Conventional Total Variation Research Articles

CT reconstruction from few-views with anisotropic edge-guided total variance

To overcome the oversmoothing drawback in the edge areas when reconstructing few-view CT with total variation (TV) minimization, in this paper, we propose an anisotropic edge-guided TV minimization framework for few-view CT reconstruction. In the framework, anisotropic TV is summed with pre-weighted image gradient and then used as the object function for minimizing. It includes edge-guided TV minimization (EGTV) and edge-guided adaptive-weighted TV minimization (EGAwTV) algorithms. For EGTV algorithm, the weights of the TV discretization term are updated by anisotropic edge information detected from the image, whereas the weights for EGAwTV are determined based on edge information and local image-intensity gradients. To solve the minimization problem of the proposed algorithm, a similar TV-based minimization implementation is developed to address the raw data fidelity and other constraints. The evaluation results using both computer simulations with the Shepp-Logan phantom and experimental data from a physical phantom demonstrate that the proposed algorithms exhibit noticeable gains in the merits of spatial resolution compared with the conventional TV and other modified TV algorithms.

Weighted Total Variation Iterative Reconstruction for Hyperspectral Pushbroom Compressive Imaging

Compressed sensing is suitable for remote hyperspectral imaging, as it can simplify the architecture of the onboard sensors. To reconstruct hyperspectral image from pushbroom compressive imaging, we present iterative prediction reconstruction architecture based on total variation in this paper. As the conventional total variation prior is not effective at capturing the correlation within spatial-spectral arrays, an improved weighted total variation is proposed. Experimental results run on raw data from AVIRIS confirm the validity of the proposed method.

Assessment of Limiting Processes of Numerical Schemes on Hypersonic Aeroheating Predictions

This paper deals with a systematic assessment study on the performance of conventional MUSCL slope limiters and recently developed multidimensional limiting processes in the context of aeroheating predictions of hypersonic flows. Three test cases are considered: 1) the flow () around a cylindrical leading-edge configuration, 2) the flow () around a biconic configuration, and 3) the flow () around a double-ellipsoid configuration. Through the careful comparisons between one another and with the available experimental data, numerical results are presented to demonstrate the behaviors of different limiting processes in hypersonic aeroheating predictions. It is found that the medium dissipative van Leer slope limiter could be the best compromise between accuracy and robustness of all the MUSCL slope limiters considered, whereas the multidimensional limiting processes can numerically behave better than all the MUSCL slope limiters, whether in accuracy or in robustness. The results indicate that, within the total variation diminishing framework, the multidimensional limiting processes can be identified with the double minmod slope limiter in dissipation, and can come up to the minmod slope limiter and/or the van Albada slope limiter in robustness. In addition, the multidimensional limiting and enhanced multidimensional limiting processes could compare with the conventional total variation diminishing MUSCL approach in overall computational cost. Therefore, the multidimensional limiting processes should be preferred to predict hypersonic aeroheating issues accurately with better performance. On the other hand, it is noteworthy that the postprocessing method for calculating surface heat flux proposed in this study is proven to largely reduce the grid dependence of aeroheating predictions.

Common-mask guided image reconstruction (c-MGIR) for enhanced 4D cone-beam computed tomography

