×

zbMATH — the first resource for mathematics

Parallel methods in image recovery by projections onto convex sets. (English) Zbl 0789.65039
This paper is a continuation of the author’s work [J. Math. Anal. Appl. 155, No. 2, 413-419 (1991; Zbl 0752.65045)]. He studies weak convergence of sequences \(\{S^ n x\}^ \infty_{n=0}\) to a common fixed point of a finite number of projections \(P_ 1,\dots,P_ r\) (onto convex closed subsets \(C_ 1,\dots,C_ r\)) in a Hilbert space where \(S-1\) is a suitable linear combination of the \(P_ i - 1\). This paper proves this if the operator \(S\) does not have a multiple of the identity as a convex component. The author refers to experimental studies, but without details.

MSC:
65J05 General theory of numerical analysis in abstract spaces
65Y05 Parallel numerical computation
47A50 Equations and inequalities involving linear operators, with vector unknowns
PDF BibTeX Cite
Full Text: EuDML
References:
[1] L. M. Bregman: Finding the common point of convex sets by the method of successive projection. Dokl. Akad. Nauk SSSR 162 (1965), 487-490.
[2] G. Crombez: Image recovery by convex combinations of projections. J. Math. Anal. Appl. 155 (1991), 413-419. · Zbl 0752.65045
[3] M. I. Sezan, H. Stark: Image restoration by the method of convex projections: part 2 - applications and numerical results. IEEE Trans. Medical Imaging 1 (1982), 95-102.
[4] M. I. Sezan, H. Stark: Applications of convex projection theory to image recovery in tomography and related areas. Image recovery: theory and application, Academic Press Inc. New York, 1987. · Zbl 0627.65133
[5] D. C. Youla, H. Webb: Image restoration by the method of convex projections: part 1 - theory. IEEE Trans. Medical Imaging 1 (1982), 81-94.
[6] D. C. Youla: Mathematical theory of image restoration by the method of convex projections. Image recovery: theory and application, Academic Press Inc. New York, 1987.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.