Bayesian Independent Component Analysis as Applied to One-Channel Speech Enhancement

Abstract

Our work applies a unifying Bayesian-Independent Component Analysis (BICA) framework in the context of speech enhancement and robust Automatic Speech Recognition (ASR). The corrupted speech waveform is reshaped in overlapping speech frames, and is assumed to be composed as a linear sum of the underlying clean speech and noise. Subsequently, a linear sum of latent independent functions is proposed to span each clean frame. Two different techniques are applied following a Bayesian formulation: In the first case the posterior probability of a clean speech frame is formed conditioned on the noisy one on which a maximum a posteriori (MAP) approach is applied, leading to Sparse Code Shrinkage (SCS) - a fairly new statistical technique originally presented to applied mathematics and image denoising, but its much promising potential for speech enhancement has not yet been exploited. In the second case, viewed within the Variational Bayes framework, the model for noisy speech generation is stated in a block-based fashion as a noisy, blind source separation problem from which we infer the independent basis functions that span the space of a speech frame and their mixing matrix, thus reconstructing directly the corresponding clean frames.