Limited-angle Computed Tomography Research Articles

Iterative reconstruction for limited-angle CT using implicit neural representation

Objective. Limited-angle computed tomography (CT) presents a challenge due to its ill-posed nature. In such scenarios, analytical reconstruction methods often exhibit severe artifacts. To tackle this inverse problem, several supervised deep learning-based approaches have been proposed. However, they are constrained by limitations such as generalization issue and the difficulty of acquiring a large amount of paired CT images. Approach. In this work, we propose an iterative neural reconstruction framework designed for limited-angle CT. By leveraging a coordinate-based neural representation, we formulate tomographic reconstruction as a convex optimization problem involving a deep neural network. We then employ differentiable projection layer to optimize this network by minimizing the discrepancy between the predicted and measured projection data. In addition, we introduce a prior-based weight initialization method to ensure the network starts optimization with an informed initial guess. This strategic initialization significantly improves the quality of iterative reconstruction by stabilizing the divergent behavior in ill-posed neural fields. Our method operates in a self-supervised manner, thereby eliminating the need for extensive data. Main results. The proposed method outperforms other iterative and learning-based methods. Experimental results on XCAT and Mayo Clinic datasets demonstrate the effectiveness of our approach in restoring anatomical features as well as structures. This finding was substantiated by visual inspections and quantitative evaluations using NRMSE, PSNR, and SSIM. Moreover, we conduct a comprehensive investigation into the divergent behavior of iterative neural reconstruction, thus revealing its suboptimal convergence when starting from scratch. In contrast, our method consistently produced accurate images by incorporating an initial estimate as informed initialization. Significance. This work showcases the feasibility to reconstruct high-fidelity CT images from limited-angle x-ray projections. The proposed methodology introduces a novel data-free approach to enhance medical imaging, holding promise across various clinical applications.

An interactive method based on multi-objective optimization for limited-angle CT reconstruction

Objective. Limited-angle x-ray computed tomography (CT) is a typical ill-posed inverse problem, leading to artifacts in the reconstructed image due to the incomplete projection data. Most iteration CT reconstruction methods involve optimization for a single object. This paper explores a multi-objective optimization model and an interactive method based on multi-objective optimization to suppress the artifacts of limited-angle CT. Approach. The model includes two objective functions on the dual domain within the data consistency constraint. In the interactive method, the structural similarity index measure (SSIM) is regarded as the value function of the decision maker (DM) firstly. Secondly, the DM arranges the objective functions of the multi-objective optimization model to be optimized according to their absolute importance. Finally, the SSIM and the simulated annealing (SA) method help the DM choose the desirable reconstruction image by improving the SSIM value during the iteration process. Main results. Simulation and real data experiments demonstrate that the artifacts can be suppressed by the proposed method, and the results were superior to those reconstructed by the other three reconstruction methods in preserving the edge structure of the image. Significance. The proposed interactive method based on multi-objective optimization shows some potential advantages over classical single object optimization methods.

Image reconstruction based on nonlinear diffusion model for limited-angle computed tomography

The problem of limited-angle computed tomography (CT) imaging reconstruction has a wide range of practical applications. Due to various factors such as high x-ray absorption, structural characteristics of the scanned object, and equipment limitations, it is often impractical to obtain a complete angular scan, resulting in limited-angle scan data. In this paper, we propose an iterative image reconstruction algorithm for limited-angle CT. The algorithm carries out a traditional CT reconstruction and a nonlinear diffusion process alternatively. Specifically, a subtle partial differential equation is constructed to guide the nonlinear diffusion process to eliminate limited-angle artifacts in the reconstructed image. Numerical experiments on both analytic data and real data validate the efficacy of the proposed nonlinear diffusion reconstruction algorithm. Furthermore, a linear diffusion reconstruction algorithm which combines a traditional CT reconstruction algorithm and a linear diffusion process is also presented in the paper.

