Use of trainable wavelet transform with adaptive threshold filtering for noise reduction of speech signals

Abstract

A method of noise reduction based on an adaptive threshold filtering over trainable wavelet transform was proposed. The restrictions on the trainable transform filter parameters were provided by a set of quadratic regularization terms. As an analog of the “hard” and “soft” threshold functions we used their smooth infinitely differentiable versions. The parameters of trainable wavelet transform, and threshold values were estimated by backpropagation and gradient-based optimization algorithm with an adaptive momentum estimation. Results of the proposed method were compared with an approach based on fixed discrete wavelet transform and non-adaptive global and level-depended threshold algorithms on the model problem. We used signal-to-noise ratio between suppressed and clean signals to numerically estimate the efficiency of noise reduction. We showed that the best results were obtained when the proposed trainable method with Daubechies 4 wavelet filters fine-tuning and adaptive level-dependent thresholding were applied.