Insights into the frequency domain ICA approach

In this article, we examine and provide insights into the frequency domain ICA approach. We develop the concept of a dynamic random process to model the frequency domain source signals. It formalizes the concept of signals that are stationary in a frame but exhibit dynamics at the frame level. Frame dynamics is an important characteristics of these signals and this work demonstrates its significant role in the success of the ICA methods in each frequency bin. We show that the independence between the marginal distributions of the source signals in each frequency bin is related to the independence of the frame dynamics of the time domain source signals. The frame dynamics also naturally leads to the marginal distribution of the source signal in each frequency bin being modeled by a Gaussian scale mixture (GSM). Concentrating on the bin-wise ICA methods, a significant contribution of the paper is to show that signals modeled using variance dependent GSM density can be separated using ICA even though they might be dependent on each other as long as the the frame dynamics of the source signals are different almost surely.