Abstract
Independent vector analysis (IVA) is a special form of independent component analysis (ICA), which has demonstrated its prominent performance in solving convolutive blind source separation (BSS) problems in the frequency domain. Most IVA algorithms are based on optimizing certain contrast functions, where the main difficulty of these approaches lies in finding a reliable and fast estimation of the unknown distribution of sources. Despite the rich availability of efficient tensorial approaches to the standard ICA problem, these methods have not been explored considerably for IVA. In this article, we propose a matrix joint diagonalization approach to solve the complex IVA problem. The new factorization neither relies on a whitening process, nor does it require an estimate of the joint probability distribution of the dependent signal groups. The latter is in contrast to most IVA approaches up to date. The underlying geometry of the problem is investigated together with a critical point analysis of the resulting cost function. A conjugate gradient algorithm on the appropriate manifold setting is developed.
Highlights
Independent component analysis (ICA) is a standard statistical tool for solving the blind source separation (BSS) problem
8 Conclusion We propose a matrix joint diagonalization approach to solve the complex Independent vector analysis (IVA) problem which does not rely on a pre-whitening step nor on the estimation of the unknown distribution of the sources
This leads in a natural way to a smooth manifold structure that we call complex oblique projective manifold, due to its close relation to the oblique manifold which consists of invertible matrices with normalized columns
Summary
Independent component analysis (ICA) is a standard statistical tool for solving the blind source separation (BSS) problem. In many applications, there exist groups of signals of interest, where components from different groups are mutually statistically independent but where mutual statistical dependence occurs between components in the same group. Such problems can be tackled by a technique referred to as multidimensional independent component analysis (MICA) [1], or independent subspace analysis (ISA) [2]. Joint block diagonalization approaches are shown to be effective methods for solving the ISA problem, cf [11,12], and are inherently applicable to IVA. Recent study in [13] proposes a joint diagonalization approach of cross cumulant matrices to solve the complex IVA problem. An efficient conjugate gradient (CG) based IVA algorithm is proposed, and numerical experiments are provided to demonstrate the convergence properties of the proposed CG algorithm, and to compare its performance with two recently developed IVA algorithms in terms of separation quality
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