Fast phase retrieval for high dimensions: A block-based approach

TL;DR

This paper introduces a block-based approach to phase retrieval in high dimensions, significantly reducing computational and memory costs by solving smaller subproblems and merging results with minimal global measurements.

Contribution

It proposes a novel block-diagonal measurement matrix framework that enables scalable phase retrieval in high dimensions, improving efficiency over existing methods.

Findings

Reduces computational cost by orders of magnitude

Decreases memory requirements significantly

Maintains accuracy with minimal global measurements

Abstract

This paper addresses fundamental scaling issues that hinder phase retrieval (PR) in high dimensions. We show that, if the measurement matrix can be put into a generalized block-diagonal form, a large PR problem can be solved on separate blocks, at the cost of a few extra global measurements to merge the partial results. We illustrate this principle using two distinct PR methods, and discuss different design trade-offs. Experimental results indicate that this block-based PR framework can reduce computational cost and memory requirements by several orders of magnitude.