Compared to 3D cone beam computed tomography (3D CBCT), the image quality of commercially available four-dimensional (4D) CBCT is severely impaired due to the insufficient amount of projection data available for each phase. Since the traditional Feldkamp-Davis-Kress (FDK)-based algorithm is infeasible for reconstructing high quality 4D CBCT images with limited projections, investigators had developed several compress-sensing (CS) based algorithms to improve image quality. The aim of this study is to develop a novel algorithm which can provide better image quality than the FDK and other CS based algorithms with limited projections. We named this algorithm ‘the common mask guided image reconstruction’ (c-MGIR).In c-MGIR, the unknown CBCT volume is mathematically modeled as a combination of phase-specific motion vectors and phase-independent static vectors. The common-mask matrix, which is the key concept behind the c-MGIR algorithm, separates the common static part across all phase images from the possible moving part in each phase image. The moving part and the static part of the volumes were then alternatively updated by solving two sub-minimization problems iteratively. As the novel mathematical transformation allows the static volume and moving volumes to be updated (during each iteration) with global projections and ‘well’ solved static volume respectively, the algorithm was able to reduce the noise and under-sampling artifact (an issue faced by other algorithms) to the maximum extent. To evaluate the performance of our proposed c-MGIR, we utilized imaging data from both numerical phantoms and a lung cancer patient. The qualities of the images reconstructed with c-MGIR were compared with (1) standard FDK algorithm, (2) conventional total variation (CTV) based algorithm, (3) prior image constrained compressed sensing (PICCS) algorithm, and (4) motion-map constrained image reconstruction (MCIR) algorithm, respectively. To improve the efficiency of the algorithm, the code was implemented with a graphic processing unit for parallel processing purposes.Root mean square error (RMSE) between the ground truth and reconstructed volumes of the numerical phantom were in the descending order of FDK, CTV, PICCS, MCIR, and c-MGIR for all phases. Specifically, the means and the standard deviations of the RMSE of FDK, CTV, PICCS, MCIR and c-MGIR for all phases were 42.64 ± 6.5%, 3.63 ± 0.83%, 1.31% ± 0.09%, 0.86% ± 0.11% and 0.52 % ± 0.02%, respectively. The image quality of the patient case also indicated the superiority of c-MGIR compared to other algorithms.The results indicated that clinically viable 4D CBCT images can be reconstructed while requiring no more projection data than a typical clinical 3D CBCT scan. This makes c-MGIR a potential online reconstruction algorithm for 4D CBCT, which can provide much better image quality than other available algorithms, while requiring less dose and potentially less scanning time.

Real time dynamic MRI by exploiting spatial and temporal sparsity

Online imaging requires that the reconstruction of current frame only depends on the previous frames, and real time imaging is the desired case. In this work, we propose a novel scheme for real time dynamic magnetic resonance imaging (dMRI) reconstruction. Different from previous methods, the reconstructions of the second frame to the last frame are independent in our scheme, which only require the first frame as the reference image. Therefore, this scheme can be naturally implemented in parallel. After the first frame is reconstructed, all the later frames can be processed as soon as the k-space data are acquired. As an extension of the conventional spatial total variation, a new online model called dynamic total variation is used to exploit the sparsity on both spatial and temporal domains in dMRI. In real time dMRI, each frame is required to be reconstructed very fast. We then design a novel reweighted least squares algorithm to solve the challenging problem. Motivated by the special structure of partial Fourier transform in sparse MRI, this algorithm is accelerated by the preconditioned conjugate gradient descent method. The proposed method is compared with 4 state-of-the-art online and offline methods on two in-vivo cardiac dMRI datasets. The experimental results show that our method significantly outperforms previous online methods, and is comparable to the offline methods in terms of reconstruction accuracy.

Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging.

With recent advancement in hardware of optoacoustic imaging systems, highly detailed cross-sectional images may be acquired at a single laser shot, thus eliminating motion artifacts. Nonetheless, other sources of artifacts remain due to signal distortion or out-of-plane signals. The purpose of image reconstruction algorithms is to obtain the most accurate images from noisy, distorted projection data. In this paper, the authors use the model-based approach for acoustic inversion, combined with a sparsity-based inversion procedure. Specifically, a cost function is used that includes the L1 norm of the image in sparse representation and a total variation (TV) term. The optimization problem is solved by a numerically efficient implementation of a nonlinear gradient descent algorithm. TV-L1 model-based inversion is tested in the cross section geometry for numerically generated data as well as for in vivo experimental data from an adult mouse. In all cases, model-based TV-L1 inversion showed a better performance over the conventional Tikhonov regularization, TV inversion, and L1 inversion. In the numerical examples, the images reconstructed with TV-L1 inversion were quantitatively more similar to the originating images. In the experimental examples, TV-L1 inversion yielded sharper images and weaker streak artifact. The results herein show that TV-L1 inversion is capable of improving the quality of highly detailed, multiscale optoacoustic images obtained in vivo using cross-sectional imaging systems. As a result of its high fidelity, model-based TV-L1 inversion may be considered as the new standard for image reconstruction in cross-sectional imaging.

