Convolution-based framework for signal recovery and applications

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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.

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