Learning statistically efficient features in time domain for single channel signal separation

Abstract

When human listeners hear the sounds from a number of mixed sources, they can remarkably recognize and follow each stream -acoustic object- separately from the other sources. Researchers in signal processing and many other related fields have strived for the realization of this human ability in machines; however, except in limited certain applications, thus far they have failed to produce the desired outcomes. In this thesis, we develop a couple of approaches for the signal separation problem, with a strict restriction that only single sensor observations are available. To derive separation algorithms, an efficient representation of the source signals by a statistical method is proposed. The efficient statistical representation is constructed by assuming a sound signal to be generated by a linear combination of a set of basis functions, and the source distributions are modeled by adapting the basis functions so that each source component is statistically independent. These features are source dependent characteristics and enable to compute probability of signals given the basis functions, by a flexible model known as generalized Gaussian priors for the density estimation of the highly sparse signals such as speech sounds. The basis functions of the source signals are learned a priori from a training data set and play a primary role for the separation algorithms, because the learned basis abstracts the essential information of the source signals more efficiently compared with conventional representations such as Fourier basis. With the given basis functions of the source signals that are mixed in a single channel, an adaptive separation algorithm is derived. The algorithm recovers the original auditory streams in a number of gradient-ascent adaptation steps maximizing the log likelihood of the separated signals. The algorithm performs all relevant adaptation on a single sample basis, which means that the solution is achieved by altering the sampled values of the...