Iteratively solving linear inverse problems under general convex constraints
type: Item
instance of: scholarly article
title: Iteratively solving linear inverse problems under general convex constraints
zbMATH Open document ID: 1123.65044
author: Ingrid Daubechies
author: Gerd Teschke
author: Luminita A. Vese
published in: Inverse Problems and Imaging
publication date: 2007-09-03T00:00:00Z
review text: Let \(T\) be a bounded operator from a Hilbert space \({\mathcal H}\) into itself, with \(\| T \|<1\), and \(C\) a closed convex subset of \({\mathcal H}\). For solving linear operator equations \(Tf=h\) the iterative process \(f_{n+1}=(\text{Id}-P_{\alpha C})(f_n+T^*g-T^* T f_n)\), \(\alpha>0\) is proposed. The cases of bounded and unbounded \((T^* T)^{-1}\) are considered.
reviewed by: Mikhail Yu. Kokurin
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65J22
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 5186384
zbMATH Keywords: linear inverse problems
zbMATH Keywords: Landweber iteration
zbMATH Keywords: Besov- and BV restoration
zbMATH Keywords: generalized shrinkage
zbMATH Keywords: Hilbert space
zbMATH Keywords: linear operator equations
MaRDI profile type: Publication
full work available at URL: ipi.2007.1.29
OpenAlex ID: W2145003640
DOI: 10.3934/IPI.2007.1.29
description: scientific article; zbMATH DE number 5186384