A cascading l0 regularization reconstruction method in nonsubsampled contourlet domain for limited-angle CT

In some computed tomography (CT) practical applications, the projection data is incomplete, which makes some limited-angle artifacts presented in the reconstructed image. Total variation (TV) regularization method is used to suppress the artifacts, but the edge of reconstructed image is distorted or some tiny details are missed. To preserve the edge of reconstructed image, a cascading ℓ0 regularization-based reconstruction model in nonsubsampled contourlet transform (NSCT) domain is proposed, which considers both the directional peculiarity of artifacts and the smooth of low frequency of the reconstructed image. In the proposed reconstruction model, a ℓ0 regularization term in the high frequency is used to suppress the artifacts and noise, and a ℓ0 regularization of gradient image in low frequency is used to suppress the limited-angle artifacts, to preserve the edge of object and to smooth the reconstructed image. To solve the proposed model, a proximal alternating linearized Peaceman–Rachford splitting method (PAL-PRSM) is proposed, which uses the Peaceman–Rachford splitting method that updates the Lagrange multiplier twice, one after each minimization of the subproblem, to deal with the optimization problem firstly, and then the proximal linearization is used to avoid computing the inverse of a huge system matrix. In addition, to compensate the proximal linearization, we add an additional term into Lagrange multiplier updating. Real data experiments are investigated to demonstrate the effectiveness of PAL-PRSM method, and the results show that the proposed method outperforms two other CT reconstruction methods on preserving the edge of reconstructed image. On the whole, the proposed method is a compromise between denoising and preserving the edge of reconstructed image.

Multi-scale dilated dense reconstruction network for limited-angle computed tomography

Objective. Due to the incomplete projection data, the image reconstructed by limited-angle computed tomography (CT) usually suffers from significant artifacts, by which the structural details are heavily blurred. In this study, we aim to develop a novel approach to improve the limited-angle CT reconstruction performance, especially for the narrow scanning angular range. Approach. A deep learning based iterative framework for limited-angle tomography is proposed, which is named multi-scale dilated dense reconstruction network (MSDDRNet). The MSDDRNet utilizes a multi-scale dilated dense convolution neural network (MSDD-CNN) with conventional reconstruction algorithm for predicting image from incomplete projection data. The MSDD-CNN enhances the image features in the network by merging the DenseNet-Like structure, which serves to restore invisible singularities and reduce artifacts, as well as introducing constraints on the projection domain data into the iterative process to achieve better image detail recovery. Additionally, to improve the training speed of the network, we use a strategy of pre-training and model migration. Main results. Numerical experiments demonstrate that the proposed MSDDRNet performs well in terms of artifact correction, noise reduction and structure recovery compared to existing methods with limited scan angles, and we also extend the proposed method to more general scanning condition and other application such as dental CT data. Significance. The proposed method is a general framework, which can be applied to other CT problems, such as low dose CT, sparse-data CT and spectral CT.

LRIP-Net: Low-Resolution Image Prior-Based Network for Limited-Angle CT Reconstruction

In the practical applications of computed tomography (CT) imaging, the projection data may be acquired within a limited-angle range and corrupted by noises due to the limitation of scanning conditions. The noisy incomplete projection data results in the ill-posedness of the inverse problems. Based on the observation that the low-resolution reconstruction problem has better numerical stability, we propose a novel low-resolution image prior-based CT reconstruction model for limited-angle reconstruction. More specifically, we build up a low-resolution reconstruction problem on the down-sampled projection data, and use the reconstructed low-resolution image as prior knowledge for the high-resolution limited-angle CT problem. The constrained minimization problem is then solved by the alternating direction method with all subminimization problems approximated by the convolutional neural networks. Numerical experiments demonstrate that our double-resolution network outperforms both the variational method and popular learning-based reconstruction methods on noisy limited-angle reconstruction problems.

Structure-guided computed tomography reconstruction from limited-angle projections.

