation dose).

[0055] Example 4 In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0056] Example 5 In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0057] In summary, the sparse spiral CT reconstruction method, system, device, medium and program product based on back projection tensor interpolation provided in this application have the following beneficial effects by adopting the above technical solution: (1) By using back projection tensor domain interpolation, the error is limited to a local range, avoiding the problem of global error amplification in traditional methods; (2) The encoder-decoder network design effectively encodes the geometric characteristics of CT rotation scanning, improving reconstruction quality; (3) The framework has good generalization ability and is suitable for different CT scan geometry and parameter settings; (4) While significantly reducing radiation dose, it can achieve diagnostic-grade image quality.

[0058] The various embodiments in this specification are described in a progressive manner. For directly identical or similar parts of the embodiments, refer to each other. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0059] 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 it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A sparse spiral CT reconstruction method based on back-projection tensor interpolation, characterized in that, Includes the following steps: Generate back-projection tensor data under sparse angles, wherein the back-projection tensor data represents the intermediate data of the back-projection process in the filtered back-projection algorithm; The sparse angle backprojection tensor data is interpolated using a deep learning network to generate full-angle backprojection tensor data. Image reconstruction is performed based on the full-angle backprojection tensor data to obtain the final CT image.

2. The method according to claim 1, characterized in that, The generation of back-projection tensor data under sparse angles is specifically achieved by: rearranging sparse spiral CT projection data into fan-beam projection data and then calculating it; or by directly calculating it under spiral scanning geometry based on a weighted filtering back-projection algorithm.

3. The method according to claim 1, characterized in that, The deep learning network is an encoder-decoder structure used to synthesize backprojection tensor data of missing intermediate angles by taking sparse backprojection tensor data of adjacent angles as input, extracting multi-scale features and establishing motion correlations.

4. The method according to claim 1, characterized in that, The image reconstruction based on the full-angle backprojection tensor data specifically involves inputting multiple full-angle backprojection tensor data adjacent along the slice direction into a residual network, and outputting the final CT image from the residual network.

5. The method according to claim 1, characterized in that, The loss functions used when training the deep learning network include backprojection tensor loss, geometric consistency loss for constraining multi-scale features of the intermediate layers of the network, and image reconstruction loss.

6. A sparse spiral CT reconstruction system for performing the method according to any one of claims 1 to 5, characterized in that, include: The data generation module is used to perform the step of generating back-projection tensor data under sparse angles in the method; The tensor interpolation module is used to perform the step of interpolating the back-projection tensor data in the method. The image reconstruction module is used to perform the step of image reconstruction to obtain the final CT image in the method.

7. The system according to claim 6, characterized in that, The tensor interpolation module includes a deep learning network with an encoder-decoder structure; the image reconstruction module includes a residual network.

8. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method as described in any one of claims 1 to 5.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 5.

10. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 5.

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