Denis G. Fantinato

Blind separation of convolutive mixtures over Galois fields

The efforts of Yeredor, Gutch, Gruber and Theis have established a theory of blind source separation (BSS) over finite fields that can be applied to linear and instantaneous mixing models. In this work, the problem is treated for the case of convolutive mixtures, for which the process of BSS must be understood in terms of space-time processing. A method based on minimum entropy and deflation is proposed, and structural conditions for perfect signal recovery are defined, establishing interesting points of contact with canonical MIMO equalization. Simulation results give support to the applicability of the proposed algorithm and also reveal the important role of efficient entropy estimation when the complexity of the mixing system is increased.

Multivariate PDF matching via kernel density estimation

In this work, a measure of similarity based on the matching of multivariate probability density functions (PDFs) is proposed. In consonance with the information theoretic learning (ITL) framework, the affinity comparison between the joint PDFs is performed using a quadratic distance, estimated with the aid of the Parzen window method with Gaussian kernels. The motivation underlying this proposal is to introduce a criterion capable of quantifying, to a significant extent, the statistical dependence present on information sources endowed with temporal and/or spatial structure, like audio, images and coded data. The measure is analyzed and compared with the canonical ITL-based approach - correntropy - for a set of blind equalization scenarios. The comparison includes elements like surface analysis, performance comparison in terms of bit error rate and a qualitative discussion concerning image processing. It is also important to remark that the study includes the application of two computational intelligence paradigms: extreme learning machines and differential evolution. The results indicate that the proposal can be, in some scenarios, a more informative formulation than correntropy.

A Joint Second-Order Statistics and Density Matching-Based Approach for Separation of Post-Nonlinear Mixtures

In the context of Post-Nonlinear (PNL) mixtures, source separation can be performed in a two-stage approach, which encompasses a nonlinear and a linear compensation part. In the former part, it is usually required the knowledge of all the source distributions. In this work, we propose a less restrictive approach, where only one source distribution is needed to be known – here, chosen to be a colored Gaussian. The other sources are only required to present a time structure. The method combines, in a joint-based approach, the use of the second-order statistics (SOS) and the matching of distributions, which shows to be less costly than the classical method of computing the marginal entropy for all sources. The simulation results are favorable to the proposal.

A comparative study of non-MSE criteria in nonlinear equalization

This work studies the application of non-MSE criteria to adapt the linear readout of Extreme Learning Machines (ELMs) in the context of communication channel equalization. A qualitative and experimental analysis is performed, in terms of bit error rate, optimization surface and decision boundary. The results reached by the ELM-based equalizer, considering three different noise models, did not reveal clear advantages of using criteria based on the concepts of error entropy, correntropy, and the L1-norm of the error. Notwithstanding, the observed results motivate a theoretical investigation on the conditions under which the potential discrepancies between the optimal solutions of these criteria may be stressed.

Analysis of a Novel Density Matching Criterion Within the ITL Framework for Blind Channel Equalization

In blind channel equalization, the use of criteria from the field of information theoretic learning (ITL) has already proved to be a promising alternative, since the use of the high-order statistics is mandatory in this task. In view of the several existent ITL propositions, we present in this work a detailed comparison of the main ITL criteria employed for blind channel equalization and also introduce a new ITL criterion based on the notion of distribution matching. The analyses of the ITL framework are held by means of comparison with elements of the classical filtering theory and among the studied ITL criteria themselves, allowing a new understanding of the existing ITL framework. The verified connections provide the basis for a comparative performance analysis in four practical scenarios, which encompasses discrete/continuous sources with statistical independence/dependence, and real/complex-valued modulations, including the presence of Gaussian and non-Gaussian noise. The results indicate the most suitable ITL criteria for a number of scenarios, some of which are favorable to our proposition.

A second-order statistics method for blind source separation in post-nonlinear mixtures

Abstract In the context of nonlinear Blind Source Separation (BSS), the Post-Nonlinear (PNL) model is of great importance due to its suitability for practical nonlinear problems. Under certain mild constraints on the model, Independent Component Analysis (ICA) methods are valid for performing source separation, but requires use of Higher-Order Statistics (HOS). Conversely, regarding the sole use of the Second-Order Statistics (SOS), their study is still in an initial stage. In that sense, in this work, the conditions and the constraints on the PNL model for SOS-based separation are investigated. The study encompasses a time-extended formulation of the PNL problem with the objective of extracting the temporal structure of the data in a more extensive manner, considering SOS-based methods for separation, including the proposition of a new one. Based on this, it is shown that, under some constraints on the nonlinearities and if a given number of time delays is considered, source separation can be successfully achieved, at least for polynomial nonlinearities. With the aid of metaheuristics called Differential Evolution and Clonal Selection Algorithm for optimization, the performances of the SOS-based methods are compared in a set of simulation scenarios, in which the proposed method shows to be a promising approach.

Using Taylor Series Expansions and Second-Order Statistics for Blind Source Separation in Post-Nonlinear Mixtures

In the context of Post-Nonlinear (PNL) mixtures, source separation based on Second-Order Statistics (SOS) is a challenging topic due to the inherent difficulties when dealing with nonlinear transformations. Under the assumption that sources are temporally colored, the existing SOS-inspired methods require the use of Higher-Order Statistics (HOS) as a complement in certain stages of PNL demixing. However, a recent study has shown that the sole use of SOS is sufficient for separation if certain constraints on the separation system are obeyed. In this paper, we propose the use of a PNL separating model based on constrained Taylor series expansions which is able to satisfy the requirements that allow a successful SOS-based source separation. The simulation results corroborate the proposal effectiveness.

Gaussian Processes for Source Separation in Overdetermined Bilinear Mixtures

In this work, we consider the nonlinear Blind Source Separation (BSS) problem in the context of overdetermined Bilinear Mixtures, in which a linear structure can be employed for performing separation. Based on the Gaussian Process (GP) framework, two approaches are proposed: the predictive distribution and the maximization of the marginal likelihood. In both cases, separation can be achieved by assuming that the sources are Gaussian and temporally correlated. The results with synthetic data are favorable to the proposal.