## Convolution-based framework for signal recovery and applications

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 *l*_{2} (or *L*_{2}) 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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