Blind separation of sources, Part II: problems statement
Signal Processing
Blind separation of sources, Part III: stability analysis
Signal Processing
The Handbook of Mathematics and Computational Science
The Handbook of Mathematics and Computational Science
Three easy ways for separating nonlinear mixtures?
Signal Processing - Special issue on independent components analysis and beyond
Blind separation of linear-quadratic mixtures of real sources using a recurrent structure
IWANN '03 Proceedings of the 7th International Work-Conference on Artificial and Natural Neural Networks: Part II: Artificial Neural Nets Problem Solving Methods
IEEE Transactions on Signal Processing
Source separation in post-nonlinear mixtures
IEEE Transactions on Signal Processing
Self-adaptive source separation. II. Comparison of the direct,feedback, and mixed linear network
IEEE Transactions on Signal Processing
Analysis of the convergence properties of self-normalized sourceseparation neural networks
IEEE Transactions on Signal Processing
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Blind source separation of overdetermined linear-quadratic mixtures
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Bayesian Source Separation of Linear and Linear-quadratic Mixtures Using Truncated Priors
Journal of Signal Processing Systems
Separation of sparse signals in overdetermined linear-quadratic mixtures
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Hi-index | 0.08 |
While most reported source separation methods concern linear mixtures, we here address the nonlinear case. Even for a known nonlinear mixing model, creating a system which implements the exact inverse of this model is not straightforward for most nonlinear models. We first define a large class of possibly nonlinear models, i.e. ''additive-target mixtures'' (ATM), for which this inversion may be achieved thanks to the nonlinear recurrent networks that we propose to this end. We then further extend this approach to the ''extractable-target mixtures'' (ETM) that we also introduce in this paper. We illustrate these general approaches for two specific classes of mixtures, i.e. linear-quadratic mixtures, and quadratic ones. We then focus on our networks suited to linear-quadratic mixtures and we provide a detailed analysis of their equilibrium points and their stability. This allows us to introduce an automated procedure for selecting their free weights so as to guarantee the stability of a separating point for any source signals. Test results show the effectiveness of this approach for various types of source signals.