New features for speech enhancement using bivariate shrinkage based on redundant wavelet filter-banks

• There are some dependencies among wavelet coefficients.
• Bivariate shrinkage was proposed based on parent–child coefficients dependencies.
• Two-channel critically sampled filter-bank is not suitable for bivariate shrinkage.
• Multi-channel redundant wavelet filter-banks lead to better results.

In most of the wavelet based speech enhancement methods, it is assumed that the wavelet coefficients are independent of each other. However, investigating the joint histogram of the wavelet coefficients reveals some dependencies among them. In this regard, Sendur proposed a probability density function (pdf) that models the relation between a wavelet coefficient of image signal and its parent. Then, this pdf is utilized to propose a bivariate shrinkage function which uses the dependencies between the child–parent wavelet coefficients of Image signals to enhance the noisy images. In this paper, we intend to find wavelet structures which are more suitable for speech enhancement based on bivariate shrinkage. We show that the dependencies between the child–parent wavelet coefficients can only be modeled rather easily up to two stages of two-channel discrete wavelet transform using the Sendur's pdf. However, the bivariate shrinkage function works better in three-channel redundant wavelet filter-bank with dilation 2, since it has a joint distribution which is similar to the Sendur's pdf up to the fourth stage of decomposition for speech signals. Furthermore, we show that three-channel higher density wavelet obtained by eliminating the downsampling part of the third channel is more suitable for the bivariate shrinkage function when it is utilized for speech enhancement. Then, appropriate filter values for three-channel higher density wavelet filter-bank are found. Moreover, we propose four-channel double density discrete wavelet filter-bank which leads to some improvement in speech enhancement results. Since the probability of speech presence is higher in lower frequencies, we suggest level-dependent bivariate shrinkage. Finally, Sendur bivariate shrinkage is optimized for speech enhancement and new methods are proposed by combining former successful methods with the bivariate shrinkage function.