Phaseless Rcovery using Gauss-Newton Method

TL;DR

This paper introduces a Gauss-Newton algorithm for phase retrieval that starts with a spectral initialization and converges quadratically, demonstrating superior performance and minimal measurement requirements.

Contribution

The paper presents a new Gauss-Newton based phase retrieval algorithm with proven quadratic convergence and improved empirical performance over existing methods.

Findings

Quadratic convergence of the proposed algorithm.

Near-minimal measurement requirement for real case.

Superior performance in numerical experiments.

Abstract

In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step. We prove that a re-sampled version of this algorithm quadratically converges to the solution for the real case with the number of random measurements being nearly minimal. Numerical experiments also show that Gauss-Newton method has better performance over the other algorithms.