**ABSTRACT**
### Reconstruction of signals from irregular samples of its short-time
Fourier transform

#### H.G.Feichtinger, W.Kozek and T.Strohmer

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.

**Keywords:** algorithms, irregular sampling, numerical work

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