Efficient TpV minimization for circular, cone-beam computed tomography reconstruction via non-convex optimization

An efficient iterative algorithm, based on recent work in non-convex optimization and generalized p-shrinkage mappings, is proposed for volume image reconstruction from circular cone-beam scans. Conventional total variation regularization makes use of L1 norm of gradient magnitude images (GMI). However, this paper utilizes a generalized penalty function, induced by p-shrinkage, of GMI which is proven to be a better measurement of its sparsity. The reconstruction model is formed using generalized total p-variation (TpV) minimization, which differs with the state of the art methods, with the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. Theoretically, the proximal mapping for penalty functions induced by p-shrinkage has an exact and closed-form expression; thus, the constrained optimization can be stably and efficiently solved by the alternating direction minimization (ADM) scheme. Each sub-problem decoupled by variable splitting is minimized by explicit and easy-to-implement formulas developed by ADM. The proposed algorithm is efficiently implemented using a graphics processing unit and is referred to as “TpV-ADM.” This method is robust and accurate even for very few view reconstruction datasets. Verifications and comparisons performed using various datasets (including ideal, noisy, and real projections) illustrate that the proposed method is effective and promising.

Approach to Restoration of Blurring Image Based on Total Variation with Content Aware and Texture Enhancement

In this paper, a new approach to restoration of blurring image with content aware and texture enhancement is presented, in which the content aware term is embedded into the objective function of optimal decision. In this way, the content aware term can play a role to reinforce the restoration effect in the optimal decision. Thus the conventional total variation methodology is employed as a basic tool to solve such optimal decision problem with content aware in its objective function. Meanwhile, the image texture is enhanced by layer decomposition and edge preserving filter. A series of experiment results manifest the proposed algorithm can achieve better restoration effect than the conventional total variation method.

Compressed sensing with gradient total variation for low-dose CBCT reconstruction

This paper describes the improvement of convergence speed with gradient total variation (GTV) in compressed sensing (CS) for low-dose cone–beam computed tomography (CBCT) reconstruction. We derive a fast algorithm for the constrained total variation (TV)-based a minimum number of noisy projections. To achieve this task we combine the GTV with a TV-norm regularization term to promote an accelerated sparsity in the X-ray attenuation characteristics of the human body. The GTV is derived from a TV and enforces more efficient computationally and faster in convergence until a desired solution is achieved. The numerical algorithm is simple and derives relatively fast convergence. We apply a gradient projection algorithm that seeks a solution iteratively in the direction of the projected gradient while enforcing a non-negatively of the found solution. In comparison with the Feldkamp, Davis, and Kress (FDK) and conventional TV algorithms, the proposed GTV algorithm showed convergence in ≤18 iterations, whereas the original TV algorithm needs at least 34 iterations in reducing 50% of the projections compared with the FDK algorithm in order to reconstruct the chest phantom images. Future investigation includes improving imaging quality, particularly regarding X-ray cone–beam scatter, and motion artifacts of CBCT reconstruction.

The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising

Let $u \in \mbox{BV}(\Omega)$ solve the total variation denoising problem with $L^2$-squared fidelity and data $f$. Caselles et al. [Multiscale Model. Simul. 6 (2008), 879--894] have shown the containment $\mathcal{H}^{m-1}(J_u \setminus J_f)=0$ of the jump set $J_u$ of $u$ in that of $f$. Their proof unfortunately depends heavily on the co-area formula, as do many results in this area, and as such is not directly extensible to higher-order, curvature-based, and other advanced geometric regularisers, such as total generalised variation (TGV) and Euler's elastica. These have received increased attention in recent times due to their better practical regularisation properties compared to conventional total variation or wavelets. We prove analogous jump set containment properties for a general class of regularisers. We do this with novel Lipschitz transformation techniques, and do not require the co-area formula. In the present Part 1 we demonstrate the general technique on first-order regularisers, while in Part 2 we will extend it to higher-order regularisers. In particular, we concentrate in this part on TV and, as a novelty, Huber-regularised TV. We also demonstrate that the technique would apply to non-convex TV models as well as the Perona-Malik anisotropic diffusion, if these approaches were well-posed to begin with.

Compressed sensing MR image reconstruction exploiting TGV and wavelet sparsity.

Compressed sensing (CS) based methods make it possible to reconstruct magnetic resonance (MR) images from undersampled measurements, which is known as CS-MRI. The reference-driven CS-MRI reconstruction schemes can further decrease the sampling ratio by exploiting the sparsity of the difference image between the target and the reference MR images in pixel domain. Unfortunately existing methods do not work well given that contrast changes are incorrectly estimated or motion compensation is inaccurate. In this paper, we propose to reconstruct MR images by utilizing the sparsity of the difference image between the target and the motion-compensated reference images in wavelet transform and gradient domains. The idea is attractive because it requires neither the estimation of the contrast changes nor multiple times motion compensations. In addition, we apply total generalized variation (TGV) regularization to eliminate the staircasing artifacts caused by conventional total variation (TV). Fast composite splitting algorithm (FCSA) is used to solve the proposed reconstruction problem in order to improve computational efficiency. Experimental results demonstrate that the proposed method can not only reduce the computational cost but also decrease sampling ratio or improve the reconstruction quality alternatively.

Iterative CT reconstruction via minimizing adaptively reweighted total variation

Iterative reconstruction via total variation (TV) minimization has demonstrated great successes in accurate CT imaging from under-sampled projections. When projections are further reduced, over-smoothing artifacts appear in the current reconstruction especially around the structure boundaries. We propose a practical algorithm to improve TV-minimization based CT reconstruction on very few projection data. Based on the theory of compressed sensing, the L-0 norm approach is more desirable to further reduce the projection views. To overcome the computational difficulty of the non-convex optimization of the L-0 norm, we implement an adaptive weighting scheme to approximate the solution via a series of TV minimizations for practical use in CT reconstruction. The weight on TV is initialized as uniform ones, and is automatically changed based on the gradient of the reconstructed image from the previous iteration. The iteration stops when a small difference between the weighted TV values is observed on two consecutive reconstructed images. We evaluate the proposed algorithm on both a digital phantom and a physical phantom. Using 20 equiangular projections, our method reduces reconstruction errors in the conventional TV minimization by a factor of more than 5, with improved spatial resolution. By adaptively reweighting TV in iterative CT reconstruction, we successfully further reduce the projection number for the same or better image quality.

Image restoration with dual-prior constraint models based on Split Bregman

In order to utilizing the local and non-local information in the image, we proposed a novel sparse scheme for image restoration in this paper. The new scheme includes two important contributions. The first one is that we extended the image prior model in conventional total variation to the dual-prior models for combining the local smoothness and non-local sparsity under regularization framework. The second one is we developed a modified iterative Split Bregman majorization method to solve the objective function with dual-prior models. The experimental results show that the proposed scheme achieved the state-of-the-art performance compared to the current restoration algorithms.

Improving IMRT delivery efficiency with reweighted L1‐minimization for inverse planning

This study presents an improved technique to further simplify the fluence-map in intensity modulated radiation therapy (IMRT) inverse planning, thereby reducing plan complexity and improving delivery efficiency, while maintaining the plan quality. First-order total-variation (TV) minimization (min.) based on L1-norm has been proposed to reduce the complexity of fluence-map in IMRT by generating sparse fluence-map variations. However, with stronger dose sparing to the critical structures, the inevitable increase in the fluence-map complexity can lead to inefficient dose delivery. Theoretically, L0-min. is the ideal solution for the sparse signal recovery problem, yet practically intractable due to its nonconvexity of the objective function. As an alternative, the authors use the iteratively reweighted L1-min. technique to incorporate the benefits of the L0-norm into the tractability of L1-min. The weight multiplied to each element is inversely related to the magnitude of the corresponding element, which is iteratively updated by the reweighting process. The proposed penalizing process combined with TV min. further improves sparsity in the fluence-map variations, hence ultimately enhancing the delivery efficiency. To validate the proposed method, this work compares three treatment plans obtained from quadratic min. (generally used in clinic IMRT), conventional TV min., and our proposed reweighted TV min. techniques, implemented by a large-scale L1-solver (template for first-order conic solver), for five patient clinical data. Criteria such as conformation number (CN), modulation index (MI), and estimated treatment time are employed to assess the relationship between the plan quality and delivery efficiency. The proposed method yields simpler fluence-maps than the quadratic and conventional TV based techniques. To attain a given CN and dose sparing to the critical organs for 5 clinical cases, the proposed method reduces the number of segments by 10-15 and 30-35, relative to TV min. and quadratic min. based plans, while MIs decreases by about 20%-30% and 40%-60% over the plans by two existing techniques, respectively. With such conditions, the total treatment time of the plans obtained from our proposed method can be reduced by 12-30 s and 30-80 s mainly due to greatly shorter multileaf collimator (MLC) traveling time in IMRT step-and-shoot delivery. The reweighted L1-minimization technique provides a promising solution to simplify the fluence-map variations in IMRT inverse planning. It improves the delivery efficiency by reducing the entire segments and treatment time, while maintaining the plan quality in terms of target conformity and critical structure sparing.

