**ABSTRACT:**

Motivated by the channel estimation problem in wireless communication matrices are considered that have a sparse representation in terms of elementary matrices. The basic problem under consideration consists of identifying such a matrix

from its action on only one vector. This can be

restated in terms of a sparse approximation or sparse recovery (compressed sensing) problem. So many algorithms from this field apply to perform the practical reconstruction, and there are direct consequences from known

results on random measurement matrices, such as the Gaussian, Bernoulli and partial Fourier ensemble.

However, the main focus will be on identifying an operator being the sum of a few time frequency-shifts (that is, it has sparse spreading function). Reconstruction results for basis pursuit (ell_1 minimization) will be presented. They

can as well be interpreted as sparse approximation

results for particular finite Gabor frames.

This is joint work with Götz Pfander (International University of Bremen)

and Jared Tanner (University of Utah).