Journal ArticleDOI
Blind separation of Gaussian sources via second-order statistics with asymptotically optimal weighting
TLDR
It is shown that substantial improvement over SOBI can be attained when the joint diagonalization is transformed into a properly weighted nonlinear least squares problem.Abstract:
Blind separation of Gaussian sources with different spectra can be attained using second-order statistics. The second-order blind identification (SOBI) algorithm, proposed by Belouchrani et al. (1997), uses approximate joint diagonalization. We show that substantial improvement over SOBI can be attained when the joint diagonalization is transformed into a properly weighted nonlinear least squares problem. We provide an iterative solution and derive the optimal weights for our weights-adjusted SOBI (WASOBI) algorithm. The improvement is demonstrated by analysis and simulations.read more
Citations
More filters
Journal ArticleDOI
Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation
TL;DR: This work proposes an iterative alternating-directions algorithm for minimizing the WLS criterion with respect to a general (not necessarily orthogonal) diagonalizing matrix and proves weak convergence in the sense that the norm of parameters update is guaranteed to fall below any arbitrarily small threshold within a finite number of iterations.
Journal ArticleDOI
Diversity in Independent Component and Vector Analyses: Identifiability, algorithms, and applications in medical imaging
TL;DR: This overview article presents ICA, and then its generalization to multiple data sets, IVA, both using mutual information rate, and presents conditions for the identifiability of the given linear mixing model and derive the performance bounds.
Journal ArticleDOI
Fast Approximate Joint Diagonalization Incorporating Weight Matrices
Petr Tichavsky,Arie Yeredor +1 more
TL;DR: A new low-complexity approximate joint diagonalization (AJD) algorithm, which incorporates nontrivial block-diagonal weight matrices into a weighted least-squares (WLS) AJD criterion, is proposed, giving rise to fast implementation of asymptotically optimal BSS algorithms in various scenarios.
Journal ArticleDOI
Blind source separation, wavelet denoising and discriminant analysis for EEG artefacts and noise cancelling
R. Romo Vázquez,R. Romo Vázquez,Hugo Vélez-Pérez,Hugo Vélez-Pérez,Radu Ranta,V. Louis Dorr,Didier Maquin,Louis Maillard +7 more
TL;DR: The proposed methodology successfully rejected a good percentage of artefacts and noise, while preserving almost all the cerebral activity, and presents a very good improvement compared with recorded raw EEG: 96% of the EEGs are easier to interpret.
Journal ArticleDOI
Independent Component Analysis by Entropy Bound Minimization
Xi-Lin Li,Tulay Adali +1 more
TL;DR: A novel (differential) entropy estimator is introduced where the maximum entropy bound is used to approximate the entropy given the observations, and is computed using a numerical procedure thus resulting in accurate estimates for the entropy.
References
More filters
Journal ArticleDOI
A blind source separation technique using second-order statistics
TL;DR: A new source separation technique exploiting the time coherence of the source signals is introduced, which relies only on stationary second-order statistics that are based on a joint diagonalization of a set of covariance matrices.
Journal ArticleDOI
Jacobi Angles for Simultaneous Diagonalization
TL;DR: This note gives the required Jacobi angles in close form for simultaneous diagonalization of several matrices.
Journal ArticleDOI
A least-squares approach to joint diagonalization
Mati Wax,J. Sheinvald +1 more
TL;DR: A new least-squares-based approach for the joint diagonalization problem arising in blind beamforming is presented and the resulting estimation criterion turns out to coincide with that proposed by Cardoso and Souloumaic on intuitive grounds, thus establishing the optimality of their criterion in the least-Squares (LS) sense.
Dissertation
Blind Signal Separation by Second Order Statistics
TL;DR: The problem of separating uncorrelated signals from equally many observed mixtures is considered and the Cramer Rao Lower Bound is derived, the lowest possible variance achievable of the estimated parameters, given Gaussian signals.