Limited-angle computed tomography (CT) imaging is one of the common imaging problems. The reconstructed images often encounter obvious artifacts and structure degradation. In recent years, the recoverability prior of image structure has been widely explored in limited-angle CT reconstruction, and the image quality has been greatly improved. However, the artifacts and structure degradation still exist. In this study, we establish a new reconstruction model based on weighted relative structure (wRS) determined by image gradients, which serves as weights to guide image reconstruction in order to reduce artifacts and preserve structures. Then, we develop an efficient algorithm using a surrogate function to solve this model. Moreover, this method is compared with some of other popular reconstruction methods, such as anisotropic total variation method and image gradient L0 norm minimization method and so on. Experiments on digital phantoms, real carved cheese and walnut projection are reported to demonstrate its superiority. Several quantitative indices including RMSE, PSNR, and SSIM of the reconstruction images from 90°-data of FORBILD head phantom are 0.0120, 43.52, and 0.9961. The experimental results indicate that the image obtained by our method is the closest to reference image. By comparing reconstruction images or their residual images, images reconstructed from real CT data, the experimental results of the residual images and the respective quantitative data analysis also demonstrate that the images reconstructed using our new method suffer from less artifacts and structure degradation.

An Innovative Low-dose CT Inpainting Algorithm based on Limited-angle Imaging Inpainting Model.

With the popularity of computed tomography (CT) technique, an increasing number of patients are receiving CT scans. Simultaneously, the public's attention to CT radiation dose is also increasing. How to obtain CT images suitable for clinical diagnosis while reducing the radiation dose has become the focus of researchers. To demonstrate that limited-angle CT imaging technique can be used to acquire lower dose CT images, we propose a generative adversarial network-based image inpainting model-Low-dose imaging and Limited-angle imaging inpainting Model (LDLAIM), this method can effectively restore low-dose CT images with limited-angle imaging, which verifies that limited-angle CT imaging technique can be used to acquire low-dose CT images. In this work, we used three datasets, including chest and abdomen dataset, head dataset and phantom dataset. They are used to synthesize low-dose and limited-angle CT images for network training. During training stage, we divide each dataset into training set, validation set and testing set according to the ratio of 8:1:1, and use the validation set to validate after finishing an epoch training, and use the testing set to test after finishing all the training. The proposed method is based on generative adversarial networks(GANs), which consists of a generator and a discriminator. The generator consists of residual blocks and encoder-decoder, and uses skip connection. We use SSIM, PSNR and RMSE to evaluate the performance of the proposed method. In the chest and abdomen dataset, the mean SSIM, PSNR and RMSE of the testing set are 0.984, 35.385 and 0.017, respectively. In the head dataset, the mean SSIM, PSNR and RMSE of the testing set are 0.981, 38.664 and 0.011, respectively. In the phantom dataset, the mean SSIM, PSNR and RMSE of the testing set are 0.977, 33.468 and 0.022, respectively. By comparing the experimental results of other algorithms in these three datasets, it can be found that the proposed method is superior to other algorithms in these indicators. Meanwhile, the proposed method also achieved the highest score in the subjective quality score. Experimental results show that the proposed method can effectively restore CT images when both low-dose CT imaging techniques and limited-angle CT imaging techniques are used simultaneously. This work proves that the limited-angle CT imaging technique can be used to reduce the CT radiation dose, and also provides a new idea for the research of low-dose CT imaging.

A new limited-angle CT reconstruction algorithm based on the local anisotropic total variation restoration of continuity

A new limited-angle computed tomography(CT) reconstruction algorithm based on local detail information restoration in the CT image projection domain was proposed in this paper. The lost projection information could be repaired with the new algorithm called local anisotropic total variation repair method of sinogram (LATV). According to the continuity of local gradient in sinogram, local high frequency characteristics can be improved which are blurred by conventional TVM. A series of numerical reconstruction experiments were conducted to validate the new algorithm. The overall quality of images reconstructed by new algorithm was better than conventional TVM algorithm when quantitatively evaluated. Then, a local region with rich details was selected in order to evaluate the reconstruction effect of the internal details. From the perspective of three image quality evaluation parameters, it was shown that the local high frequency details were well repaired. Finally, the reconstruction quality was evaluated by actual CT experimental data. The new method also performed better than conventional method. Therefore, the new LATV algorithm proposed in this paper may be a new method suitable for limited-angle CT reconstruction problems.

