Incorporation of a priori moment constraints into signal recovery and synthesis problems via the method of convex projections

The a priori information on generalized moments is shown to restrict the function f to lie in closed convex sets C^r, r = 0, 1, ..., N, in a Hilbert space setting. Therefore the a priori moment information can also be incorporated into the method of projections onto convex sets (POCS). Given the partial information (including both measurements and a priori constraints), the method of POCS reconstructs or synthesizes a feasible solution. The a priori knowledge of moments up to a finite order is assumed to synthesize a nonnegative function, consistent with a well-defined Rayleigh distribution, via the method of POCS.