New bounds for strong restricted isometry constants with tight frames for phase retrieval

This paper discusses the l p (0 < p ≤ 1)$minimization model for the compressive phase retrieval problem in a Hilbert space. To recoversparse signals in terms of a tight frame D frommagnitude-only measurements, we first prove that the null space property(NSP) of themeasurement matrix guarantees exact recovery in the noiseless case.Furthermore, we establish new sufficient conditions based on the strong D-restrictedisometry property(S-DRIP) of the measurement matrix, which can providestable recovery of unknown signals in the presence of noise.