Generalized Phase (Norm) Retrieval Hermitian Matrices and G-frames

This paper is an analysis of the generalized phase (norm) retrieval problem, which aims to reconstruct a signal from its quadratic measurements. We provide some connections between phase (norm) retrieval G-frames and generalized phase (norm) retrieval Hermitian matrices Aⱼⱼ₌₁ⁿ with real entries. In particular, we investigate some characterizations of phase retrieval G-frames by using their induced frames on real Hilbert spaces. With regard to phase (norm) retrieval frames, the study uncovers new aspects of G-frames that possess phase (norm) retrieval properties and concludes with a detailed consideration of a phase retrieval dual G-frames. Finally, we obtain some sufficient conditions under which phase retrieval G-frames are stable under small perturbations.