Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm

TL;DR

This paper introduces prSAMP, a robust phase retrieval algorithm capable of handling ill-conditioned measurement matrices and high noise levels, improving reliability in optical imaging and compressed sensing applications.

Contribution

The paper presents a new phase retrieval algorithm that effectively works with both Gaussian and binary measurement matrices, addressing convergence issues and noise robustness.

Findings

Effective with Gaussian and binary matrices

Robust to high noise levels

Improves convergence in ill-conditioned scenarios

Abstract

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices, they suffer serious convergence issues some ill-conditioned matrices. As an example, this happens in optical imagers using binary intensity-only spatial light modulators to shape the input wavefront. The problem of ill-conditioned measurement matrices has also been a topic of interest for compressed sensing researchers during the past decade. In this paper, using recent advances in generic compressed sensing, we propose a new phase retrieval algorithm that well-adopts for both Gaussian i.i.d. and binary matrices using both sparse and dense input signals. This algorithm is also robust to the strong noise levels found in some imaging applications.