  In this paper, we address the speech denoising problem, where Gaussian, pink
and blue additive noises are 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, using as baseline three Gabor transforms
generated by state-of-the-art window vectors in time-frequency analysis and
compare their performance to the proposed Gabor transform. The results show
that our proposed redundant Gabor transform outperforms all others,
consistently for all signals.
