Machine learning algorithms for independent vector analysis and blind source separation.

摘要

Blind signal separation (BSS) aims at recovering unknown source signals from the observed sensor signals where the mixing process is also unknown. As a popular method to solve this problem, independent component analysis (ICA) maximizes the mutual independence among, or equivalently the non-Gaussianity of, the signals and has been very successful especially when the unknown mixing process is instantaneous. In most realistic situations, however, there are time delay and reverberations which involve long filter lengths in the time domain.;Such convolutive BSS problems are often tackled in the frequency domain, or short-time Fourier transform (STFT) domain, mainly because the convolutive mixture model can be approximated to bin-wise instantaneous mixtures given the frame size is long enough to cover the main part of the convolved impulse responses. While the bin-wise instantaneous mixtures can be separated by the ICA algorithms for complex-valued variables, there are several factors that have significant influence on the final separation performance, which are the permutation problem, incomplete bin-wise separation, and noise.;Permutation problem refers to the random alignment of the STFT components that are separated by ICA. It is due to the permutation indeterminacy of ICA and it hinders proper reconstruction of the original time-domain signals. To solve this problem, a multidimensional ICA framework that is called independent vector analysis (IVA) has been proposed. IVA exploits the mutual dependence among the STFT components originating from the same source and employs a multivariate dependence model. In this thesis, various dependence models and methods are proposed in the framework of IVA to solve the convolutive BSS problem, which include Lp-norm invariant joint densities, density functions represented by overlapped cliques in graphical models, Newton's update optimization, and an EM algorithm using a mixture of multivariate Gaussians prior where Gaussian noise is added in the model.;While IVA is an effective framework to solve the convolutive BSS, the high dimensionality in the STFT domain makes it difficult to model the joint probability density function (PDF) of the fullband STFT components. On the other hand, binwise separation is a simpler task for which a permutation correction algorithm has to follow. For permutation correction, overall measures of magnitude correlation have been popular. However, the positive correlation is stronger between STFT components that are close to each other and correlation is a measure computed pair-wise. Thus, in this thesis, subband likelihood functions are proposed for the permutation correction which is fast to obtain and robust in solving the permutation problem.