Signal recovery with similarity constraints

The method of projections onto convex sets (POCS) is a technique for restoring signals from the available data and prior constraints. In general each additional constraint helps to narrow the set of feasible solutions consistent with the data and prior constraints. We discuss a new constraint, which we call similarity. The similarity constraint is associated with a closed, convex set and hence is useful in POCS. We compute the similarity projector, discuss its properties, and illustrate its application in signal recovery and synthesis with examples. © 1989 Optical Society of America.