A stochastic alternating minimizing method for sparse phase retrieval
This addresses the challenge of sparse signal recovery in applied sciences, offering a globally convergent method with optimal sample complexity, though it appears incremental as it builds on existing techniques like HTP.
The paper tackles the problem of sparse phase retrieval by proposing the StormSpar algorithm, which empirically recovers n-dimensional s-sparse signals from O(s log n) measurements without needing a good initial guess, as validated through numerical experiments.
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.