On Modelling the Frequency Components of Speech with Norm-Invariant Joint Densities

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in frequency-domain blind source separation. Instead of running ICA in each frequency bin and matching the permutation afterwards, IVA exploits the dependency among the frequency components of a source and deal with them altogether as a multivariate data by capturing the dependency with a multivariate joint probability density function (PDF). For modelling the frequency components of speech, sparse and spherically symmetric PDFs have been chosen. In this paper, we compare the separation performance of IVA with a group of PDFs where the density is uniformly distributed for the data points of the same l^p-norm value by changing both the value of p and the sparseness. Also we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimension. Simulation results show that sparseness and spherical symmetry together is a good assumption for the speech model in the frequency domain.