Given X a function space consisting of complex-valued functions, the corresponding phase retrieval problem is to reconstruct F ∈ X from phase-less observations, that is from (samples of) its modulus |F|. Among other difficulties, the lack of convexity makes such a problem a challenging task.
We discuss the case where X is the image of L2 under the short-time Fourier transform (STFT) with Gaussian window, i.e., reconstruction of the STFT from the spectrogram.
We propose a reconstruction scheme which is based on solving two convex problems and argue that the method accurately reconstructs F (up to a constant phase factor) provided that F is connected in a certain graph-theoretic sense (note that the problem at hand requires some sort of connectivity to be well-posed).
This is joint work with P. Jaming (U. Bordeaux)
https://univienna.zoom.us/j/64895816787?pwd=L0tHVnBPUkJFQVVSR3Y2QnhVRXRGZz09