Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems
type: Item
instance of: scholarly article
title: Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems
zbMATH Open document ID: 0714.65045
DOI: 10.1016/0024-3795(90)90210-4
author: Henry E. Fleming
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: The author considers stable methods for the approximate solution of ill- conditioned systems of linear equations by means of Phillips-Tikhonov regularization, and by means of truncated iterative methods (i.e. iterative methods that are stopped after a fixed number of steps). It is proved that these two (families of) methods are equivalent in the sense that the endresult of a method of one family can be obtained via a process from the other method with suitable smoothing- resp. iteration- matrix. This applies to overdetermined as well as underdetermined systems of linear equations.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4176352
zbMATH Keywords: ill-posed problems
zbMATH Keywords: overdetermined systems
zbMATH Keywords: ill-conditioned systems
zbMATH Keywords: Phillips-Tikhonov regularization
zbMATH Keywords: truncated iterative methods
zbMATH Keywords: underdetermined systems
reviewed by: Paul P. B. Eggermont
MaRDI profile type: Publication
full work available at URL: 0024-3795(90)90210-4
OpenAlex ID: W2086260534
cites work: Q4125663
cites work: An Application of the Wiener-Kolmogorov Smoothing Theory to Matrix Inversion
cites work: A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
cites work: Q4047075
cites work: Theory and Methods Related to the Singular-Function Expansion and Landweber’s Iteration for Integral Equations of the First Kind
cites work: Some aspects of the behavior of regularized solutions as the amount of smoothing is varied
cites work: Q3742670
cites work: A formal comparison of methods proposed for the numerical solution of first kind integral equations
cites work: Q3779677
cites work: Q5185900
description: scientific article; zbMATH DE number 4176352