Limited-angle Computed Tomography Reconstruction Research Articles

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.

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.

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.

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.

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>

Limited-Angle Computed Tomography Reconstruction using Combined FDK-Based Neural Network and U-Net.

The limited-angle cone-beam Computed Tomography (CT) is often used in C-arm for clinical diagnosis with the advantages of cheap cost and radiation dose reduction. However, due to incomplete projection data, the 3-dimensional CT images reconstructed by conventional methods, such as the Feldkamp, Davis and Kres (FDK) algorithm [1], suffer from heavy artifacts and missing features. In this paper, we propose a novel pipeline of neural networks jointly by a FDK-based neural network revisited from Würfl et al.'s work [2] and an image domain U-Net to enhance the 3-dimensional reconstruction quality for limited projection sinogram less than 180 degrees, i.e. 145 degrees in our work. Experimental results, on simulated projections of real-scan CTs, show that the proposed pipeline can reduce some of the major artifacts caused by the limited views while keep the key features, with a 16.60% improvement than Würfl et al.'s work on peak signal-to-noise ratio.

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).

Self-Guided Limited-Angle Computed Tomography Reconstruction Based on Anisotropic Relative Total Variation

In some computed tomography (CT) applications, limited-angle projections are used for image reconstruction, and traditional reconstruction methods, such as filtered back-projection (FBP) or simultaneous algebraic reconstruction technique (SART), cannot reconstruct high-quality CT images without prior knowledge assistance. For limited-angle CT reconstruction, total variation minimization (TVM) method is not conductive to recovering image structures. Image reconstruction methods based on anisotropic total variation (ATV) and reweighted anisotropic total variation (RwATV) can significantly reduce the shading artifacts using prior knowledge of the scanning angular range and image sparsity. However, using the knowledge of image sparsity does not further improve image quality in some applications. In this paper, we propose a new reconstruction method based on anisotropic relative total variation (ARTV) for limited-angle CT reconstruction. In ARTV, the windowed inherent variation (WIV) indicates the strength of structure information and WIV values are adaptively determined by local structure information. In limited-angle CT, particular scanning angular range urges us into exerting different strengths on different directions of ARTV. Experiments on FORBILD HEAD phantom, a thoracic image and real projections of a walnut are performed to test the new method. Experimental results show that the destroyed structures are recovered to some extent, and we acquire higher image quality compared to some existing limited-angle CT reconstruction methods.

ADMM-based deep reconstruction for limited-angle CT

In the real applications of computed tomography (CT) imaging, the projection data of the scanned objects are usually acquired within a limited-angle range because of the limitation of the scanning condition. Under these circumstances, conventional analytical algorithms, such as filtered back-projection (FBP), do not work because the projection data are incomplete. The regularization method has proven to be effective for tomographic reconstruction from under-sampled measurements. To deal with the limited-angle CT reconstruction problem, the regularization method is commonly used, but it is difficult to find a generic regularization term and choose the regularization parameters. Moreover, in some cases, the quality of reconstructed images is less than satisfactory. To solve this problem, we developed an alternating direction method of multipliers (ADMM)-based deep reconstruction (ADMMBDR) algorithm for limited-angle CT. First, we used the ADMM algorithm to decompose a regularization reconstruction model. Then, we utilized a deep convolutional neural network (CNN) to replace a part of the ADMM algorithm to reduce artifacts and avoid the choice of the regularization term and the regularization parameter. Furthermore, we conducted some numerical experiments to evaluate the feasibility and the advantages of the proposed algorithm. The results showed that the proposed algorithm had a better performance than several state-of-the-art algorithms; with respect to structure preservation and artifact reduction.

