Alternating projections with applications to Gerchberg-Saxton error reduction

TL;DR

This paper analyzes the convergence of alternating projection methods on non-convex sets and applies these results to improve understanding of algorithms like Gerchberg-Saxton, EM, and Cadzow's algorithm.

Contribution

It provides new convergence analysis for alternating projections on non-convex sets and applies this to key algorithms in signal processing and machine learning.

Findings

Convergence conditions for alternating projections on non-convex sets.

Application of convergence results to Gerchberg-Saxton error reduction.

Insights into the behavior of EM and Cadzow's algorithms.

Abstract

We consider convergence of alternating projections between non-convex sets and obtain applications to convergence of the Gerchberg-Saxton error reduction method, of the Gaussian expectation-maximization algorithm, and of Cadzow's algorithm.