Blind Source Separation in Nonlinear Mixture for Colored Sources Using Signal Derivatives

Abstract

International audienceWhile Blind Source Separation (BSS) for linear mixtures has been well studied, the problem for nonlinear mixtures is still thought not to have a general solution. Each of the techniques proposed for solving BSS in nonlinear mixtures works mainly on specific models and cannot be generalized for many other realistic applications. Our approach in this paper is quite different and targets the general form of the problem. In this advance, we transform the nonlinear problem to a time-variant linear mixtures of the source derivatives. The proposed algorithm is based on separating the derivatives of the sources by a modified novel technique that has been developed and specialized for the problem, which is followed by an integral operator for reconstructing the sources. Our simulations show that this method separates the nonlinearly mixed sources with outstanding performance; however , there are still a few more steps to be taken to get to a comprehensive solution which are mentioned in the discussion

Blind Source Separation in Nonlinear Mixtures: Separability and a Basic Algorithm

“…Parts of this work have already been presented in the conference paper [34]. The present paper not only extends the example proposed in that one, but also elaborates, details (with mathematical expressions) and discusses more the proposed method, and provides simulations with noticeable results.…”

Nonlinear blind source separation for sparse sources

“…while we have information about none of h ij (•) functions. The "unknown" values mentioned in (10) and (11) are because, generally, we do not have enough information to separate the outliers (when more than one source are simultaneously active) and they actually cause the error in separation. More discussion on this can be found in the following.…”

“…It is shown through counter examples that ICA does not separate the sources which are non-linearly mixed [9], [10]. Therefore, except a few general approaches which try to investigate the separability of any kind of nonlinear mixture models [11], [12], studies on nonlinear BSS are focused on specific mixture model and source signals, out of which we can name Post Nonlinear (PNL) [13] and Bi-Linear (or Linear Quadratic) mixtures [14], Convolutive Post Nonlinear mixtures [10] and conformal mappings [15].…”

Blind compensation of polynomial mixtures of Gaussian signals with application in nonlinear blind source separation

“…While this problem has been well studied for linear mixtures and many algorithms have been already proposed in this regard [5,6,7,8,9,10], there is not much progress in general nonlinear cases. Consequently, except a few works on nonlinear BSS in general case [11,12], studies on this issue were focused on specific applications with restricted mixing models [13,14,15,16,17,18]. This is why it is thought that in general, roughly speaking, linear mixtures are separable while nonlinear ones are not.…”