Image reconstruction model for limited-angle CT based on prior image induced relative total variation

• Suppressing shading artifacts is challenging for limited-angle CT . • Incorporating a prior image or some structures is a promising attempt. • Relative total variation can extract structures from noise. • Structures will guide image reconstruction and reduce shading artifacts. • Modified relative total variation is not sensitive to noise in the prior image. Limited-angle computed tomography (CT) reconstruction has a great potential to reduce X-ray radiation dose or scanning time. Suppressing shading artifacts is challenging, but of great practical significance in limited-angle CT. Traditional methods based on total variation (TV) cannot effectively remove the shading artifacts, prior image constrained compressed sensing (PICCS) is a promising method, but is sensitive to the quality of the prior image. In micro-CT, a prior image reconstructed by filtered back-projection (FBP) may contain high-level noise. An image reconstructed by PICCS tends to inherit both structures and noise of the prior image. In this study, to suppress noise and shading artifacts, we propose a new limited-angle CT reconstruction model called prior image induced relative total variation (piiRTV), that uses the structure information of a prior image to guide limited-angle CT reconstruction. The proposed piiRTV is compared to TV and PICCS. Numerical simulations and experiments on real CT projections demonstrate the effectiveness of piiRTV in suppression of noise and shading artifacts. In addition, the proposed piiRTV is more robust to the prior image quality than PICCS.

Guided Image Filtering Based Limited-Angle CT Reconstruction Algorithm Using Wavelet Frame

Computed tomography (CT) has its irreplaceable function in nondestructive testing and medical diagnosis. In some practical CT imaging applications, the limited-angle scanning is common due to X-ray’s potential harm to human and the limitation of the scanning conditions. Under these circumstances, analytic reconstruction algorithms, like filtered backprojection (FBP), will not obtain satisfactory results because of lacking the projection data. Iterative reconstruction (IR) methods that can incorporate prior knowledge have attracted attention in many fields, and wavelet frame-based regularization reconstruction algorithms have proven to be a useful means to reduce slope artifacts and noise for limited-angle CT. However, with the obtained projection data of the scanned object further reduces, the edge structures and the details of the reconstructed image worsen. For the sake of improving the quality of the reconstructed image from the limited-angle projection data, a guided image filtering (GIF)-based limited-angle CT reconstruction algorithm using wavelet frame was proposed. In each iteration of the proposed algorithm, the reconstructed result constrained by the wavelet frame was used as the guidance image to transfer the important features it contains to the reconstructed result of SART method by GIF. Furthermore, some simulated experiments and real data tests were conducted to evaluate the feasibility and validity of the proposed algorithm, and the qualitative and quantitative indexes indicated that the proposed algorithm was superior to other iterative reconstruction algorithms in artifacts reduction, noise suppression, and structure preservation.

A variational proximal alternating linearized minimization in a given metric for limited-angle CT image reconstruction

• A nonconvex and nonsmooth optimization model is investigated for limited-angle CT imaging. • The proposed method can avoid computing the inverse of a large system matrix. • We show that each bounded sequence generated by our method globally converges to a critical point. • The results by our method are shown superior than some classical CT reconstruction methods by real data experiments. Due to the restriction of computed tomography (CT) scanning environment, the acquired projection data may be incomplete for exact CT reconstruction. Though some convex optimization methods, such as total variation minimization based method, can be used for incomplete data reconstruction, the edge of reconstruction image may be partly distorted for limited-angle CT reconstruction. To promote the quality of reconstruction image for limited-angle CT imaging, in this paper, a nonconvex and nonsmooth optimization model was investigated. To solve the model, a variational proximal alternating linearized minimization (VPALM) method based on proximal mapping in a given metric was proposed. The proposed method can avoid computing the inverse of a huge system matrix thus can be used to deal with the larger-scale inverse problems. What’s more, we show that each bounded sequence generated by VPALM globally converges to a critical point based on the Kurdyka–Lojasiewicz property . Real data experiments are used to demonstrate the viability and effectiveness of VPALM method, and the results show that the proposed method outperforms two classical CT reconstruction methods.