Sam's Net: A Self-Augmented Multistage Deep-Learning Network for End-to-End Reconstruction of Limited Angle CT.

Limited angle reconstruction is a typical ill-posed problem in computed tomography (CT). Given incomplete projection data, images reconstructed by conventional analytical algorithms and iterative methods suffer from severe structural distortions and artifacts. In this paper, we proposed a self-augmented multi-stage deep-learning network (Sam's Net) for end-to-end reconstruction of limited angle CT. With the merit of the alternating minimization technique, Sam's Net integrates multi-stage self-constraints into cross-domain optimization to provide additional constraints on the manifold of neural networks. In practice, a sinogram completion network (SCNet) and artifact suppression network (ASNet), together with domain transformation layers constitute the backbone for cross-domain optimization. An online self-augmentation module was designed following the manner defined by alternating minimization, which enables a self-augmented learning procedure and multi-stage inference manner. Besides, a substitution operation was applied as a hard constraint for the solution space based on the data fidelity and a learnable weighting layer was constructed for data consistency refinement. Sam's Net forms a new framework for ill-posed reconstruction problems. In the training phase, the self-augmented procedure guides the optimization into a tightened solution space with enriched diverse data distribution and enhanced data consistency. In the inference phase, multi-stage prediction can improve performance progressively. Extensive experiments with both simulated and practical projections under 90-degree and 120-degree fan-beam configurations validate that Sam's Net can significantly improve the reconstruction quality with high stability and robustness.

Limited-Angle CT Reconstruction with Generative Adversarial Network Sinogram Inpainting and Unsupervised Artifact Removal

High-quality limited-angle computed tomography (CT) reconstruction is in high demand in the medical field. Being unlimited by the pairing of sinogram and the reconstructed image, unsupervised methods have attracted wide attention from researchers. The reconstruction limit of the existing unsupervised reconstruction methods, however, is to use [0°, 120°] of projection data, and the quality of the reconstruction still has room for improvement. In this paper, we propose a limited-angle CT reconstruction generative adversarial network based on sinogram inpainting and unsupervised artifact removal to further reduce the angle range limit and to improve the image quality. We collected a large number of CT lung and head images and Radon transformed them into missing sinograms. Sinogram inpainting network is developed to complete missing sinograms, based on which the filtered back projection algorithm can output images with most artifacts removed; then, these images are mapped to artifact-free images by using artifact removal network. Finally, we generated reconstruction results sized 512×512 that are comparable to full-scan reconstruction using only [0°, 90°] of limited sinogram projection data. Compared with the current unsupervised methods, the proposed method can reconstruct images of higher quality.

Image reconstruction method for limited-angle CT based on total variation minimization using guided image filtering.

Radiation is harmful to the human body, which is coupled with the fact that scanning conditions pose a number of restrictions. As a result, the projection data of a scanned object are generally acquired within a limited-angle range in practical computed tomography (CT) applications. Under this circumstance, classical image reconstruction methods cannot obtain high-quality images, and limited-angle artifacts appear in the reconstructed image. In recent years, the l1 norm of a gradient image-based total variation minimization (TVL1) image reconstruction method has often been used to deal with the image reconstruction problem from undersampling projection data, but limited-angle artifacts have been encountered near the edges for limited-angle CT. The l0 norm of a gradient image-based total variation minimization (TVL0) image reconstruction method can better preserve the edges, but it cannot obtain acceptable results when the scanning angle range is further reduced. Inspired by the advantages of guided image filtering (GIF), which can better smooth an image and preserve its structure, we used it to improve the reconstructed image quality for limited-angle CT by transferring reconstructed results of the TVL1 method to those of the TVL0 method. Simulation experiments show that the proposed method can better preserve structures and suppress limited-angle artifacts and noise than several related reconstruction methods.

