Sparse finite angle CBCT reconstruction method and system based on residual diffusion and storage medium

Abstract

The invention discloses a sparse finite angle CBCT reconstruction method and system based on residual diffusion and a storage medium, and the method comprises the steps: carrying out the CBCT sparse finite angle scanning of a to-be-detected target, and obtaining sparse projection data; fDK reconstruction is carried out on the sparse projection data to obtain an initial CBCT image; generating a first optimized CBCT image from the initial CBCT image through an image pre-training network; through the first optimized CBCT image and the sparse projection data, using the trained residual diffusion model to determine a residual image of the to-be-detected target; summing the first optimized CBCT image of the to-be-detected target and the residual image of the to-be-detected target to obtain a second optimized CBCT image of the to-be-detected target, and the second optimized CBCT image is a final CBCT reconstruction image. According to the method, the problems of stripe artifacts and low-contrast tissue annihilation under limited angle scanning are solved, the large-view CBCT reconstruction resolution is improved, and the radiation dose is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of image reconstruction, and in particular relates to a sparse limited-angle CBCT reconstruction method, system and storage medium based on residual diffusion. Background Art

[0002] CT imaging is the core basis for clinical lesion detection and anatomical structure analysis, but the high radiation dose caused by its spiral scanning mode (typical head CT dose is about 2mSv, chest CT about 7mSv) poses a cumulative radiation risk to cancer patients and sensitive populations who require long-term follow-up, restricting the clinical application of early screening. Especially for diseases such as breast cancer and lung cancer that require multi-phase efficacy evaluation, the dose limitation of traditional CT and the problem of insufficient soft tissue contrast coexist, making it difficult to meet the clinical needs of precise radiotherapy target delineation and dynamic monitoring of tiny lesions. With its advantages such as open gantry design, low-dose imaging and submillimeter spatial resolution, Cone Beam Computed Tomography (CBCT) has become an important technical supplement in the fields of tumor radiotherapy positioning and interventional navigation.

[0003] However, conventional CBCT systems can achieve high-quality imaging through full-angle scanning in small-field scenarios such as the oral cavity. However, in large-field imaging such as chest, abdomen, and orthopedics, projection data is often limited to sparse angles (number of projections ≤ 120) and a limited scanning angle range (angle coverage < 180°) due to the detector's physical size and mechanical motion range. This sparse, limited-angle scanning pattern leads to severe undersampling of the Radon space. Images reconstructed using traditional filtered back-projection algorithms are commonly subject to streak artifacts, anatomical distortion, and low-contrast tissue annihilation. Although deep learning methods partially suppress high-frequency artifacts through end-to-end mapping, their black-box nature results in a lack of physical mechanism modeling, and the reconstruction residual exhibits a complex mixture of low-frequency grayscale offsets and mid- and high-frequency unstructured noise. Especially in the case of large-field, long-range integration paths, data mismatch errors are accumulated and amplified by the back-projection operator, further exacerbating edge blurring and the risk of coverage of small lesions.

[0004] Therefore, a high-quality CBCT reconstruction method under sparse effective angle scanning is needed. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a sparse limited-angle CBCT reconstruction method, system and storage medium based on residual diffusion, so as to overcome the problems of streak artifacts and low-contrast tissue annihilation under limited-angle scanning, achieve improved resolution of large-field-of-view CBCT reconstruction and reduce radiation dose.

[0006] One aspect of the present invention provides a sparse limited-angle CBCT reconstruction method based on residual diffusion, the method comprising:

[0007] Perform CBCT sparse limited angle scanning on the target to be detected to obtain sparse projection data of the target to be detected;

[0008] Perform FDK reconstruction on the sparse projection data of the target to be detected to obtain the initial CBCT image of the target to be detected;

[0009] Passing the initial CBCT image of the target to be detected through the image pre-training network to generate a first optimized CBCT image of the target to be detected;

[0010] Determining a residual image of the target to be detected by using a trained residual diffusion model using a first optimized CBCT image of the target to be detected and sparse projection data of the target to be detected, wherein the residual diffusion model is used to estimate image degradation components in a CBCT image reconstruction process, and the residual diffusion model is a variance exploding diffusion model;

[0011] The first optimized CBCT image of the target to be detected and the residual image of the target to be detected are summed to obtain a second optimized CBCT image of the target to be detected, and the second optimized CBCT image is the final CBCT reconstructed image.

[0012] Furthermore, the image pre-training network is a pre-trained lightweight encoder-decoder network with a symmetrical structure in the encoding and decoding stages. In the encoding stage, a five-level convolution module is adopted to extract the multi-scale features of the image through the downsampling operation of each convolution module; in the decoding stage, cross-layer connections are made through transposed convolution and the output of the convolution module of the corresponding size in the encoding stage, and the channel attention mechanism is used to adaptively select effective features.

