Phase retrieval from noisy data based on sparse approximation of object phase and amplitude

TL;DR

This paper introduces a variational algorithm leveraging sparsity in the transform domain for phase and amplitude retrieval from noisy optical data, outperforming existing methods under high noise conditions.

Contribution

It develops a novel sparsity-based variational approach for phase retrieval from Poissonian data, including simplified versions, with demonstrated superiority in noisy scenarios.

Findings

Outperforms Gerchberg-Saxton and Wirtinger flow algorithms in noisy conditions.

Sparsity modeling enhances robustness to noise in phase retrieval.

Simplified algorithms without sparsity are less effective under high noise.

Abstract

A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of wavefronts. The transform domain sparsity is applied for the amplitude and phase modeling. It is demonstrated that this modeling results in the essential advantage of the developed algorithm for heavily noisy observations corresponding to a short exposure time in optical experiments. We consider also two simplified versions of this algorithm where the sparsity modeling of phase and amplitude is omitted. In the simulation study we compare the developed algorithms versus the Gerchberg-Saxton and truncation Wirtinger flow algorithms. The latter algorithm being the maximum likelihood based is the state-of-the-art for the phase retrieval from Poissonian observations. For noisy and very noisy observations the proposed algorithm demonstrates a valuable advantage.