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Fast Nonoverlapping Block Jacobi Method for the Dual Rudin--Osher--Fatemi Model

Chang-Ock Lee, Jongho Park
2019 SIAM Journal of Imaging Sciences  
We consider nonoverlapping domain decomposition methods for the RudinOsherFatemi (ROF) model, which is one of the standard models in mathematical image processing.  ...  We show that the nonoverlapping relaxed block Jacobi method for a dual formulation of the ROF model has the O(1/n) convergence rate of the energy functional, where n is the number of iterations.  ...  In this paper, we consider block Jacobi methods for the Rudin-Osher-Fatemi (ROF) model [22] , which is one of the standard models in variational image processing given by (1.1) min u∈BV (Ω) α 2 Ω (u −  ... 
doi:10.1137/18m122604x fatcat:2plrlxnxrnbtvmcm4pawzzpfci

Pseudo-linear Convergence of an Additive Schwarz Method for Dual Total Variation Minimization [article]

Jongho Park
2020 arXiv   pre-print
In this paper, we propose an overlapping additive Schwarz method for total variation minimization based on a dual formulation.  ...  In addition, we introduce an interesting convergence property called pseudo-linear convergence of the proposed method; the energy of the proposed method decreases as fast as linearly convergent algorithms  ...  The author would like to thank Professor Chang-Ock Lee for insightful discussions and comments.  ... 
arXiv:1911.06639v3 fatcat:zcpxbyw4r5bkpdtb2vhju6cxqq

Pseudo-linear convergence of an additive Schwarz method for dual total variation minimization

Jongho Park
2021 Electronic Transactions on Numerical Analysis  
In this paper, we propose an overlapping additive Schwarz method for total variation minimization based on a dual formulation.  ...  In addition, we introduce an interesting convergence property of the proposed method called pseudo-linear convergence; the energy decreases as fast as for linearly convergent algorithms until it reaches  ...  The author would like to thank Professor Chang-Ock Lee for insightful discussions and comments.  ... 
doi:10.1553/etna_vol54s176 fatcat:hqp42evfkjeuniee66ofuouq4a

Domain Decomposition Methods for Nonlocal Total Variation Image Restoration

Huibin Chang, Xiaoqun Zhang, Xue-Cheng Tai, Danping Yang
2013 Journal of Scientific Computing  
Introduction Total variation (TV) based image restoration models introduced by Rudin, Osher, and Fatemi (ROF) in [30] have been largely applied in the image restoration and medical image reconstruction  ...  In [10], a fast translation algorithm was proposed for computing the nonlocal weight.  ...  We also thank the reviewers for the comments, which have greatly improved the paper.  ... 
doi:10.1007/s10915-013-9786-9 fatcat:eywwr6xiizbr7mjjaixghuo23e

An Overlapping Domain Decomposition Framework without Dual Formulation for Variational Imaging Problems [article]

Jongho Park
2020 arXiv   pre-print
Thus, the proposed method can be applied not only to total variation minimization but also to those with complex dual problems such as higher order models.  ...  As a solver for the constructed formulation, we propose a decoupled augmented Lagrangian method for untying the coupling of adjacent subdomains.  ...  The famous Rudin-Osher-Fatemi (ROF) model which uses total variation as a regularizer for image denoising was proposed in [28] , and it successfully removes Gaussian noise while it preserves edges of  ... 
arXiv:2002.10070v2 fatcat:h4nxqs7tsfhbjf7expeugawufy