Phase retrieval from short-time Fourier transform in LCA groups

Abstract

We study the short-time Fourier transform phase retrieval problem in locally compact abelian groups. Using probabilistic methods, we show that for a large class of groups G and compact subsets K\subseteq G there exists a window function and a uniformly discrete set in G\times \wh{G} allowing phase retrieval in L^2(K). We also study the obstructions for STFT phase retrieval on L^2(G), motivating the restriction to compactly supported function spaces.