Comparative performance analysis of non orthogonal joint diagonalization algorithms

Mesloub, Ammar; Abed-Meraim, Karim; Belouchrani, Adel

doi:10.1109/wosspa.2013.6602335

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…Another problem that may degrade the performance of the JD methods is the additive noise. Since the rows of the separating matrix are simultaneously extracted, while each of them is corresponding to a specific source, the error propagation may occur in the estimation of the sources when there is additive noise [40].…”

Section: Introductionmentioning

confidence: 99%

Geometry‐based solution of joint diagonalisation in blind source separation

Akhavan

Esmaeili

Soltanian‐Zadeh

2019

IET signal process.

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Joint diagonalisation (JD) of a set of target matrices is a common approach to solve the blind source separation (BSS) problem. In fact, the separating matrix (the inverse of the mixing matrix) of the sources is the joint diagonaliser of the target matrices. In this study, the authors show that each row of the separating matrix maps the target matrices using a linear mapping into the new vectors which are located on a direct line along the corresponding column of the mixing matrix. Based on this geometrical interpretation, the authors propose a method for solving JD problem, which let us estimate the rows of the separating matrix and the columns of the mixing matrix, (i) independently and in parallel, (ii) consecutively or (iii) simultaneously. Simulation results in different scenarios such as additive noise, ill-posed mixing matrix, and high-dimensional data demonstrate the effectiveness of the proposed method relative to state-of-the-art JD methods. The authors also propose an approach to omit the effect of outlier data, which severely degrades parameters estimation. The proposed approach can be used in JD algorithms to improve their performance in the presence of outlier data.

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Section: Introductionmentioning

confidence: 99%

Geometry‐based solution of joint diagonalisation in blind source separation

Akhavan

Esmaeili

Soltanian‐Zadeh

2019

IET signal process.

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“…Minimization of the least-squares (LS) criterion requires the mixing matrix to be mathematically equivalent for approximate joint diagonalization (AJD) of the cross-spectral density matrices of the observed signals. The AJD problem [1,2,3,4,5] entails finding the diagonalizing matrix and diagonal matrices. The LS-AJD estimate is suitable for blind separation of quasistationary sources by estimating the epoch-by-epoch cross-spectral density matrices of the source signal and the mixing matrix simultaneously.…”

Section: Introductionmentioning

confidence: 99%

An alternating least-squares algorithm for approximate joint diagonalization and its application to blind source separation

Oishi

Furukawa

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper presents an iterative alternating least-squares (ALS) algorithm for alternately solving two different leastsquares approximate joint diagonalization (LS-AJD) problems for application to convolutive frequency-domain blind source separation (BSS). The constrained forward-model LS-AJD criterion is minimized to estimate the mixing matrix by using the method of Lagrange multipliers. The other criterion, based on backward modeling, is to find the diagonal matrices by the method of least squares. The method of Lagrange multipliers is well suited for accelerating the convergence of the ALS algorithm. The correlation between the interfrequency power ratios is used to prevent misalignment permutation for the new BSS. Finally, we compare our results with those of conventional BSS in highly reverberant environments.

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Comparative performance analysis of non orthogonal joint diagonalization algorithms

Cited by 2 publications

References 17 publications

Geometry‐based solution of joint diagonalisation in blind source separation

Geometry‐based solution of joint diagonalisation in blind source separation

An alternating least-squares algorithm for approximate joint diagonalization and its application to blind source separation

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