Phase retrieval by power iterations

TL;DR

This paper demonstrates that the power iteration method can effectively solve the phase retrieval problem under specific conditions, with numerical tests showing rapid convergence in a single iteration.

Contribution

It introduces a novel application of power iteration to phase retrieval, showing convergence when relative phases between pixel groups are known.

Findings

Power iteration converges under certain conditions.

Inverse block iteration recovers solutions in one step.

Numerical tests validate the method's efficiency.

Abstract

I show that the power iteration method applied to the phase retrieval problem converges under special conditions. One is given the relative phases between small non-overlapping groups of pixels of a recorded intensity pattern, but no information on the phase between the groups of pixels. Numerical tests show that the inverse block iteration recovers the solution in 1 iteration.