After a postdoctoral stay at the Mathematical Institute of Bordeaux, Martin Rathmair begins the return phase of his Schrödinger fellowship, funded by the Austrian Science Fund. One of Martin's main focus points is the so-called phase-retrieval problem, that is, the problem of reconstructing phase information of usually complex-valued functions from magnitude-only observations. Martin investigates this problem particularly in the context of the wavelet and short-time Fourier transform.