[0013] Furthermore, the method also includes training a residual diffusion model, which specifically includes the following steps:

[0014] Acquire a training data set, wherein the training data set includes full projection data of the scanned object and corresponding sparse projection data;

[0015] Perform FDK reconstruction on the full projection data to generate a reference CBCT image;

[0016] Perform FDK reconstruction on the sparse projection data to generate initial training CBCT images;

[0017] Passing the initial training CBCT image through the image pre-training network to generate a first optimized training CBCT image;

[0018] generating a residual training image by using the reference CBCT image and the first optimized training CBCT image;

[0019] The residual diffusion model is trained by using the residual training image and establishing the residual diffusion objective function, where the residual diffusion objective function for:

[0020]

[0021] Among them, θ represents the parameters in the residual diffusion model, z (0) Represents the residual training image, that is, the residual diffusion model The initial value of the diffusion process, σ(t) is the noise scheduling function, σ(t) = σ min (σ max / σ min ) t , σ min and σ max represent the minimum noise level at the beginning of the diffusion process and the maximum noise level at the end of the diffusion process, respectively; is the normal distribution function, I represents the identity matrix; represents the mean, ‖‖2 represents the L2 norm, z (t) =z (0) +σ(t)ε, represents the residual image of time step t, t∈[0,T], T represents the last time step of the diffusion process, and the diffusion process constructs a forward perturbation model in the time domain through stochastic differential equations, that is, dz represents the derivative with respect to z, dw represents the derivative with respect to w, and w is the standard Wiener process.

[0022] Furthermore, using the trained residual diffusion model, determining the residual image of the target to be detected specifically includes: establishing a joint objective function, and solving the joint objective function through a dual-domain alternating optimization method, so as to determine the residual image of the target to be detected, wherein the joint objective function includes a data fidelity term, a projection consistency constraint, and a diffusion prior constraint.

[0023] Furthermore, the joint objective function is:

[0024]

[0025] z (t-1) represents the residual image predicted at time step t-1; p (t-1) represents the projection error predicted at time step t-1; z and p represent the residual image to be predicted and the projection error respectively; y represents the sparse projection data; A represents the system matrix of the sparse projection; x p represents the first optimized training CBCT image; μ and ρ are trade-off parameters; is the network output of the diffusion model at time step t, ‖‖ F represents the F-norm.

[0026] Furthermore, the method includes solving the joint objective function by a dual-domain alternating optimization method, specifically comprising the following steps:

[0027] S1: Projection error update, that is, fix the residual z, solve the projection domain minimization problem, and obtain the analytical solution p of the projection error p (t-1) ;

[0028] S2: Image residual update, that is, fix the projection error p, solve the image domain residual optimization problem, and obtain the closed-form solution z (t -1) ,

[0029] S3: Diffusion time stepping mechanism, that is, looping S1 and S2 until the preset number of iterations or convergence threshold is reached, until the residual estimate z is obtained (0) , which is the residual image of the target to be detected.

[0030] The present invention also provides a sparse limited-angle CBCT reconstruction system based on residual diffusion, the system comprising:

[0031] a memory configured to store a computer program;

[0032] A processor is configured to execute the computer program to implement the sparse limited-angle CBCT reconstruction method based on residual diffusion as described above.

[0033] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the sparse limited-angle CBCT reconstruction method based on residual diffusion as described above is implemented.

[0034] The beneficial effects of the present invention are:

[0035] To address the issue of reconstruction quality degradation in CBCT imaging systems with large thoracic and abdominal field-of-view, this paper proposes a sparse limited-angle CBCT reconstruction method based on residual diffusion. This method, a residual refinement reconstruction method based on a diffusion prior and physical constraints, models the initial reconstruction residuals of the pre-trained network as controlled diffusion by establishing a stochastic differential equation model of the residual field and an iterative optimization mechanism to achieve a progressive correction of the residual components. This diffusion process utilizes a variance-exploding stochastic differential equation to construct a continuous perturbation path from the true residual distribution to an isotropic Gaussian, and learns the multi-scale gradient features of the residuals through score matching. At the optimization level, an alternating direction minimization architecture is designed to jointly constrain image domain residual correction and projection domain data consistency. The score function of the diffusion model is embedded in the iterative process as a dynamic regularization term, and physical constraints on X-ray projection are simultaneously applied. This method breaks through the single reliance of traditional deep learning on data-driven approaches. By explicitly fusing imaging physics mechanisms with data generation priors, it provides a theoretical framework and technical support for high-quality CBCT reconstruction under sparse sampling conditions.

[0036] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0038] Figure 1 is a schematic flowchart of a sparse limited-angle CBCT reconstruction method based on residual diffusion;

[0039] Figure 2(a) is a schematic diagram of CBCT image degradation under sparse limited-angle scanning;

[0040] FIG2( b ) is a schematic block diagram of a sparse limited-angle CBCT reconstruction method based on residual diffusion;

[0041] Figure 3(a) is a sinusoidal diagram of the reference standard data;

[0042] Figure 3(b) is the gold standard reference image;

[0043] Figure 3(c) is the sparse data sinusoidal graph;

[0044] Figure 3(d) is a low-quality initial image;

[0045] FIG3( e ) is a reconstructed image obtained by using the method of the present invention;

[0046] Figure 4 This is a comparison chart of the method of the present invention and other methods. DETAILED DESCRIPTION

[0047] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the preferred embodiments are only for illustrating the present invention, and are not intended to limit the scope of protection of the present invention.

