An e cient procedure for the blind inversion of a nonlinear Wiener system is proposed. We proved that the problem can be expressed as a problem of blind source separation in nonlinear mixtures, for which a solution has been recently proposed. Based on a quasi-nonparametric relative gradient descent, the proposed algorithm can perform e ciently even in the presence of hard distortions.

In the linear case statistical independence is a sufficient criterion for performing blind source separation. In the nonlinear case, however, it leaves an ambiguity in the solutions that has to be resolved by additional criteria. Here we argue that temporal slowness complements statistical independence well and that a combination of the two leads to unique solutions of the nonlinear blind sourc...

In this work, we deal with the problem of nonlinear blind source separation (BSS). We propose a new method for BSS in overdetermined linear-quadratic (LQ) mixtures. By exploiting the assumption that the sources are sparse in a transformed domain, we define a framework for canceling the nonlinear part of the mixing process. After that, separation can be conducted by linear BSS algorithms. Experi...

Two major approaches for Blind Source Separation (BSS) are respectively based on the maximum likelihood (ML) principle and mutual information (MI) minimization. They have been mainly studied for simple linear mixtures. We here show that they additionally involve indirect functional dependencies for general nonlinear mixtures. Moreover, the notations commonly employed by the BSS community in cal...

Research results from so-called “classical” separation logics are not easily ported to so-called “intuitionistic” separation logics, and vice versa. Basic questions like, “Can the frame rule be proved independently of whether the programming language is garbage-collected?” “Can amortized resource analysis be ported from one separation logic to another?” should be straightforward. But they are n...

This paper presents a new statistical model for speech signals, which consists of a time-invariant dictionary incorporating a set of the power spectral densities of excitation signals and a set of all-pole filters where the gain of each pair of excitation and filter elements is allowed to vary over time. We use this model to develop a combined blind separation and dereverberation method for spe...

Blind source separation based on time-frequency distributions (TFD’s) allows the separation of Gaussian sources with identical spectral shape but different t-f localization properties. As TFD’s spread noise power while localizing the source energy in the t-f domain, the time-frequency BSS is characterized by robustness of separation and improved overall performance. However, quadratic TFD’s, wh...

We compare independent component analysis (ICA) [Bell and Sejnowski, 1995] to an alternative method [Fisher and Principe, 1996] for blind source separation of instantaneous linear mixtures. The method and its application to blind source separation of instantaneous linear mixtures is reviewed. Empirical results separating sources of varying kurtosis and a limited number of samples are presented....

The task of recovering a set of unknown sources from another set of mixtures directly observable and little more information about the way they were mixed is called the blind source separation problem. If the assumption in order to obtain the original sources is their statistical independence, then ICA (Independent Component Analysis) may be the technique to recover the signals. In this contrib...