On Relaxed Averaged Alternating Reflections (RAAR) Algorithm for Phase Retrieval from Structured Illuminations

TL;DR

This paper introduces a modified RAAR algorithm for phase retrieval using structured illuminations with deterministic phase shifts, demonstrating improved convergence and stability over existing methods through theoretical analysis and numerical simulations.

Contribution

The paper develops a new RAAR algorithm adapted for multiple diffraction patterns and operates in the Fourier domain, with proven local convergence and enhanced performance.

Findings

The modified RAAR algorithm converges locally and globally in tests.

Numerical simulations show superior stability compared to HIO.

The algorithm effectively handles structured illuminations with deterministic phase shifts.

Abstract

In this paper, as opposed to the random phase masks, the structured illuminations with a pixel-dependent deterministic phase shift are considered to derandomize the model setup. The RAAR algorithm is modified to adapt to two or more diffraction patterns, and the modified RAAR algorithm operates in Fourier domain rather than space domain. The local convergence of the RAAR algorithm is proved by some eigenvalue analysis. Numerical simulations is presented to demonstrate the effectiveness and stability of the algorithm compared to the HIO (Hybrid Input-Output) method. The numerical performances show the global convergence of the RAAR in our tests.