Proximity algorithms for the L1/TV image denoising model
type: Item
instance of: scholarly article
title: Proximity algorithms for the L1/TV image denoising model
zbMATH Open document ID: 1275.65014
author: Charles A. Micchelli
author: Yuesheng Xu
author: Xueying Zeng
author: Lixin Shen
published in: Advances in Computational Mathematics
publication date: 2013-04-15T00:00:00Z
review text: The authors introduce a proximity operator framework for the direct treatment of the L1/TV image denoising model. The L1/TV image denoising model minimizes the sum of a data fidelity term measured in the \(\ell^1\)-norm and the total-variation regularization term. In this paper, a general model constructed as a minimization of the sum of the \(\ell^1\) fidelity term, an indicator term and a regularization term in the form of the composition of a convex function and a matrix is investigated. The difficulties in the numerical treatment of this model caused by its nondifferentiability are overcome by introducing a new fixed-point equation. An alternative model replacing the nondifferentiable convex function in the formulation of the total variation with its differentiable Moreau envelope is presented, too. Numerical results are presented for impulsive noise removal to demonstrate the approximation accuracy and computational efficiency of the proposed algorithm. The obtained results can be widely used, e.g. in computer vision, biomedical imaging, optical flow, object tracking and shape denoising.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 68U10
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 65D19
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 6153898
zbMATH Keywords: image processing
zbMATH Keywords: L1/TV image denoising model
zbMATH Keywords: L2/TV model
zbMATH Keywords: ROF image denoising model
zbMATH Keywords: proximity operator
zbMATH Keywords: Gaussian noise
zbMATH Keywords: non-Gaussian noise
zbMATH Keywords: total-variation regularization
zbMATH Keywords: numerical result
zbMATH Keywords: computer vision
zbMATH Keywords: biomedical imaging
zbMATH Keywords: optical flow
zbMATH Keywords: object tracking
zbMATH Keywords: shape denoising
describes a project that uses: FTVd
MaRDI profile type: Publication
full work available at URL: s10444-011-9243-y
OpenAlex ID: W2032363154
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DOI: 10.1007/S10444-011-9243-Y
description: scientific article; zbMATH DE number 6153898