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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 5, Iss. 8 — Aug. 1, 1988
  • pp: 1193–1200

Convolution-based framework for signal recovery and applications

A. Enis Çetin and Rashid Ansari  »View Author Affiliations


JOSA A, Vol. 5, Issue 8, pp. 1193-1200 (1988)
http://dx.doi.org/10.1364/JOSAA.5.001193


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Abstract

The method of projections on convex sets is a procedure for signal recovery when partial information about the signal is available in the form of suitable constraints. We consider the use of this method in an inner-product space in which the vector space consists of real sequences and vector addition is defined in terms of the convolution operation. Signals with a prescribed Fourier-transform magnitude constitute a closed and convex set in this vector space, a condition that is not valid in the commonly used l2 (or L2) Hilbert-space framework. This new framework enables us to construct minimum-phase signals from the partial Fourier-transform magnitude and/or phase information.

© 1988 Optical Society of America

History
Original Manuscript: May 5, 1986
Manuscript Accepted: April 21, 1988
Published: August 1, 1988

Citation
A. Enis Çetin and Rashid Ansari, "Convolution-based framework for signal recovery and applications," J. Opt. Soc. Am. A 5, 1193-1200 (1988)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-5-8-1193

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