Phase Retrieval Via Reweighted Wirtinger Flow

TL;DR

This paper introduces a reweighted Wirtinger flow method for phase retrieval, improving convergence and reducing sampling complexity compared to existing methods, especially in low sampling scenarios.

Contribution

The paper proposes a novel reweighted Wirtinger flow algorithm that guarantees geometric convergence and outperforms traditional Wirtinger flow and truncated Wirtinger flow in low sampling regimes.

Findings

RWF achieves geometric convergence from a deliberate initialization.

RWF has lower sampling complexity than WF.

RWF outperforms TWF when the sampling ratio is small.

Abstract

Phase retrieval(PR) problem is a kind of ill-condition inverse problem which is arising in various of applications. Based on the Wirtinger flow(WF) method, a reweighted Wirtinger flow(RWF) method is proposed to deal with PR problem. RWF finds the global optimum by solving a series of sub-PR problems with changing weights. Theoretical analyses illustrate that the RWF has a geometric convergence from a deliberate initialization when the weights are bounded by 1 and $\frac{10}{9}$. Numerical testing shows RWF has a lower sampling complexity compared with WF. As an essentially adaptive truncated Wirtinger flow(TWF) method, RWF performs better than TWF especially when the ratio between sampling number $m$ and length of signal $n$ is small.