Blind Source Separation Using Independent Component Analysis in the Spherical Harmonic Domain

Spherical microphone arrays provide a new and promising tool for the spatial analysis of complex sound fields. Most current frameworks, including HOA (Higher Order Ambisonics), rely on the spherical harmonic expansion of the sound field to form directional beams. Working in the spherical harmonic domain presents a number of advantages that include scalability (keeping the low-order components leads to a lower spatial resolution) and the ability to rotate the sound scene by a simple matrix operation on the signals. In this paper, we show that the spherical harmonic domain also provides significant advantages for the application of ICA (Independent Component Analysis) to separate and localise multiple sound sources. 1. BLIND SOURCE SEPARATION USING INDEPENDENT COMPONENT ANALYSIS Independent Component Analysis (ICA) is a statistical method that was developed in the 1980’s [1] and in this paper we are primarily interested in its application to the blind source separation (BSS) problem, although its applicability is more general. Assume that a vector of time signals, X(t), measured byN sensors are observed. In the BSS problem, we assume that these sensor signals consist of a linear mixture of some underlying source signals, i.e. there exists an N -by-M matrix A and a vector of M signals S(t) so that: