Alternating algorithms for total variation image reconstruction
from random projections

Xiao, Yunhai; Yang, Junfeng; Yuan, Xiaoming

doi:10.3934/ipi.2012.6.547

Cited by 51 publications

(29 citation statements)

References 33 publications

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“…Rather, an approximate solution can be used. We introduce a proximal point technique [ 41 , 42 ] to avoid the prohibitive cost and solve the subproblem efficiently.…”

Section: Methodsmentioning

confidence: 99%

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

et al. 2016

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Total generalized variation (TGV)-based computed tomography (CT) image reconstruction, which utilizes high-order image derivatives, is superior to total variation-based methods in terms of the preservation of edge information and the suppression of unfavorable staircase effects. However, conventional TGV regularization employs l1-based form, which is not the most direct method for maximizing sparsity prior. In this study, we propose a total generalized p-variation (TGpV) regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems. To solve the nonconvex optimization problem of the TGpV minimization model, we then present an efficient iterative algorithm based on the alternating minimization of augmented Lagrangian function. All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying alternating minimization method and generalized p-shrinkage mapping. In addition, approximate solutions that can be easily performed and quickly calculated through fast Fourier transform are derived using the proximal point method to reduce the cost of inner subproblems. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to validate the efficiency and feasibility of the proposed method. Overall, the proposed method exhibits reasonable performance and outperforms the original TGV-based method when applied to few-view problems.

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“…Rather, an approximate solution can be used. We introduce a proximal point technique [ 41 , 42 ] to avoid the prohibitive cost and solve the subproblem efficiently.…”

Section: Methodsmentioning

confidence: 99%

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

et al. 2016

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show abstract

“…Moreover, decomposing the variables by using ADM has a low computation cost. The ADM approach decouples the augmented Lagrange function into two subproblems, namely, the w -subproblem and the f -subproblem [ 29 ].…”

Section: Methodsmentioning

confidence: 99%

NUFFT-Based Iterative Image Reconstruction via Alternating Direction Total Variation Minimization for Sparse-View CT

Yan

Zhao

Zhang

et al. 2015

Computational and Mathematical Methods in Medicine

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Sparse-view imaging is a promising scanning method which can reduce the radiation dose in X-ray computed tomography (CT). Reconstruction algorithm for sparse-view imaging system is of significant importance. The adoption of the spatial iterative algorithm for CT image reconstruction has a low operation efficiency and high computation requirement. A novel Fourier-based iterative reconstruction technique that utilizes nonuniform fast Fourier transform is presented in this study along with the advanced total variation (TV) regularization for sparse-view CT. Combined with the alternating direction method, the proposed approach shows excellent efficiency and rapid convergence property. Numerical simulations and real data experiments are performed on a parallel beam CT. Experimental results validate that the proposed method has higher computational efficiency and better reconstruction quality than the conventional algorithms, such as simultaneous algebraic reconstruction technique using TV method and the alternating direction total variation minimization approach, with the same time duration. The proposed method appears to have extensive applications in X-ray CT imaging.

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“…The ADMM from Ref. [38] was used to solve the unconstrained model (6.3), and the results are presented in Table 4. It is notable that SNRs for the images recovered by these models are almost the same.…”

Section: Inpainting From Impulsive Noisementioning

confidence: 99%

Minimisation and Parameter Estimation in Image Restoration Variational Models with ℓ<sub>1</sub>-Constraints

Tao¹

2018

EAJAM

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Minimisation of the total variation regularisation for linear operators under ℓ 1 -constraints applied to image restoration is considered, and relationships between the Lagrange multiplier for a constrained model and the regularisation parameter in an unconstrained model are established. A constrained ℓ 1 -problem reformulated as a separable convex problem is solved by the alternating direction method of multipliers that includes two sequences, converging to a restored image and the "optimal" regularisation parameter. This allows blurry images to be recovered, with a simultaneous estimation of the regularisation parameter. The noise level parameter is estimated, and numerical experiments illustrate the efficiency of the new approach.

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Alternating algorithms for total variation image reconstruction from random projections

Cited by 51 publications

References 33 publications

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

NUFFT-Based Iterative Image Reconstruction via Alternating Direction Total Variation Minimization for Sparse-View CT

Minimisation and Parameter Estimation in Image Restoration Variational Models with ℓ<sub>1</sub>-Constraints

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