Perceptual wavelet-representation of speech signals and its application to speech enhancement

When considering the speech as a non-stationary signal and giving up the quasi-stationary approach, the wavelet transform is a possible analysis method. Though this technique has been applied to a wide variety of speech processing tasks, the problem of how to derive the speech-tailored wavelets is not solved definitely. Therefore, in this paper the so-called perceptual wavelet transform and the corresponding speech representation are introduced as possible solutions. Although the proposed transform has been derived heuristically-namely, to be optimal in the perceptual frequency scale in Gabor-sense and to perform a 1 CB speech analysis-it appears that this is a self-invertible, overcomplete, shiftable transform. This is an important fact in the light of recent results in the so-called wavelet-frame-based denoising; moreover, the concept of soft-thresholding of the latter can also be introduced heuristically by applying the auditory masking phenomenon. The recent paper describes the perceptual wavelet functions in detail, presents the properties of this method in a time-domain analysis example, and two novel speech representations are given, which are somewhat similar to each other and to the conventional spectrogram. Finally, a new speech enhancement method is proposed, which consists of three stages: a perceptual wavelet-decomposition, followed by a compressive non-linearity (with adjustable parameters to the noise process), and summing. (C) 1996 Academic Press Limited.