  In this paper, we address the speech denoising problem, where white Gaussian
additive noise is to be removed from a given speech signal. Our approach is
based on a redundant, analysis-sparse representation of the original speech
signal. We pick an eigenvector of the Zauner unitary matrix and -- under
certain assumptions on the ambient dimension -- we use it as window vector to
generate a spark deficient Gabor frame. The analysis operator associated with
such a frame, is a (highly) redundant Gabor transform, which we use as a
sparsifying transform in denoising procedure. We conduct computational
experiments on real-world speech data, solving the analysis basis pursuit
denoising problem, with four different choices of analysis operators, including
our Gabor analysis operator. The results show that our proposed redundant Gabor
transform outperforms -- in all cases -- Gabor transforms generated by
state-of-the-art window vectors of time-frequency analysis.