An adaptive iteration reconstruction method for limited-angle CT image reconstruction

Abstract The limited-angle computed tomography (CT) reconstruction problem is an ill-posed inverse problem, and the parameter selection for limited-angle CT iteration reconstruction is a difficult issue in practical application. In this paper, to alleviate the instability of limited-angle CT reconstruction problem and automatize the reconstruction process, we propose an adaptive iteration reconstruction method that the regularization parameter is chosen adaptively via the plot of the normalized wavelet coefficients fitting residual versus that the ℓ 0 {\ell_{0}} regularization part. The experimental results show that the reconstructed images using the method with adapted regularization parameter are almost as good as that using the non-adapted parameter method in terms of visual inspection, in addition, our method has an advantage in adaptively choosing the regularization parameter.

Limited angle CT reconstruction by simultaneous spatial and Radon domain regularization based on TV and data-driven tight frame

Limited angle computed tomography (CT) reconstruction is widely performed in medical diagnosis and industrial testing because of the size of objects, engine/armor inspection requirements, and limited scan flexibility. Limited angle reconstruction necessitates usage of optimization-based methods that utilize additional sparse priors. However, most of conventional methods solely exploit sparsity priors of spatial domains. When CT projection suffers from serious data deficiency or various noises, obtaining reconstruction images that meet the requirement of quality becomes difficult and challenging. To solve this problem, this paper developed an adaptive reconstruction method for limited angle CT problem. The proposed method simultaneously uses spatial and Radon domain regularization model based on total variation (TV) and data-driven tight frame. Data-driven tight frame being derived from wavelet transformation aims at exploiting sparsity priors of sinogram in Radon domain. Unlike existing works that utilize pre-constructed sparse transformation, the framelets of the data-driven regularization model can be adaptively learned from the latest projection data in the process of iterative reconstruction to provide optimal sparse approximations for given sinogram. At the same time, an effective alternating direction method is designed to solve the simultaneous spatial and Radon domain regularization model. The experiments for both simulation and real data demonstrate that the proposed algorithm shows better performance in artifacts depression and details preservation than the algorithms solely using regularization model of spatial domain. Quantitative evaluations for the results also indicate that the proposed algorithm applying learning strategy performs better than the dual domains algorithms without learning regularization model

Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data

The limited-angle projection data of an object, in some practical applications of computed tomography (CT), are obtained due to the restriction of scanning condition. In these situations, since the projection data are incomplete, some limited-angle artifacts will be presented near the edges of reconstructed image using some classical reconstruction algorithms, such as filtered backprojection (FBP). The reconstructed image can be fine approximated by sparse coefficients under a proper wavelet tight frame, and the quality of reconstructed image can be improved by an available prior image. To deal with limited-angle CT reconstruction problem, we propose a minimization model that is based on wavelet tight frame and a prior image, and perform this minimization problem efficiently by iteratively minimizing separately. Moreover, we show that each bounded sequence, which is generated by our method, converges to a critical or a stationary point. The experimental results indicate that our algorithm can efficiently suppress artifacts and noise and preserve the edges of reconstructed image, what's more, the introduced prior image will not miss the important information that is not included in the prior image.

A limited-angle CT reconstruction method based on anisotropic TV minimization

This paper presents a compressed sensing (CS)-inspired reconstruction method for limited-angle computed tomography (CT). Currently, CS-inspired CT reconstructions are often performed by minimizing the total variation (TV) of a CT image subject to data consistency. A key to obtaining high image quality is to optimize the balance between TV-based smoothing and data fidelity. In the case of the limited-angle CT problem, the strength of data consistency is angularly varying. For example, given a parallel beam of x-rays, information extracted in the Fourier domain is mostly orthogonal to the direction of x-rays, while little is probed otherwise. However, the TV minimization process is isotropic, suggesting that it is unfit for limited-angle CT. Here we introduce an anisotropic TV minimization method to address this challenge. The advantage of our approach is demonstrated in numerical simulation with both phantom and real CT images, relative to the TV-based reconstruction.