Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction

Zhang, Xiaoqun; Burger, Martin; Bresson, Xavier; Osher, Stanley

doi:10.1137/090746379

Cited by 628 publications

(525 citation statements)

References 31 publications

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“…To treat a more general A, the Bregman operator splitting (BOS) method [44] replaces Au − f 2 2 by a proximal-like term…”

Section: Related Workmentioning

confidence: 99%

“…If this problem is solved using a split Bregman method [21], then this is equivalent to BOS [44], which can accommodate an arbitrary matrix A. In [40], Ye et al proposed a variation of BOS utilizing the Barzilai-Borwein stepsize to significantly improve the efficiency; however, the convergence of the algorithm is not known, although it seems to converge in numerical experiments.…”

Section: Related Workmentioning

confidence: 99%

“…We compare performance of AM (18), ADMM (25), and APD (28) to that of the Bregman operator splitting (BOS) in [44] and a slightly modified version (SBB) of the algorithm proposed in [40].…”

Section: Numerical Experimentsmentioning

confidence: 99%

See 2 more Smart Citations

Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging

Chen¹,

Hager²,

Huang³

et al. 2012

SIAM J. Imaging Sci.

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This paper presents two fast algorithms for total variation-based image reconstruction in partially parallel magnetic resonance imaging (PPI) where the inversion matrix is large and ill-conditioned. These algorithms utilize variable splitting techniques to decouple the original problem into more easily solved subproblems. The first method reduces the image reconstruction problem to an unconstrained minimization problem, which is solved by an alternating proximal minimization algorithm. One phase of the algorithm solves a total variation (TV) denoising problem, and second phase solves an ill-conditioned linear system. Linear and sublinear convergence results are given, and an implementation based on a primal-dual hybrid gradient (PDHG) scheme for the TV problem and a Barzilai-Borwein scheme for the linear inversion is proposed. The second algorithm exploits the special structure of the PPI reconstruction problem by decomposing it into one subproblem involving Fourier transforms and another subproblem that can be treated by the PDHG scheme. Numerical results and comparisons with recently developed methods indicate the efficiency of the proposed algorithms.

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“…To treat a more general A, the Bregman operator splitting (BOS) method [44] replaces Au − f 2 2 by a proximal-like term…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging

Chen¹,

Hager²,

Huang³

et al. 2012

SIAM J. Imaging Sci.

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show abstract

“…The nonlocal models they proposed are very useful in image processing. Their models have been used and extended in various problems; see, for example, [32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

An Improved Image Denoising Model Based on Nonlocal Means Filter

Jin

Jiang

Shao

et al. 2018

Mathematical Problems in Engineering

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The nonlocal means filter plays an important role in image denoising. We propose in this paper an image denoising model which is a suitable improvement of the nonlocal means filter. We compare this model with the nonlocal means filter, both theoretically and experimentally. Experiment results show that this new model provides good results for image denoising. Particularly, it is better than the nonlocal means filter when we consider the denoising for natural images with high textures.

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“…In addition to sparsity, non-local self-similarity is another significant property of natural images [27,28]. A number of non-local regularization terms, exploiting the non-local self-similarity, are employed in solving inverse problems [29,30]. Fusing image sparsity with non-local self-similarity produces better results in recently reported image restoration techniques [31,32].…”

Section: Introductionmentioning

confidence: 99%

Non-Local Sparse Image Inpainting for Document Bleed-Through Removal

et al. 2018

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Bleed-through is a frequent, pervasive degradation in ancient manuscripts, which is caused by ink seeped from the opposite side of the sheet. Bleed-through, appearing as an extra interfering text, hinders document readability and makes it difficult to decipher the information contents. Digital image restoration techniques have been successfully employed to remove or significantly reduce this distortion. This paper proposes a two-step restoration method for documents affected by bleed-through, exploiting information from the recto and verso images. First, the bleed-through pixels are identified, based on a non-stationary, linear model of the two texts overlapped in the recto-verso pair. In the second step, a dictionary learning-based sparse image inpainting technique, with non-local patch grouping, is used to reconstruct the bleed-through-contaminated image information. An overcomplete sparse dictionary is learned from the bleed-through-free image patches, which is then used to estimate a befitting fill-in for the identified bleed-through pixels. The non-local patch similarity is employed in the sparse reconstruction of each patch, to enforce the local similarity. Thanks to the intrinsic image sparsity and non-local patch similarity, the natural texture of the background is well reproduced in the bleed-through areas, and even a possible overestimation of the bleed through pixels is effectively corrected, so that the original appearance of the document is preserved. We evaluate the performance of the proposed method on the images of a popular database of ancient documents, and the results validate the performance of the proposed method compared to the state of the art.

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Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction

Cited by 628 publications

References 31 publications

Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging

Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging

An Improved Image Denoising Model Based on Nonlocal Means Filter

Non-Local Sparse Image Inpainting for Document Bleed-Through Removal

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