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 <i>l</i><sub>2</sub> (or <i>L</i><sub>2</sub>) 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
A. Enis Çetin and Rashid Ansari, "Convolution-based framework for signal recovery and applications," J. Opt. Soc. Am. A 5, 1193-1200 (1988)