Recent study in proposes a joint diagonalization approach of cross cumulant matrices to solve the complex IVA problem.
However, such general joint block diagonalization approaches do not take the intrinsic structure of the IVA problem into account. In particular, joint block diagonalization approaches are shown to be effective methods for solving the ISA problem, cf.
On the other hand, tensorial approaches are efficient and richly available to solve both the ICA and ISA problems. The main difficulty of these contrast function based approaches lies in estimating the unknown distribution of the sources, which usually requires a large number of observations. In the current literature, the majority of IVA algorithms are based on optimizing certain contrast functions, cf. Besides its application in convolutive BSS problem, IVA has also recently been applied to analyze multivariate Gaussian models, cf. To avoid this problem, a new approach named independent vector analysis (IVA) has been proposed in. After solving the subproblems individually, the final stage faces the challenge of aligning all statistically dependent components from different groups, which is referred to as the permutation problem. After transferring the convolutive observations into the frequency domain via short-time Fourier transforms, the convolutive BSS problem results in a collection of instantaneous complex BSS problems in each frequency bin. Ī special form of ISA arises in solving the BSS problem with convolutive mixtures. Such problems can be tackled by a technique now referred to as multidimensional independent component analysis (MICA), or independent subspace analysis (ISA). However, in many applications, there exist groups of signals of interest, where components from different groups are mutually statistically independent indeed, but where mutual statistical dependence occurs between components in the same group. Application of the standard ICA model is often limited, since it requires mutual statistical independence between all individual components. BSS aims to recover source signals from the observed mixtures, without knowing either the distribution of the sources or the mixing process. Independent component analysis (ICA) is a standard statistical tool for solving the blind source separation (BSS) problem.
A conjugate gradient algorithm on the appropriate manifold setting is developed. The underlying geometry of the problem is investigated together with a critical point analysis of the resulting cost function. The latter is in contrast to most IVA approaches up to date. 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.
In this article, we propose a matrix joint diagonalization approach to solve the complex IVA problem. Despite the rich availability of efficient tensorial approaches to the standard ICA problem, these methods have not been explored considerably for IVA. 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. 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.
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