13Independent Component and Vector Analysis

Hiroshi Sawada and Zbyněk Koldovský

The concept of blind source separation (BSS) has been introduced in previous chapters. The term “blind” means that no a priori information is used for separation and that all parameters are estimated from observed signals based on assumed (general) properties of the unknown original signals. For example, in Chapter 8, nonnegative matrix factorization (NMF) was introduced as a blind method which relies only on nonnegativity. This chapter is devoted to methods that rely on signal independence, a condition that is often encountered in real‐world situations where signals originate from different processes that have no mutual connection between each other, e.g. speech and noise.

Efficient mathematical models of the independence come from probability theory. The signals to be separated can be modeled as stochastically independent random processes. Then, objective functions that quantify the independence can be derived based on the model and used to find independent signals. This gives rise to independent component analysis (ICA), a tool popular in BSS.

In principle, ICA assumes instantaneous mixing while audio mixtures are convolutive. This chapter is mainly focused on a solution that is called frequency‐domain ICA (FD‐ICA). The convolutive mixture is transformed by short‐time Fourier transform (STFT) into a set of instantaneous mixtures, one mixture per frequency bin. Each frequency is separated using ICA independently ...

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