A model-based deep network for limited-angle computed tomography image reconstruction

In this paper, we propose a variational model for the limited-angle computed tomography (CT) image reconstruction and convert it into an end-to-end deep network. We first use the penalty method to solve the model and divide it into three iterative subproblems, where the first subproblem completes the sinograms, the second refines the CT images, and the last merges the outputs of the first two subproblems. In each iteration, we use the convolutional neural networks (CNNs) to approximate the solutions of the first two subproblems and, thus, obtain an end-to-end deep network for the limited-angle CT image reconstruction. Our network tackles both the sinograms and the CT images, and can simultaneously suppress the artifacts caused by the incomplete data and recover fine structural information in the CT images. Experimental results show that our method outperforms the related methods for the limited-angle CT image reconstruction.

Anisotropic structure property based image reconstruction method for limited-angle computed tomography.

Limited-angle computed tomography (CT) may appear in restricted CT scans. Since the available projection data is incomplete, the images reconstructed by filtered back-projection (FBP) or algebraic reconstruction technique (ART) often encounter shading artifacts. However, using the anisotropy property of the shading artifacts that coincide with the characteristic of limited-angle CT images can reduce the shading artifacts. Considering this concept, we combine the anisotropy property of the shading artifacts with the anisotropic structure property of an image to develop a new algorithm for image reconstruction. Specifically, we propose an image reconstruction method based on adaptive weighted anisotropic total variation (AwATV). This method, termed as AwATV method for short, is designed to preserve image structures and then remove the shading artifacts. It characterizes both of above properties. The anisotropy property of the shading artifacts accounts for reducing artifacts, and the anisotropic structure property of an image accounts for preserving structures. In order to evaluate the performance of AwATV, we use the simulation projection data of FORBILD head phantom and real CT data for image reconstruction. Experimental results show that AwATV can always reconstruct images with higher SSIM and PSNR, and smaller RMSE, which means that AwATV enables to reconstruct images with higher quality in term of artifact reduction and structure preservation.

A fast image reconstruction method for planar objects CT inspired by differentiation property of Fourier transform (DPFT)

In planar objects computed tomography (CT), restricted to the scanning environment, projections can only be collected from limited angles. Moreover, limited by the emitting power of the x-ray source, only a few photons penetrate the long side of the planar objects, which results in the noise increasing in projections. Planar objects CT reconstruction based on these two conditions is mathematically corresponding to solving an ill-posed inverse problem. Although several iterative reconstruction algorithms of limited-angle CT were proposed, high-quality planar objects CT reconstruction algorithms with fast convergence are still the goals of many researchers. In order to address the aforementioned problems, we proposed a new optimization model for planar objects CT reconstruction. Inspired by the theory of ‘visible boundary and invisible boundary’ in limited-angle CT and the differentiation property of Fourier transform, a new optimization objective function is proposed in this paper. Based on the statistical noise model of existing CT system, the convex set constraint of the optimization model is given. Besides, the optimization model is solved by convex set projection and Fourier transform differentiation property. The proposed algorithm was evaluated with both simulated data and real data. The experimental results show that the proposed algorithm can achieve the effect of noise suppression, limited-angle artifacts reduction, and fast structure reconstruction when it applies to planar objects CT.

Guided image filtering based ℓ0 gradient minimization for limited-angle CT image reconstruction

Abstract Limited-angle computed tomography (CT) reconstruction problem arises in some practical applications due to restrictions in the scanning environment or CT imaging device. Some artifacts will be presented in image reconstructed by conventional analytical algorithms. Although some regularization strategies have been proposed to suppress the artifacts, such as total variation (TV) minimization, there is still distortion in some edge portions of image. Guided image filtering (GIF) has the advantage of smoothing the image as well as preserving the edge. To further improve the image quality and protect the edge of image, we propose a coupling method, that combines ℓ 0 {\ell_{0}} gradient minimization and GIF. An intermediate result obtained by ℓ 0 {\ell_{0}} gradient minimization is regarded as a guidance image of GIF, then GIF is used to filter the result reconstructed by simultaneous algebraic reconstruction technique (SART) with nonnegative constraint. It should be stressed that the guidance image is dynamically updated as the iteration process, which can transfer the edge to the filtered image. Some simulation and real data experiments are used to evaluate the proposed method. Experimental results show that our method owns some advantages in suppressing the artifacts of limited angle CT and in preserving the edge of image.