[0048] CBCT imaging technology is based on a linear projection model of attenuation information following X-ray interaction with an object, reconstructing three-dimensional structures from two-dimensional projection data acquired from multiple angles. Complete linear imaging relies on sufficient and evenly distributed projection information in Radon space. Accurate reconstruction is typically achieved using a full-angle continuous scanning mode combined with classic algorithms such as filtered back projection. Sparse projection scanning significantly reduces radiation dose and increases acquisition speed by reducing the number of projection angles or the number of detector element activations. However, severe undersampling of the projection data leads to highly pathological reconstruction problems, with reconstructed images prone to streaking artifacts and loss of detail. Figure 2(a) is a schematic diagram of the CBCT reconstruction process. Limited by mechanical structure and detector size, conventional CBCT systems can achieve full-angle scanning in small field-of-view scenarios, such as the oral cavity. However, in large field-of-view imaging scenarios, the actual acquired projection data is often limited to a limited angular range due to insufficient detector coverage and limited mechanical motion. Limited-angle scanning and sparse projection together exacerbate the information loss in the projection data, further degrading the reconstructed image quality, manifesting as feature distortion, blurred edges, and the annihilation of low-contrast structures.

[0049] Among existing methods, deep learning demonstrates advantages in suppressing artifacts and improving reconstruction efficiency by constructing an end-to-end mapping model from the projection domain to the image domain and utilizing large-scale training data to drive network parameter optimization. However, the data-driven black-box nature results in insufficient modeling of the physical imaging mechanism, and the reconstruction results often deviate from the optimal solution space, manifesting as difficulty in completely eliminating the remaining image residuals. During network training, optimization based on pixel-level loss functions tends to capture low-frequency contour information, while high-frequency detail features are susceptible to gradient vanishing or over-smoothing effects in multi-layer nonlinear transformations, resulting in a decrease in the resolution of small structures. While adversarial training strategies can enhance texture realism, they carry the risk of mode collapse and are prone to generating spurious features or noise amplification under noise interference. In addition, the end-to-end mapping lacks explicit projective geometric constraints and statistical prior embedding, and the model decision process lacks a traceable physical basis, which may lead to systematic deviations when the data distribution shifts or scanning conditions suddenly change. Therefore, to address the core issues existing in the above-mentioned CBCT sparse limited-angle projection reconstruction, such as image residual, projection data mismatch, limited model generalization and noise sensitivity, the present invention proposes a sparse limited-angle CBCT reconstruction method, system and storage medium based on residual diffusion.

[0050] Figure 1 This is a schematic flow chart of the sparse limited-angle CBCT reconstruction method based on residual diffusion. Figure 1 As shown, the method includes the following steps:

[0051] Step 1: Perform CBCT sparse limited angle scanning on the target to be detected to obtain sparse projection data of the target to be detected, wherein the target to be detected can be any part of the body to be detected;

[0052] Step 2: Perform FDK reconstruction on the sparse projection data of the target to be detected to obtain the initial CBCT image of the target to be detected. The specific process of steps 1 and 2 can be seen in the schematic block diagram of the "CBCT sparse limited angle scan" section in Figure 2(b);

[0053] Step 3: The initial CBCT image of the target to be detected is passed through the image pre-training network to generate a first optimized CBCT image of the target to be detected;

[0054] The image pre-training network (also referred to as the "pre-training network") is a pre-trained lightweight encoder-decoder network with a symmetrical structure during the encoding and decoding stages. In the encoding stage, a five-level convolutional module is used to extract multi-scale features of the image through downsampling operations in each convolutional module. In the decoding stage, cross-layer connections are made through transposed convolutions and the outputs of convolutional modules of the corresponding size in the encoding stage, and a channel attention mechanism is used to adaptively select effective features. As shown in the "Pre-training Initial Restoration" section in Figure 2(b), the CBCT image obtained from a sparse limited-angle scan (i.e., the initial CBCT image) is used as the input of the image pre-training network. The output of this image pre-training network retains the original structural information through skip connections, forcing the network to focus on residual modeling of artifacts and noise. The downsampling path uses a five-level convolutional module to extract multi-scale features, and the maximum pooling operation induces the network to preferentially capture low-frequency priors such as organ contours (as shown by the black arrows in the "Pre-training Initial Recovery" section of Figure 2(b)). The upsampling path reconstructs high-frequency details through transposed convolution (ConvTranspose3D as shown in Figure 2(b)) and cross-layer connections (connecting information of the same scale in the encoding and decoding stages), and the batch normalization layer constrains the stability of the feature space distribution (as shown by the orange arrows in the "Pre-training Initial Recovery" section of Figure 2(b)). The symmetric structure of the encoder and decoder forms a contraction-expansion topology, which is equivalent to constructing multi-layer receptive field constraints in the image space, suppressing abnormal high-frequency oscillations caused by pathological reconstruction. Before pre-training, the network parameters are initialized using a truncated normal distribution to avoid gradient explosion while maintaining feature diversity. During the forward propagation process, the encoder compresses invalid noise patterns step by step, and the decoder adaptively selects valid features through the channel attention mechanism. The residual connection of the output layer transforms the reconstruction process into an image degradation component estimation problem, which is equivalent to the traditional variational model. Introducing a deep regularization term in, Characterizes the nonlinear transformation of the pre-trained network, λ represents the regularization coefficient, x FDK represents the image generated by FDK reconstruction, Represents the output of the image pre-training network. The training phase of this image pre-training network utilizes mean squared error (MSE) loss supervision, forcing the network to learn the residual mapping from FDK images (i.e., CBCT images) to ground truth images, achieving a balance between data fidelity and implicit regularization. This architecture, through end-to-end optimization, compresses the multi-step regularization process of traditional iterative algorithms into a single forward inference pass, maintaining reconstruction efficiency while inheriting the stability advantages of model-driven approaches.

