Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction

By Xiaoqun Zhang, Martin Burger, Xavier Bresson, Stanley J. Osher. SIAM Journal of Imaging Sciences, 2010

738 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6fd53bc2c657fd7eb847e0388e8e92966123fcd1

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Citations in the corpus

Proximal Algorithms (2013, methodology): “In the image processing literature, it is known as the split inexact Uzawa method [80, 205, 204, 104].”
Non-local Regularization of Inverse Problems (2008, methodology): “Several efficient first order schemes have been devised to perform such a minimization, among which forwardbackward splitting [13, 4], Nesterov’s algorithm [41, 1] and Bregman iterations [58].”
On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers (2015, methodology): “As in [10], in order to treat the original ADMM in [7] and the split inexact Uzawa method in [13] uniformly, we study the following ADMM scheme for (1.”
Accelerating magnetic resonance imaging via deep learning (2016, methodology): “partial Fourier) have already been applied in commercial scanners as a routine protocol for shortening the total scan time [2, 3, 4, 5, 6].”
Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization (2012, methodology): “In particular, we establish the global convergence for the linearized ALM (3.7), which is stronger than those in [58].”
Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization (2010, methodology): “This NL self-similarity prior was later employed in image deblurring [8], [20] and super-resolution [41].”
Seismic data restoration via data-driven tight frame (2014, methodology): “We shall forgo the detailed derivation of the algorithm; interested readers can consult Zhang et al. (2010, 2011) and the references therein.”
Compressive Sensing via Nonlocal Low-Rank Regularization (2014, background): “F. Huang is with Philips Healthcare, Suzhou 234000, China (e-mail: f.huang@philips.com).”
Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models (2010, background): “Recently, Bregman iteration and split Bregman iteration attract much attention in signal recovery and image processing community [7, 8, 22, 30, 43, 44, 47].”
Sparse Representation Based Image Interpolation With Nonlocal Autoregressive Modeling (2013, methodology): “Such kind of nonlocal similarity is very helpful to improve the image restoration output, and it has been successfully used in image denoising [31-34], deblurring [35-36] and super-resolution [37-38, 49].”
Nonlocally Centralized Sparse Representation for Image Restoration (2013, background): “(2), such as iterative thresholding algorithms [9]–[11] and Bregman split algorithms [24], [25].”
An introduction to continuous optimization for imaging (2016, background): “Of course, the reader expert in these approaches Optimization for imaging 235 will see right away that it leads to exactly the same computations as those we would perform for an ADMM implementation (Esser 2009, Zhang et al. 2011, Zhang et al. 2010, Getreuer 2012).”
Image restoration: Total variation, wavelet frames, and beyond (2012, methodology): “The split Bregman algorithm was first proposed in [19] and was shown to be powerful in [19, 62] when it is applied to various PDE based image restoration approaches, e.”
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration (2010, methodology): “The linearized Bregman in [9, 11, 21, 42] and the Bregmanized Operator Splitting (BOS) in [51] are actually obtained by applying only one inner step for the subproblem (1.”