Limited-angle CT reconstruction with generalized shrinkage operators as regularizers

<p style='text-indent:20px;'>Limited-angle reconstruction is a very important but challenging problem in the field of computed tomography (CT) which has been extensively studied for many years. However, some difficulties still remain. Based on the theory of visible and invisible boundary developed by Quinto et.al, we propose a reconstruction model for limited-angle CT, which encodes the visible edges as priors to recover the invisible ones. The new model utilizes generalized shrinkage operators as regularizers to perform edge-preserving smoothing such that the visible edges are employed as anchors to recover piecewise-constant or piecewise-smooth reconstructions, while noises and artifacts are suppressed or removed. This work extends our previous research on limited-angle reconstruction which employs gradient <inline-formula><tex-math id="M1">\begin{document}$ \ell_0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \ell_1 $\end{document}</tex-math></inline-formula> norm regularizers. The effectiveness of the proposed model and its corresponding solving algorithm shall be verified by numerical experiments with simulated data as well as real data.</p>

Nonlocal Low-Rank and Prior Image-Based Reconstruction in a Wavelet Tight Frame Using Limited-Angle Projection Data

Computed tomography (CT) reconstruction for limited-angle projection data is an ill-posed inverse problem, that often produces artifacts near the edges of an image. In this study, a hybrid minimization model based on a nonlocal low-rank approximation and a prior image in a wavelet tight framework is proposed to improve reconstructions from limited-angle projections. Low-frequency wavelet coefficients of the reconstructed image were estimated using a nonlocal low-rank approximation and the $l_{2}$ norm minimization was applied to the difference between the high-frequency components of a prior image and the reconstructed image. In addition, the alternative direction method of multipliers (ADMM) was used for alternately minimization to solve two regularization terms which produce the most parameters. Experimental results demonstrated that the proposed algorithm offers several advantages over conventional iterative reconstruction techniques, including faster convergence, suppression of limited-angle artifacts, noise reduction, and the preservation of edges and other image details. This study represents the first time that nonlocal low-rank prior information has been applied to limited-angle CT.

A sequential regularization based image reconstruction method for limited-angle spectral CT

In spectral computed tomography (CT), the object is respectively scanned under different x-ray spectra. Multiple projection data can be collectively used for reconstructing basis images and virtual monochromatic images, which have been used in material decomposition, beam-hardening correction, bone removal, and so on. In practice, projection data may be obtained in a limited scanning angular range. Images reconstructed from limited-angle data by conventional spectral CT reconstruction methods will be deteriorated by limited-angle related artifacts and basis image decomposition errors. Motivated by observations of limited-angle spectral CT, we propose a sequential regularization-based limited-angle spectral CT reconstruction model and its numerical solver. Both simulated and real data experiments validate that our method is capable of suppressing artifacts, preserving edges and reducing decomposition errors.

Limited-Angle X-Ray CT Reconstruction Using Image Gradient ℓ₀-Norm With Dictionary Learning

Limited-angle X-ray computed tomography (CT) reconstruction is a typical ill-posed problem. To recover satisfied reconstructed images with limited-angle CT projections, prior information is usually introduced into image reconstruction, such as the piece-wise constant, nonlocal image similarity, and so on. To further improve the image quality for limited-angle CT reconstruction, the dictionary learning (DL) and image gradient ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm are combined into image reconstruction model, it can be called as ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> DL reconstruction technique. The advantages of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> DL can be divided into two aspects. On one hand, the proposed ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> DL method can inherit the advantages of DL in image details preservation and features recovery by exploring an over-complete dictionary. On the other hand, the image gradient ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm minimization can further protect image edges and reduce shadow artifact. Both numerical simulation and preclinical mouse experiments are performed to validate and evaluate the outperformances of proposed ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> DL method by comparing with other state-of-the-art methods, such as total variation (TV) minimization and TV with low rank (TV + LR).