[0055] This image pretraining network improves the quality of input images and generates optimized images. For a target to be detected, this image pretraining network can generate an optimized image of the initial CBCT image of the target, known as the first optimized image. This pretraining network effectively suppresses major artifacts in the reconstructed image.

[0056] Although the pre-trained network can effectively suppress the main artifacts, there are still unstructured residuals between the reconstruction results and the reference image. This residual is due to the lack of two physical constraints: first, the data fidelity term only acts on the image domain, and does not explicitly constrain the reconstruction results to satisfy the linear integral equation in the projection domain. Where y represents the projection data and A represents the system matrix. This results in the projection data mismatch error being converted into a low-frequency diffuse residual in the image domain after the back-projection operator. Secondly, the network regularization term, constrained by the limited receptive field and local convolution characteristics, does not adequately model global non-local correlation features, making it difficult to completely eliminate residual components of structured noise such as stripe and ring artifacts. This residual error manifests as an abnormal distribution of mid- and high-frequency energy in the frequency domain and as local grayscale distortion in the spatial domain, potentially masking subtle lesions or causing anatomical structural deformation. Therefore, based on the initial solution provided by the pre-trained network, the present invention constructs a diffusion model-guided residual iterative refinement mechanism. By modeling the remaining residual as a controlled random process, the residual components are gradually decoupled within a collaborative optimization framework driven by physical constraints and data. First, a forward noise injection model for the diffusion process is established to gradually perturb the residual distribution to an isotropic Gaussian distribution. Then, an inverse denoising process is designed to integrate the projection domain data consistency constraint into the gradient field update of the diffusion model through conditional score matching, ensuring that each iteration satisfies both the image domain prior matching and the projection domain geometric constraints. This dual-domain collaborative mechanism can not only correct the systematic residuals not eliminated by the pre-trained network, but also suppress the generation of new artifacts during the iterative process, thus entering step 4.

[0057] Step 4: Determine a residual image of the target to be detected using the first optimized CBCT image of the target to be detected and the sparse projection data of the target to be detected, using a trained residual diffusion model, wherein the residual diffusion model is used to estimate image degradation components during CBCT image reconstruction, and the residual diffusion model is a variance exploding diffusion model;

[0058] Step 5: Summing the first optimized CBCT image of the target to be detected and the residual image of the target to be detected to obtain a second optimized CBCT image of the target to be detected, where the second optimized CBCT image is the final CBCT reconstructed image.

[0059] The training of the residual diffusion model includes the following steps:

[0060] Acquire a training data set, wherein the training data set includes full projection data of the scanned object and corresponding sparse projection data;

[0061] Perform FDK reconstruction on the full projection data to generate a reference CBCT image (i.e., a high-quality image);

[0062] Perform FDK reconstruction on the sparse projection data to generate initial training CBCT images (i.e., low-quality images);

[0063] The initial training CBCT image is passed through the image pre-training network to generate a first optimized training CBCT image. The process of generating the first optimized training CBCT image using the image pre-training network is the same as the process of generating the first optimized CBCT image of the target to be detected, and will not be repeated here.

[0064] Generate a residual training image (i.e., the “residual” in the “diffusion residual reconstruction” section of Figure 2 ) by using the reference CBCT image (i.e., the “reference result” in the “diffusion residual reconstruction” section of Figure 2 (b)) and the first optimized training CBCT image (i.e., the “output result” in the “diffusion residual reconstruction” section of Figure 2 (b)).

[0065] The residual diffusion model is trained by using the residual training image and establishing the residual diffusion objective function.

[0066] The present invention adopts the Variance Exploding (VE) diffusion model to perform probability modeling on the residual error (i.e., the residual error between the reference result and the output result) of the pre-trained network output. Assume that the initial residual field is z0=x gt -x p , where x gt is the real tomographic image (i.e., reference result), x pRepresents the image reconstructed by the pre-trained network (i.e., the output result). The diffusion process constructs a forward perturbation model in the time domain through the stochastic differential equation (SDE), namely:

[0067]

[0068] Where dz represents the derivative of z, dw represents the derivative of w, w is the standard Wiener process, σ(t) is the noise scheduling function, and the exponential scheduling strategy is selected, that is, σ(t) = σ min (σ max / σ min ) t , which makes the noise variance grow exponentially with t, σ min and σ max They represent the minimum noise level at the beginning of the diffusion process and the maximum noise level at the end of the diffusion process. min At the beginning of the diffusion, it can be set to a small positive value (close to 0, but not 0). As the diffusion process proceeds, at t = T, the process gradually transforms the initial residual distribution P0(z) into an isotropic Gaussian distribution. A continuous and gradual noise injection path is formed.