WE-G-WAB-04: Ultra-Fast Dynamic MRI for Lung Tumor Tracking Based On Compressed Sensing and Low-Rank Decomposition in the Spatial-Temporal Domain

Purpose: Dynamic MRI is an attractive tool for internal organ motion monitoring but its speed is yet to be improved for real time 3D imaging. The purpose of the study is to accelerate the imaging acquisition using a hybrid compressed-sensing and low rank decomposition method (k-t SLR) exploiting data sparsity in the spatial-temporal domain. Methods: Six retrospective lung cancer patients were included in the study. For each subject, 120 continuously dynamic 2D MR images were acquired using a fast steady state precession imaging sequence. To test the feasibility of accelerated MR acquisition, fully sampled k-space data were down-sampled by 5–20 folds before reconstruction. The under-sampled low rank spatial-temporal matrix was recovered by a k-t SLR method computing the matrix of minimum nuclear norm that fits the data. The k-t SLR results were compared against conventional total variation (TV) reconstruction of individual dynamic MR frames. Results: High imaging fidelity and low noise levels were achieved with the k-t SLR method even at the most aggressive down-sampling ratio while TV reconstruction showed substantial loss of details and subsequently greater tracking errors. The k-t SLR method resulted in an average normalized mean square error less than 0.05 as opposed to 0.23 by using the TV reconstruction on individual frames. In addition to the high correlation coefficients (>0.90) in the tumor trajectories automatically tracked from the original images and the k-t SLR reconstructed images, less than 6% points showed tracking errors greater than 1 mm with 20 fold down-sampling, as opposed to the lower correlation coefficient (0.87) and 15% tracking error from using TV alone with 10 fold data down-sampling. Conclusion: We have demonstrated the potential to significantly reduce the amount data samples required for lung MR image reconstruction in the radiotherapy context where long imaging acquisition of a repetitive anatomic process is performed. The study is supported in part by NIH 1R21CA144063 and R21CA161670

TH‐C‐103‐03: Iterative CT Reconstruction Via Minimizing Adaptively Reweighted Total Variation

Purpose: Iterative reconstruction via total variation (TV) minimization has demonstrated great successes in accurate CT imaging from under‐sampled projections. When projections are further reduced, over‐smoothing artifacts appear in the current reconstruction especially around the structure boundaries. We propose a practical algorithm to improve TV‐minimization based CT reconstruction on very few projection data. Methods: The L‐0 norm approach is more desirable from the perfective of further reducing the projection views. To overcome the computational difficulty of the non‐convex optimization of the L‐0 norm, we implement an adaptive weighting scheme to approximate the solution via a series of TV minimizations for practical use in CT reconstruction. The weight on TV is initialized as uniform ones, and is adaptively changed based on the gradient of the reconstructed image from the previous iteration. The iteration stops when a small difference between the weighted TV values is observed on two consecutive reconstructed images. Results: On the digital Shepp‐Logan phantom, the proposed method reduces reconstruction errors in the conventional TV minimization from 7.3% to 1.4% with 20 projections, and from 25% to 6.5% with 15 projections. With 20 projections on the Catphan600 phantom, our method reduces contrast errors in the ROIs from 45 HU to 6 HU. The rise width at the object edges in the image is also reduced by 40%, showing a substantial image resolution improvement. Conclusion: By adaptively reweighting TV in iterative CT reconstruction, we successfully further reduce the projection number for the same or better image quality. The technique is attractive in the applications of CT reconstruction on a small size of projection data.

A C2‐continuous high‐resolution upwind convection scheme

SUMMARYA bounded upwinding scheme for numerical solution of hyperbolic conservation laws and Navier–Stokes equations is presented. The scheme is based on convection boundedness criterion and total variation diminishing stability criteria and developed by employing continuously differentiable functions. The accuracy of the scheme is verified by assessing the error and observed convergence rate on 1‐D benchmark test cases. A comparative study between the new scheme and conventional total variation diminishing/convection boundedness criterion‐based upwind schemes to solve standard nonlinear hyperbolic conservation laws is also accomplished. The scheme is then examined in the simulation of Newtonian and non‐Newtonian fluid flows of increasing complexity; a satisfactory agreement has been observed in terms of the overall behavior. Finally, the scheme is used to study the hydrodynamics of a gas‐solid flow in a bubbling fluidized bed. Copyright © 2013 John Wiley & Sons, Ltd.

