Necessary conditions for a unique solution to two-dimensional phase recovery

Abstract

In this paper we show that although in one dimension multiplicity of solutions to the phase reconstruction problem presents a serious problem, in two or more dimensions multiplicity is pathologically rare. We derive from a given solution pair (g,G) necessary conditions for the existence of alternative solution pairs (h,H), and a characterization of their form. The mathematical tools employed are from the theory of functions of two complex variables.