A Unifying Criterion for Blind Source Separation and Decorrelation: Simultaneous Diagonalization of Correlation Matrices
نویسندگان
چکیده
Blind source separation and blind output decorrelation are two well-known problems in signal processing. For instantaneous mixtures, blind source separation is equivalent to a generalized eigen-decomposition, while blind output decorrelation can be considered as an iterative method of output orthogonalization. We propose a steepest descent procedure on a new cost function based on the Frobenius norm which measures the diagonalization of correlation matrices to perform blind source separation as well as blind decorrelation. The method is applicable to both stationary and nonstationary signals and instantaneous as well as convolutive mixture models. Simulation results by Monte Carlo trials are provided to show the consistent performance of the proposed algorithm.
منابع مشابه
Convolutive Decorrelation Procedures for Blind Source Separation
Convolutive decorrelation algorithms form a class of powerful algorithms for blind source separation. In contrast to ICA, they are based on vanishing second order cross correlation functions between sources. We provide an analyze an unifying approach for convolu-tive decorrelation procedures. The convolutive decor-relation procedures impose the problem of simultaneously diagonalizing a number o...
متن کاملApproximate diagonalization approach to blind source separation with a subset of matrices
In Blind Source Separation problems it is assumed that the approximate diagonalization of a matrix set achieves more robust solutions than the simultaneous diagonalization of a matrix pencil. In this work we will analyse approximate diagonalization methods using a generalized eigendecomposition (GED) of any pair of a given matrix set. The constraints of GED solutions provide a criterion to choo...
متن کاملA generalization of joint-diagonalization criteria for source separation
In the field of blind source separation, joint-diagonalization-based approaches constitute an important framework, leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices (JADE) and simultaneous third-order tensor diagonalization (STOTD) algorithms. However, they are often restricted to the case of cumulants of order four. In this paper, we extend the...
متن کاملSimultaneous diagonalization: the asymmetric, low-rank, and noisy settings
Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint diagonalization to low-rank and asymmetric matrices, and we also provide extensions to the perturbation analysis of these methods. Our results allow joint diagonalizati...
متن کاملA new non-orthogonal approximate joint diagonalization algorithm for blind source separation
A new algorithm for approximate joint diagonalization of a set of matrices is presented. Using a weighted leastsquares (WLS) criterion, without the orthogonality constraint, it is compared with an analoguous algorithm for blind source separation (BSS). The criterion of our algorithm is on the separating matrix while the other is on the mixing matrix. The convergence of our algorithm is proved u...
متن کامل