SVD-based optimal filtering with applications to noise reduction in speech signals

A class of SVD-based signal enhancement procedures is described, which amount to a specific optimal filtering technique for the case where the so-called 'desired response' signal cannot be observed. It is shown that this optimal filter can be written as a function of the generalized singular vectors and singular values of a so-called speech and noise data matrix. A number of simple symmetry properties of the optimal filter are derived, which are valid for the white noise case as well as for the coloured noise case. Also the averaging step of the standard one-microphone SVD-based noise reduction techniques is investigated, leading to serious doubts about the necessity of this averaging step. When applying this technique for multi-microphone noise reduction, it is shown that for simple scenarios, where we consider localised sources and no multipath propagation, this technique exhibits some kind of beamforming behaviour. We further compare the performance of this technique with standard beamforming techniques, showing that for all reverberation times the performance of the SVD-based optimal filter is better than beamforming.