Fast Iterative Algorithms for Blind Phase Retrieval: A survey

TL;DR

This survey reviews recent iterative algorithms for blind phase retrieval, a key problem in nanoscale imaging and ultrafast laser applications, highlighting mathematical formulations, algorithm types, and future research directions.

Contribution

It provides a comprehensive overview of recent iterative algorithms for BPR, categorizing methods and discussing future challenges in theory and experiments.

Findings

Categorizes three main types of iterative algorithms for BPR.

Summarizes mathematical formulations and optimization problems.

Discusses future research directions in BPR.

Abstract

In nanoscale imaging technique and ultrafast laser, the reconstruction procedure is normally formulated as a blind phase retrieval (BPR) problem, where one has to recover both the sample and the probe (pupil) jointly from phaseless data. This survey first presents the mathematical formula of BPR, related nonlinear optimization problems and then gives a brief review of the recent iterative algorithms. It mainly consists of three types of algorithms, including the operator-splitting based first-order optimization methods, second order algorithm with Hessian,and subspace methods. The future research directions for experimental issues and theoretical analysis are further discussed.