UNIFIED HILBERT SPACE APPROACH TO ITERATIVE LEAST-SQUARES LINEAR SIGNAL RESTORATION.

Jorge L.C. Sanz, Thomas S. Huang

Research output: Contribution to journalArticlepeer-review

Abstract

Iterative least-squares solutions of the linear signal-restoration problem g equals Af are considered. First, several existing techniques for solving this problem with different underlying models are unified. Specifically, the following are shown to be special cases of a general iterative procedure for solving linear operator equations in Hilbert spaces: (1) a Van Cittert-type algorithm for deconvolution of discrete and continuous signals; (2) an iterative procedure for regularization when g is contaminated with noise; (3) a Papoulis-Gerchberg algorithm for extrapolation of continuous signals; (4) an iterative algorithm for discrete extrapolation of band-limited infinite-extent discrete signals right brace and the minimum-norm property of the extrapolation obtained by the iteration left brace ; and (5) a certain iterative procedure for extrapolation of band-limited periodic discrete signals. The Bialy algorithm also generalizes the Papoulis-Gerchberg iteration to cases in which the ideal low-pass operator is replaced by some other operators. In addition a suitable modification of this general iteration is shown. This technique leads us to new iterative algorithms for band-limited signal extrapolation. In numerical simulations some of these algorithms provide a fast reconstruction of the sought signal.

Original languageEnglish (US)
Pages (from-to)1455-1465
Number of pages11
JournalJournal of the Optical Society of America
Volume73
Issue number11
DOIs
StatePublished - Jan 1 1983

ASJC Scopus subject areas

  • Engineering(all)

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