A few-view reweighted sparsity hunting (FRESH) method for CT image reconstruction

In recent years, the total variation (TV) minimization method has been widely used for compressed sensing (CS) based CT image reconstruction. In this paper, we propose a few-view reweighted sparsity hunting (FRESH) method for CT image reconstruction, and demonstrate the superior performance of this method. Specifically, the key of the purposed method is that a reweighted total variation (RwTV) measure is used to characterize image sparsity in the cost function, outperforming the conventional TV counterpart. To solve the RwTV minimization problem efficiently, the Split-Bregman method and other state-of-the-art L1 optimization methods are compared. Inspired by the fast iterative shrinkage/thresholding algorithm (FISTA), a predication step is incorporated for fast computation in the Split-Bregman framework. Extensive numerical experiments have shown that our FRESH approach performs significantly better than competing algorithms in terms of image quality and convergence speed for few-view CT. High-quality images were reconstructed by our FRESH method after 250 iterations using only 15 few-view projections of the Forbild head phantom while other competitors needed more than 800 iterations. Remarkable improvements in details in the experimental evaluation using actual sheep thorax data further indicate the potential real-world application of the FRESH method.

Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction

Previous studies have shown that by minimizing the total variation (TV) of the to-be-estimated image with some data and other constraints, piecewise-smooth x-ray computed tomography (CT) can be reconstructed from sparse-view projection data without introducing notable artifacts. However, due to the piecewise constant assumption for the image, a conventional TV minimization algorithm often suffers from over-smoothness on the edges of the resulting image. To mitigate this drawback, we present an adaptive-weighted TV (AwTV) minimization algorithm in this paper. The presented AwTV model is derived by considering the anisotropic edge property among neighboring image voxels, where the associated weights are expressed as an exponential function and can be adaptively adjusted by the local image-intensity gradient for the purpose of preserving the edge details. Inspired by the previously reported TV-POCS (projection onto convex sets) implementation, a similar AwTV-POCS implementation was developed to minimize the AwTV subject to data and other constraints for the purpose of sparse-view low-dose CT image reconstruction. To evaluate the presented AwTV-POCS algorithm, both qualitative and quantitative studies were performed by computer simulations and phantom experiments. The results show that the presented AwTV-POCS algorithm can yield images with several notable gains, in terms of noise-resolution tradeoff plots and full-width at half-maximum values, as compared to the corresponding conventional TV-POCS algorithm.

Accelerated barrier optimization compressed sensing (ABOCS) reconstruction for cone-beam CT: phantom studies.

Recent advances in compressed sensing (CS) enable accurate CT image reconstruction from highly undersampled and noisy projection measurements, due to the sparsifiable feature of most CT images using total variation (TV). These novel reconstruction methods have demonstrated advantages in clinical applications where radiation dose reduction is critical, such as onboard cone-beam CT (CBCT) imaging in radiation therapy. The image reconstruction using CS is formulated as either a constrained problem to minimize the TV objective within a small and fixed data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning, which significantly limit the clinical use of CS-based iterative reconstruction. In this paper, we propose an optimization algorithm for CS reconstruction which overcomes the above two drawbacks. The data fidelity tolerance of CS reconstruction can be well estimated based on the measured data, as most of the projection errors are from Poisson noise after effective data correction for scatter and beam-hardening effects. We therefore adopt the TV optimization framework with a data fidelity constraint. To accelerate the convergence, we first convert such a constrained optimization using a logarithmic barrier method into a form similar to that of the conventional TV regularization based reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection with an adaptive Barzilai-Borwein step-size selection scheme. The proposed algorithm is referred to as accelerated barrier optimization for CS (ABOCS), and evaluated using both digital and physical phantom studies. ABOCS directly estimates the data fidelity tolerance from the raw projection data. Therefore, as demonstrated in both digital Shepp-Logan and physical head phantom studies, consistent reconstruction performances are achieved using the same algorithm parameters on scans with different noise levels and∕or on different objects. On the contrary, the penalty weight in a TV regularization based method needs to be fine-tuned in a large range (up to seven times) to maintain the reconstructed image quality. The improvement of ABOCS on computational efficiency is demonstrated in the comparisons with adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS), an existing CS reconstruction algorithm also using constrained optimization. ASD-POCS alternatively minimizes the TV objective using adaptive steepest descent (ASD) and the data fidelity error using projection onto convex sets (POCS). For similar image qualities of the Shepp-Logan phantom, ABOCS requires less computation time than ASD-POCS in MATLAB by more than one order of magnitude. We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter settings for different datasets. These advantages have been demonstrated on phantom studies.