[0069] Diffusion Network The U-Net structure based on the attention mechanism is adopted. Its core components include multi-resolution encoder, time condition injection, attention mechanism and frequency domain fusion branch. The denoising score matching framework is used in the diffusion network training, and the objective function is:

[0070]

[0071] Where tU(0,T) means t belongs to a uniform distribution between 0 and T, λ(t)=1 / σ(t) 2 is the signal-to-noise ratio weighting coefficient, z t That is z (t) , represents the residual of time step t, z0: that is, z (0) , represents the initial residual, and the conditional probability gradient term can be analytically expressed as:

[0072]

[0073] In actual training, an equivalent reparameterization technique is used to transform the network prediction target into a noise estimation task, that is, the mean square error loss is used to measure the difference between the noise predicted by the model and the actual noise, and the residual diffusion objective function is It can be expressed as:

[0074]

[0075] Among them, θ represents the parameters in the residual diffusion model, z (0) Represents the residual training image, that is, the residual diffusion model The initial value of the diffusion process; is the normal distribution function, I represents the identity matrix; Indicates the mean, ||||2 indicates the L2 norm, z (t) =z (0) +σ(t)ε, represents the residual image at time step t, t∈[0,T] is a virtual time variable, and T represents the last time step of the diffusion process. The course learning strategy is introduced during the training process to gradually expand σ max To improve the modeling ability of strong noise. Specifically, the training can be divided into multiple stages through segmented training, and different σ is used in each stage. max , for example, a smaller σ can be used in the early stages of training max , gradually increase σ in the later period max In some embodiments, σ can also be dynamically adjusted based on the training progress or model performance (such as changes in the loss function). max For example, after several epochs, σ max Increase according to the predetermined plan; in some embodiments, different σ can be mixed in each training batch. max Level samples to make the transition smoother.

[0076] After training the residual diffusion model, the trained residual diffusion model can be used to determine the residual image of the target to be detected. In view of the data incompleteness and residual structured characteristics in sparse limited-angle CBCT reconstruction, the present invention constructs an alternating optimization framework that integrates the diffusion residual prior and projection consistency. Specifically, the variables to be optimized are defined as the residual z and projection error p between the real image and the pre-trained network output, a joint objective function is established, and the joint objective function is solved through a dual-domain alternating optimization method to determine the residual image of the target to be detected, wherein the joint objective function includes a data fidelity term, a projection consistency constraint, and a diffusion prior constraint.

[0077] Furthermore, the joint objective function is:

[0078]

[0079] Among them, the first term on the right side of the equation is the data fidelity term, the second term is the projection consistency constraint, and the third term is the diffusion prior constraint. (t-1) represents the residual image predicted at time step t-1; p (t-1)represents the projection error predicted at time step t-1; z and p represent the residual image to be predicted and the projection error respectively; y represents the sparse projection data; A represents the system matrix of the sparse projection; x p represents the first optimized training CBCT image; μ and ρ are trade-off parameters; is the network output of the diffusion model at time step t, |||| F represents the F-norm.

[0080] Solving the joint objective function by a dual-domain alternating optimization method specifically includes the following steps:

[0081] S1: Projection error update, that is, fix the residual z, solve the projection domain minimization problem, and obtain the analytical solution p of the projection error p (t-1) ,Right now:

[0082]

[0083] This formula forces the updated projection error p to approach the actual measurement error y-Ax p Residual projection with current diffusion model prediction Establish a dynamic balance between data fidelity and model prediction;

[0084] S2: Image residual update, that is, fix the projection error p, solve the image domain residual optimization problem, and obtain the closed-form solution z (t -1) ,Right now:

[0085]

[0086] The residual update decomposes the residual reconstruction into two physical driving components: First, μA T p (t-1) Force the residual to satisfy the projective geometric constraints and correct the data mismatch artifacts that the pre-trained network has not eliminated; secondly, Exploiting anatomical priors implicitly encoded in a diffusion model to suppress noise amplification and enhance the continuity of small structures.

[0087] S3: Diffusion time stepping mechanism (as shown in the “test phase” section in Figure 2(b)). In each iteration, the network output of the diffusion model Estimate z based on the residual (t) The time-dependent noise scheduling strategy σ(t) gradually reduces the noise level and guides the residual to evolve from a high noise distribution to a true residual distribution. The alternating optimization process is executed cyclically through equations (6)-(7), that is, S1 and S2 are executed cyclically until the preset number of iterations or the convergence threshold is reached, until the residual estimate z is obtained. (0) , which is the residual image of the target to be detected.

[0088] The final reconstructed image can be obtained by x′=x p +z (0) This framework deeply integrates the generative power of the diffusion model with the physical constraints of the projection operator, achieving progressive correction of the residual components and enhanced anatomical fidelity under sparse limited-angle scanning conditions.

[0089] The present invention also provides a sparse limited-angle CBCT reconstruction system based on residual diffusion, the system comprising:

[0090] a memory configured to store a computer program;

[0091] A processor is configured to execute the computer program to implement the sparse limited-angle CBCT reconstruction method based on residual diffusion as described above.

[0092] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the sparse limited-angle CBCT reconstruction method based on residual diffusion as described above is implemented.

