<title>Reconstruction of signals from irregular samples of its short-time Fourier transform</title>

Abstract

The short-time Fourier transform (STFT) leads to a highly redundant linear time-frequency signal representation. In order to remove this redundancy it is usual to sample the STFT on a rectangular grid. For such regular sampling the basic features of the reconstruction problem are well understood. In this paper, we consider the problem of reconstructing a signal from irregular samples of its STFT. It may happen that certain samples of the STFT from a regular grid are lost or that the STFT has been purposely sampled in an irregular way. We investigate that problem using Weyl-Heisenberg frames, which are generated from a single atom by time- frequency-shifts (along the sampling set). We compare various iterative methods and present typical numerical experiments. Whereas standard frame iterations are doing not very well it turns out that for many reasons the conjugate gradient algorithm behaves best, most often even better than one might expect from the observations made for general frame operators.