Abstract

A feasible solution is one that satisfies all a priori constraints known about the characteristics of the true solution. Classical signal estimation methods rely on optimizing a particular cost function. Set theoretic methods can allow for the possibility of a multiplicity of solutions. The sets are defined directly from the known properties of the physical signal that is to be estimated. This is in contrast to the use of penalty functions or regularization parametersto produce qualitative properties. The set theoretic methods range from the simple alternating projection methods to fuzzy set methods. Projection is only one way of finding a feasible solution. Fuzzy set methods use vector space optimization techniques. For nonconvex sets or convex sets whose projection operator is extremely complicated, random search methods may be used to find a point in the intersection of the sets. Examples of the various methods will be presented along with a discussion of the relative advantages and disadvantages of the methods.

© 1992 Optical Society of America