A stochastic alternating minimizing method for sparse phase retrieval

TL;DR

This paper introduces StormSpar, a stochastic alternating minimizing algorithm that efficiently recovers sparse signals from few measurements without needing a good initial guess, validated through extensive experiments.

Contribution

The paper proposes StormSpar, a novel stochastic method for sparse phase retrieval that guarantees global convergence with optimal measurement complexity without initial value requirements.

Findings

Successfully recovers s-sparse signals from O(s log n) measurements.

Converges globally with random initialization.

Validated by extensive numerical experiments.

Abstract

Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underline{r}nating \underline{m}inimizing method for \underline{sp}arse ph\underline{a}se \underline{r}etrieval (\textit{StormSpar}) algorithm which {emprically} is able to recover $n$-dimensional $s$-sparse signals from only $O(s\,\mathrm{log}\, n)$ number of measurements without a desired initial value required by many existing methods. In \textit{StormSpar}, the hard-thresholding pursuit (HTP) algorithm is employed to solve the sparse constraint least square sub-problems. The main competitive feature of \textit{StormSpar} is that it converges globally requiring optimal order of number of samples with random initialization. Extensive numerical experiments are given to validate the proposed algorithm.