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.
Categories: stat.ML cs.LG stat.CO