Abstract. This paper discusses the k-sparse complex signal recovery from quadratic measurements via the -minimization model, where . We establish the restricted isometry property over simultaneously low-rank and sparse matrices, which is a weaker restricted isometry property to guarantee the successful recovery in the case. The main result is to demonstrate that -minimization can recover complex k-sparse signals from complex Gaussian quadratic measurements with high probability. The resulting sufficient condition is met by fewer measurements for smaller p and reaches when p turns to zero. Furthermore, an iteratively-reweighted algorithm is proposed. Numerical experiments also demonstrate that minimization with performs better than minimization.
How to Cite this Article:
Y. Xia, L. Zhou, The sampling complexity on nonconvex sparse phase retrieval problem, J. Nonlinear Var. Anal. 7 (2023), 607-626.
