Iterative exponential filtering for large discrete ill-posed problems
type: Item
instance of: scholarly article
title: Iterative exponential filtering for large discrete ill-posed problems
zbMATH Open document ID: 0947.65039
author: Qin Zhang
author: Daniela Calvetti
author: Lothar Reichel
published in: Numerische Mathematik
publication date: 2000-11-02T00:00:00Z
review text: This paper presents an iterative method for the solution of discrete linear ill-posed problems with a symmetric, possible indefinite or singular matrix. The rigth-hand side vector of the linear system \(Ax= g\), represents the given data and is assumed to be contaminated by measurement errors. In order to reduce the errors in the computation of the solution an exponential filter function of the form \(\varphi_\beta(t)= 1-\exp(-\beta t)\), with the regularization parameter \(\beta\geq 0\) is applied. The iterative method is derived by expanding the filter function in terms of Chebyshev polynomials. The possibilities of the extension of the iterative method by using the Morozov discrepancy principle in order to determine both a suitable value of \(\beta\) and an approximation of the associated regularized approximate solution \(x_\beta\) are discussed. The application to image restoration illustrates the performance of the proposed method.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1398752
zbMATH Keywords: iterative method
zbMATH Keywords: linear ill-posed problems
zbMATH Keywords: regularization
zbMATH Keywords: discrepancy principle
zbMATH Keywords: image restoration
zbMATH Keywords: performance
reviewed by: Florica Luban
MaRDI profile type: Publication
full work available at URL: s002119900077
OpenAlex ID: W2044468292
DOI: 10.1007/S002119900077
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description: scientific article; zbMATH DE number 1398752