[0093] In summary, the core difficulty of sparse, limited-angle, wide-field-of-view CBCT imaging stems from a fundamental conflict between the device's physical construction and imaging requirements. Limited by the detector's physical size and mechanical motion range, the actual scanning angle range in wide-field scenarios is often less than 180°, resulting in non-uniform sparse sampling of the projection data in Radon space. These engineering constraints lead to a highly ill-posed 3D reconstruction problem. Traditional filtered back-projection algorithms produce streaking artifacts due to the broken projection integration path, while the sinusoidal truncation effect caused by limited-angle scanning further leads to spatial frequency aliasing of anatomical structures, manifesting as blurred organ edges and annihilation of tiny calcifications. Furthermore, with a large field of view and long-range integration path, X-ray scattering noise caused by metallic implants or tissue interfaces is accumulated and amplified by the back-projection operator, resulting in low-frequency grayscale offsets and unstructured noise fields, significantly reducing the contrast threshold of early-stage tumor lesions. While existing deep learning methods suppress local high-frequency artifacts through end-to-end mapping, their black-box nature ignores the global integral constraints of the X-ray projection equation, making it difficult to correct for systematic data mismatch errors, resulting in a physically unexplainable diffuse distribution of reconstruction residuals. To address the imaging bottlenecks caused by the physical limitations of the equipment, this project proposes a residual iterative optimization framework based on diffusion priors and physical collaboration. The artifact distribution pattern of the FDK initial reconstruction is extracted through a pre-trained codec network, and a variance-exploding diffusion model is constructed to model the remaining residual field using stochastic differential equations. This explicitly separates the structured ring artifacts caused by finite-angle truncation, the random noise caused by the nonlinear response of the detector, and the low-frequency offset components induced by the scattering effect. This invention innovatively designs an alternating direction minimization architecture to fuse the gradient field prediction capability of the diffusion model with the X-ray projection physics equations: in the image domain, the multi-scale feature fusion capability of the attention mechanism U-Net is utilized to capture the banded energy distribution characteristics of the artifact through frequency domain branches; in the projection domain, closed-form solutions are used to enforce data consistency constraints. This blocks the positive feedback of noise during the iterative process.

[0094] The following describes the invention through specific examples.

[0095] 1. Scan device and parameter configuration

[0096] This experiment used the Somatom Definition Flash dual-source spiral computed tomography system ("spiral CT") manufactured by Siemens Healthineers as the data acquisition device. This device is equipped with a high-precision solid-state detector array, and its technical parameters are as follows:

[0097] Detector structure: composed of 736×64 detection unit matrix

[0098] Detection unit physical size: 1.2858 mm × 1.0947 mm

[0099] X-ray tube voltage: 120 kV

[0100] X-ray tube current: Automatically modulated, range 100-400 mA

[0101] Field of View: 500 mm

[0102] Layer thickness setting: 0.625 mm

[0103] Reconstruction matrix: 512×512 pixels

[0104] The system's geometric parameters are precisely configured as follows: the X-ray source to rotation center distance (Source to Center Distance) is 595.0 mm, the X-ray source to detector distance (Source to Detector Distance) is 1085.6 mm, the scanning pitch (Pitch factor) is set to 0.9, 1152 projection angles are collected every 360 degrees of rotation, and the angle coverage range is [0,2π).

[0105] 2. Data Collection Process

[0106] To compare full projection and sparse projection data, two independent scans were performed on each subject. The specific steps are as follows:

[0107] First, the subject was positioned and immobilized according to standard clinical procedures, and the first spiral CT scan was performed, acquiring data from a complete 1,152 projection angles. During the scan, dose parameters were set to levels commonly used in clinical practice, strictly controlling the subject's radiation exposure while ensuring image quality. The scan covered the target anatomical region, with a 10 mm margin left before and after the scan to minimize cone beam effects. The complete projection data acquired from this scan is designated the "reference standard projection dataset."

[0108] After the first scan is completed, a second scan is performed immediately, ensuring the subject's position remains unchanged. For the second scan, system parameters are adjusted to a sparse angle sampling mode, capturing only 64 evenly distributed projection angles. This is achieved by pulse sampling at intervals of 1152 / 64 = 18 as the CT tube rotates, triggering an X-ray exposure and recording projection data every 5.625 degrees (360° / 64 ≈ 5.625°). The projection data acquired from this scan is designated a "sparse projection dataset." This acquisition method significantly reduces the subject's radiation dose.

