Implementation of an optimal first-order method for strongly convex total variation regularization
type: Item
instance of: scholarly article
title: Implementation of an optimal first-order method for strongly convex total variation regularization
zbMATH Open document ID: 1256.65063
author: T. L. Jensen
author: Per Christian Hansen
author: S. H. Jensen
author: J. H. Jørgensen
published in: BIT
publication date: 2012-07-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.3723
review text: The paper presents a practical implementation of an optimal first-order optimization algorithm for large-scale problems. This algorithm is suited for smooth and strongly convex functions. While the underlying algorithm by \textit{Y. Nesterov} [Math. Program. 103, No. 1 (A), 127--152 (2005; Zbl 1079.90102)] requires the knowledge of two parameters that characterize the smoothness and the strong convexity, the proposed algorithm estimates these parameters during the iteration. This makes the algorithm of practical use. The mechanisms are also allowed for the application to non-strongly convex functions. The authors test the performance of the algorithm and compare it with two variants of the gradient projection algorithm and a variant of the FISTA-algorithm. They apply the method to total variation regularized tomographic reconstruction of a generic three-dimensional test problem. The software is available as a C-implementation with an interface to MATLAB.
reviewed by: Werner H. Schmidt
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65R32
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49M37
zbMATH DE Number: 6062477
zbMATH Keywords: total variation regularization
zbMATH Keywords: first-order optimization algorithm
zbMATH Keywords: large scale problems
zbMATH Keywords: strong convexity
zbMATH Keywords: Nesterov's method
zbMATH Keywords: tomography
zbMATH Keywords: software FISTA
zbMATH Keywords: numerical examples
zbMATH Keywords: gradient projection algorithm
zbMATH Keywords: tomographic reconstruction
describes a project that uses: TwIST
describes a project that uses: Matlab
describes a project that uses: NESTA
describes a project that uses: na28
describes a project that uses: TFOCS
MaRDI profile type: Publication
OpenAlex ID: W2097726319
arXiv ID: 1105.3723
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DOI: 10.1007/S10543-011-0359-8
description: scientific article; zbMATH DE number 6062477