Split Bregman Methods and Frame Based Image Restoration

By Jian-Feng Cai, Stanley J. Osher, Zuowei Shen. Multiscale Modeling & simulation, 2009

734 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cd764a73e5dbd0b5985750854abeb01cd43f7198

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Citations in the corpus

An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems (2009, methodology): “Finally, we should mention the Bregman iterative algorithm (BIA), recently proposed to solve (1) with , that is, to minimize under the equality constraint (see [11], [57] and references therein).”
Compressed Sensing with Coherent and Redundant Dictionaries (2010, neutral): “Its geometry has been studied [21] as well as its applications to image restoration [8].”
Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems (2017, methodology): “Then, a frame-based denoising algorithm [18, 13, 12] recovers the unknown signal by substituting g for f in the right side of (81) and applies a shrinkage operator Sτ to the framelet coefficients to eliminate the small magnitude noise signals:”
Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models (2010, methodology): “Recently, Bregman iteration and split Bregman iteration attract much attention in signal recovery and image processing community [7, 8, 22, 30, 43, 44, 47].”
Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization (2012, methodology): “In general, the ADM derived in [10] (and those in Section 2 of the present paper) can be viewed as the split Bregman method discussed in [7, 19] for the general problems with (cid:5) 1 -like regularization where the augmented Lagrangian functions are minimized by only one round of alternating…”
Image restoration: Total variation, wavelet frames, and beyond (2012, methodology): “The theory of [21] can be applied here, leading to the following convergence result: let u be the sequence generated by Algorithm 5.”
On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers (2016, background): “We refer to [2,4,8,12,20,22,27,31,34,36] for a few examples of applications.”
The Cosparse Analysis Model and Algorithms (2011, neutral): “An algorithm that targets the solution of (17) and its convergence analysis can be found in [6].”
Sparse dynamics for partial differential equations (2012, neutral): “We ﬁrst address sparsity induction through soft thresholding.”
Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, methodology): “This algorithm has been studied extensively, see e.g. [46,62,67–72].”
BM3D Frames and Variational Image Deblurring (2011, methodology): “These algorithms sharing many common ideas are known under different names such as split Bregman iterations[8], iterative shrinkage algorithms [9] , alternating direction method of multipliers [10], majorizationminimization algorithms [11].”