Abstract:

We explore the so-called short-time Fourier transform (STFT) phase retrieval
problem, a nonlinear inverse problem that has recently gained considerable attention in both
mathematical research and practical applications. The main results of 9 recent research papers
are outlined. A central theme revolves around the uniqueness problem when dealing with
phaseless samples. Specifically, it addresses the question of whether phaseless samples of the
STFT carry enough information to determine functions within infinite-dimensional function
spaces. A thorough investigation into this problem is conducted, focusing on five key areas: 1.
Examining the limitations of phaseless sampling on lattices; 2. Investigating lattice-based
uniqueness within particular function spaces and the numerical techniques for stable
reconstruction; 3. Analyzing irregular phaseless sampling and the advantage of employing
perturbation of lattices; 4. Exploring the use of multiple windows as an approach to the phase
retrieval problem; 5. Investigating the principles of holomorphic phase retrieval and the
concept of rigidity in this context