Phase Retrieval Algorithm Using a Convolution Based Hilbert Space

Abstract

A phase retrieval algorithm using the method of projection onto convex sets (POCS) [1,2] in a new Hilbert Space framework which is based on convolution is described. In this space, the set of sequences with a prescribed Fourier Transform magnitude constitute a closed convex set, which is not true in (or L2) Hilbert space. This property of the constraints ensures convergence in the POCS method. Examples of phase retrieval for 2-D sequences are presented.