[0109] 3. Projection data rearrangement technology

[0110] Since the original data collected by spiral CT are distributed in a spiral shape and are not suitable for direct application in two-dimensional reconstruction algorithms, this experiment developed a special projection data rearrangement technology. The process is as follows:

[0111] Helix2Fan projection realignment technology is used to convert the projection data acquired by spiral CT into two-dimensional projection data in fan-beam geometry. This technology performs the following steps:

[0112] Data extraction: Extract the projection data of the specified Z-axis position from the spiral trajectory

[0113] Interpolation reconstruction: cosine-weighted interpolation of incomplete projection angles

[0114] Geometric transformation: Converting spiral coordinate system data to fan beam coordinate system

[0115] Data calibration: performs attenuation coefficient correction and detector response homogenization

[0116] After the above processing, the rearranged fan beam projection data parameters are as follows:

[0117] The reference standard dataset maintains 1152 angles / rotations, and the sparse projection dataset retains 64 angles / rotations

[0118] Detector resolution: 736 cells / slice

[0119] Detector unit size: adjusted to 1.2858 mm × 1.0 mm

[0120] Source to center distance: remains unchanged at 595.0 mm

[0121] Source to detector distance: remains unchanged at 1085.6 mm

[0122] Pitch parameter: Due to the conversion to fan-beam geometry, this parameter is not applicable

[0123] The reordering process generates 1152×736 2D projection data (also known as a "sinogram") for the reference standard dataset and 64×736 2D projection data for the sparse projection dataset, both maintaining the angular coverage of [0, 2π]. This transformation significantly optimizes computational efficiency while ensuring data consistency and integrity.

[0124] 4. Reference image generation and dataset construction

[0125] The FDK (Feldkamp-Davis-Kress) algorithm, implemented in the TorchRadon library, was used to perform 3D reconstruction of the rearranged full projection data (1152 angles), generating high-quality CT images with a voxel size of 0.85 mm and a cross-sectional resolution of 512 × 512 pixels. This image set was designated as the "gold standard reference image" for evaluation of the reconstruction algorithm.

[0126] The FDK (Feldkamp-Davis-Kress) algorithm implemented in the TorchRadon computing library was used to reconstruct the two types of projection data: the rearranged full projection data (1152 angles) were three-dimensionally reconstructed to generate high-quality CT images with a voxel size of 0.85 mm and a cross-sectional resolution of 512×512 pixels. This image set was designated as the "gold standard reference image" for reconstruction algorithm evaluation; at the same time, the same FDK algorithm was applied to the sparse projection data (64 angles) for reconstruction to generate images with the same voxel size and resolution. However, due to insufficient projection angles, these images exhibited obvious streak artifacts and structural distortion, and served as the "low-quality initial images" to be processed.

[0127] The experiment included CT scan data from eight patients, constructing a dataset with a total capacity of 3,197 slices. The training set contained 2,426 slices from six patients, the validation set contained 441 slices from one patient, and the test set contained 330 slices from one patient. All image data were stored with 16-bit precision and normalized to ensure numerical stability. This data acquisition and processing method provides a rigorously controlled experimental basis for the study of CT sparse reconstruction algorithms, enabling accurate evaluation of the proposed method's performance in real-world clinical settings.

[0128] 4.1 Projection data and reconstruction results

[0129] The experiment first visualized the acquired data. Figure 3(a) shows a sinusoidal image (1152×736) of a single fully sampled reference standard data set from the test set, showcasing complete projection information and clear anatomical structure boundaries. The reference standard image reconstructed using this full-angle projection data using the FDK algorithm is shown in Figure 3(b). The image is high quality, with clear structures and no noticeable artifacts, and can serve as a gold standard for evaluating other reconstruction algorithms.

[0130] The sinusoidal image after sparse angular sampling (64 views) is shown in Figure 3(c). Its data size is 64×736, showing obvious angular undersampling characteristics, with a large number of information gaps between the projection data. Directly applying the FDK algorithm to reconstruct these sparse projections results in a low-quality initial image, as shown in Figure 3(d). The image contains severe streak artifacts and structural distortion, especially in edge and detail areas, significantly reducing its clinical diagnostic value.

[0131] The results of the residual diffusion-based sparse limited-angle CBCT reconstruction method proposed in this paper are shown in Figure 3(e). It can be observed that this method effectively suppresses the radiographic artifacts caused by sparse projections and restores the continuity and integrity of tissue structures. Compared to the low-quality initial images, the method of this invention significantly improves image clarity and contrast, accurately reconstructing key anatomical details and achieving a visual effect close to that of the reference standard image.

[0132] In order to comprehensively evaluate the performance of the proposed method, this experiment compared it with a variety of existing technologies, including existing FBP, Unet, DDNet, FISTA, Score-SDE and MCG. The results are as follows: Figure 4 shown. Figure 4 The images in the first row represent real images, and the red box area represents the region of interest; the first column in the second row represents the real image of the region of interest, the second column to the second to last column in the second row represent the reconstructed images of the region of interest obtained by using various existing comparison methods, and the last column in the second row represents the reconstructed image of the region of interest obtained by using the method of the present invention; the third row represents the difference map between the images in the second row and the real images of the region of interest.

[0133] pass Figure 4 It can be seen that post-processing methods, including deep learning post-processing methods based on Unet and DDNet, can suppress artifacts to a certain extent, but often introduce over-smoothing, resulting in loss of anatomical details;

[0134] Iterative unfolding method: Methods represented by FISTA jointly optimize in the projection domain and image domain, but it is still difficult to recover complex details in the case of severe undersampling.

[0135] Diffusion-based methods: including Score-SDE and MCG. Although these methods have strong generation capabilities, they have low computational efficiency and tend to be over-smoothed.

