Speech Denoising by SoftSoft Thresholding

Many noise-reduction methods are based on the possibility of representing the clean signal with a reduced number of transform coefficients, so that cancelling coefficients below a certain thresholding level produces an enhanced reconstructed signal. It is assumed that the clean signal has a sparse representation, while noise energy is spread over all coefficients. The main drawback of those methods is the speech distortion introduced by eliminating small magnitude coefficients, and the presence of artifacts ("musical noise") produced by isolated noisy coefficients randomly crossing the thresholding level. Based on the observation that the speech histogram has many important coefficients close to origin, we propose the "softsoft" thresholding function to denoise speech signals corrupted by AWGN. This function has two thresholding levels: a lower level adjusted to reduce distortion, and a higher level adjusted to remove noise. The joint optimal values can be determined by minimizing the resulting mean-square error (MSE). We also verify that this new thresholding function leads to lower MSE than the well-known soft-thresholding function, which employs only a higher level. Although the MSE improvement is not expressive, a perceptual distortion measure (the log-spectral distance) confirms the higher perceptual quality of the softsoft scheme