Convex set theoretic image recovery with inexact projection algorithms

Author

Combettes, Patrick L.

Author_Institution

Lab. d´´Analyse Numerique, Univ. Pierre et Marie Curie, Paris, France

Volume

1

fYear

2001

fDate

6/23/1905 12:00:00 AM

Firstpage

257

Abstract

In image recovery, convex projection methods have been in use for almost two decades. However, while it is well known that projections can seldom be computed exactly, the effect of inexact projections on the behavior of such methods has not yet been investigated. We propose such an analysis and establish conditions on the projection errors under which the theoretical convergence properties of various algorithms remain valid. Our analysis covers sequential, parallel, and block-iterative (subgradient) projection methods for consistent and inconsistent set theoretic image recovery problems. It is shown in particular that parallel projection methods are more robust to errors than sequential methods such as the popular POCS (projection on to convex sets) algorithm

Keywords

Hilbert spaces; convergence of numerical methods; image restoration; iterative methods; set theory; Hilbert space; algorithm convergence properties; block-iterative methods; convex projection methods; convex set theory; image reconstruction; image recovery; image restoration; inexact projection algorithms; parallel methods; sequential methods; subgradient methods; Algorithm design and analysis; Constraint theory; Convergence; Extrapolation; Hilbert space; Image analysis; Image reconstruction; Image restoration; Projection algorithms; Robustness;

fLanguage

English

Publisher

ieee

Conference_Titel

Image Processing, 2001. Proceedings. 2001 International Conference on

Conference_Location

Thessaloniki

Print_ISBN

0-7803-6725-1

Type

conf

DOI

10.1109/ICIP.2001.959002

Filename

959002