A theoretical perspective of solving phaseless compressive sensing via its nonconvex relaxation

作者：You, Guowei; Huang, Zheng-Hai^*; Wang, Yong

来源：Information Sciences, 2017, 415: 254-268.

DOI：10.1016/j.ins.2017.06.020

• Phase retrieval
• Phaseless compressive sensing
• Compressive sensing
• l(p)-minimization

As a natural extension of Compressive Sensing and the requirement of some practical problems, Phaseless Compressive Sensing (PCS) has been introduced and studied recently. Many theoretical results have been obtained for PCS with the aid of its convex relaxation. Motivated by successful applications of nonconvex relaxed methods for solving Compressive Sensing, in this paper, we try to investigate PCS via its nonconvex relaxation. Specifically, we relax PCS in the real context by the corresponding l(p)-minimization with p is an element of (0, 1). We show that there exists a constant p* is an element of (0, 1] such that for any fixed p is an element of (0; p*), every optimal solution to the l(p)-minimization also solves the concerned problem; and derive an expression of such a constant p* by making use,of the known data and the sparsity level of the concerned problem. These provide a theoretical basis for solving this class of problems via the corresponding l(p)-minimization.

• 出版日期2017-11
• 单位天津大学; 河南大学