[0136] like Figure 4 As shown, through the region of interest ROI (i.e. Figure 4 Analysis of the image (red box in the middle) and comparison of the difference maps clearly demonstrate that our method outperforms other techniques in detail preservation and overall structure recovery. The difference maps show that our method minimizes the error distribution between the reference image and the image, particularly around anatomical edges and low-contrast regions. Quantitative analysis further demonstrates that the proposed method achieves optimal performance on objective evaluation metrics such as the Structural Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR), fully validating its effectiveness and superiority in sparse-view CT reconstruction.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A sparse limited-angle CBCT reconstruction method based on residual diffusion, characterized in that: include: Perform CBCT sparse limited angle scanning on the target to be detected to obtain sparse projection data of the target to be detected; Perform FDK reconstruction on the sparse projection data of the target to be detected to obtain the initial CBCT image of the target to be detected; Passing the initial CBCT image of the target to be detected through the image pre-training network to generate a first optimized CBCT image of the target to be detected; Determining a residual image of the target to be detected by using a trained residual diffusion model using a first optimized CBCT image of the target to be detected and sparse projection data of the target to be detected, wherein the residual diffusion model is used to estimate image degradation components in a CBCT image reconstruction process, and the residual diffusion model is a variance exploding diffusion model; The first optimized CBCT image of the target to be detected and the residual image of the target to be detected are summed to obtain a second optimized CBCT image of the target to be detected, and the second optimized CBCT image is the final CBCT reconstructed image.

2. The sparse limited-angle CBCT reconstruction method based on residual diffusion according to claim 1, characterized in that: The image pre-training network is a pre-trained lightweight encoder-decoder network with a symmetrical structure between the encoding and decoding stages. In the encoding stage, a five-level convolution module is used to extract multi-scale features of the image through the downsampling operation of each convolution module. In the decoding stage, cross-layer connections are made through transposed convolution and the output of the convolution module of the corresponding size in the encoding stage, and the channel attention mechanism is used to adaptively select effective features.

3. The sparse limited-angle CBCT reconstruction method based on residual diffusion according to claim 1, characterized in that: The method further includes training a residual diffusion model, specifically comprising the following steps: Acquire a training data set, wherein the training data set includes full projection data of the scanned object and corresponding sparse projection data; Perform FDK reconstruction on the full projection data to generate a reference CBCT image; Perform FDK reconstruction on the sparse projection data to generate initial training CBCT images; Passing the initial training CBCT image through the image pre-training network to generate a first optimized training CBCT image; generating a residual training image by using the reference CBCT image and the first optimized training CBCT image; The residual diffusion model is trained by using the residual training image and establishing the residual diffusion objective function, where the residual diffusion objective function for: Among them, θ represents the parameters in the residual diffusion model, z (0) Represents the residual training image, that is, the residual diffusion model The initial value of the diffusion process, σ(t) is the noise scheduling function, σ(t) = σ min (σ max / σ min ) t ,σ min and σ max represent the minimum noise level at the beginning of the diffusion process and the maximum noise level at the end of the diffusion process, respectively; is the normal distribution function, I represents the identity matrix; represents the mean, ‖‖2 represents the L2 norm, z (t) =z (0) +σ(t)ε, represents the residual image of time step t, t∈[0,T], T represents the last time step of the diffusion process, and the diffusion process constructs a forward perturbation model in the time domain through stochastic differential equations, that is, dz represents the derivative with respect to z, dw represents the derivative with respect to w, and w is the standard Wiener process.

4. The sparse limited-angle CBCT reconstruction method based on residual diffusion according to claim 3, characterized in that: Using the trained residual diffusion model, determining the residual image of the target to be detected specifically includes: establishing a joint objective function and solving the joint objective function through a dual-domain alternating optimization method to determine the residual image of the target to be detected, wherein the joint objective function includes a data fidelity term, a projection consistency constraint, and a diffusion prior constraint.

5. The sparse limited-angle CBCT reconstruction method based on residual diffusion according to claim 3, characterized in that: The joint objective function is: z (t-1) represents the residual image predicted at time step t-1; p (t-1) represents the projection error predicted at time step t-1; z and p represent the residual image to be predicted and the projection error respectively; y represents the sparse projection data; A represents the system matrix of the sparse projection; x p represents the first optimized training CBCT image; μ and ρ are trade-off parameters; is the network output of the diffusion model at time step t, |||| F represents the F-norm.

6. The sparse limited-angle CBCT reconstruction method based on residual diffusion according to claim 4 or 5, characterized in that: The method includes solving the joint objective function by a dual-domain alternating optimization method, specifically comprising the following steps: S1: Projection error update, that is, fix the residual z, solve the projection domain minimization problem, and obtain the analytical solution p of the projection error p (t -1) ; S2: Image residual update, that is, fix the projection error p, solve the image domain residual optimization problem, and obtain the closed-form solution z (t-1) , S3: Diffusion time stepping mechanism, that is, looping S1 and S2 until the preset number of iterations or convergence threshold is reached, until the residual estimate z is obtained (0) , which is the residual image of the target to be detected.

7. A sparse limited-angle CBCT reconstruction system based on residual diffusion, characterized in that: include a memory configured to store a computer program; A processor is configured to execute the computer program to implement the sparse limited-angle CBCT reconstruction method based on residual diffusion according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the sparse limited-angle CBCT reconstruction method based on residual diffusion according to any one of claims 1 to 6 is implemented.

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