Star DGT: a robust Gabor transform for speech denoising

In this paper, we address the speech denoising problem, where Gaussian and coloured 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 the 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 the proposed redundant Gabor transform outperforms previous ones consistently for all types of examined signals of noise.