Everton Z. Nadalin

Unsupervised Processing of Geophysical Signals: A Review of Some Key Aspects of Blind Deconvolution and Blind Source Separation

This article reviews some key aspects of two important branches in unsupervised signal processing: blind deconvolution and blind source separation (BSS). It also gives an overview of their potential application in seismic processing, with an emphasis on seismic deconvolution. Finally, it presents illustrative results of the application, on both synthetic and real data, of a method for seismic deconvolution that combines techniques of blind deconvolution and blind source separation. Our implementation of this method contains some improvements overthe original method in the literature described.

An immune-inspired information-theoretic approach to the problem of ICA over a Galois field

The problem of independent component analysis (ICA) was firstly formulated and studied in the context of real-valued signals and mixing models, but, recently, an extension of this original formulation was proposed to deal with the problem within the framework of finite fields. In this work, we propose a strategy to deal with ICA over these fields that presents two novel features: (i) it is based on the use of a cost function built directly from an estimate of the mutual information and (ii) it employs an artificial immune system to perform the search for efficient separating matrices, in contrast with the existing techniques, which are based on search schemes of an exhaustive character. The new proposal is subject to a comparative analysis based on different simulation scenarios and the work is concluded by an analysis of perspectives of practical application to digital and genomic data mining.

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.

Fast communication: The modified MEXICO for ICA over finite fields

In 2007, a theory of ICA over finite fields emerged and an algorithm based on pairwise comparison of mixtures, called MEXICO, was developed to deal with this new problem. In this letter, we propose improvements in the method that, according to simulations in GF(2) and GF(3) scenarios, lead to a faster convergence and better separation results, increasing the application possibilities of the new theory in the context of large databases.

A modified version of the MEXICO algorithm for performing ICA over Galois fields

The theory of ICA over finite fields, established in the last five years, gave rise to a corpus of different separation strategies, which includes an algorithm based on the pairwise comparison of mixtures, called MEXICO. In this work, we propose an alternative version of the MEXICO algorithm, with modifications that - as shown by the results obtained for a number of representative scenarios - lead to performance improvements in terms of the computational effort required to reach a certain performance level, especially for an elevated number of sources. This parsimony can be relevant to enhance the applicability of the new ICA theory to data mining in the context of large discrete-valued databases.

Blind extraction of the sparsest component

In this work, we present a discussion concerning some fundamental aspects of sparse component analysis (SCA), a methodology that has been increasingly employed to solve some challenging signal processing problems. In particular, we present some insights into the use of l1 norm as a quantifier of sparseness and its application as a cost function to solve the blind source separation (BSS) problem. We also provide results on experiments in which source extraction was successfully made when we performed a search for sparse components in the mixtures of sparse signals. Finally, we make an analysis of the behavior of this approach on scenarios in which the source signals are not sparse.

Perceptually controlled doping for audio source separation

The separation of an underdetermined audio mixture can be performed through sparse component analysis (SCA) that relies however on the strong hypothesis that source signals are sparse in some domain. To overcome this difficulty in the case where the original sources are available before the mixing process, the informed source separation (ISS) embeds in the mixture a watermark, which information can help a further separation. Though powerful, this technique is generally specific to a particular mixing setup and may be compromised by an additional bitrate compression stage. Thus, instead of watermarking, we propose a ‘doping’ method that makes the time-frequency representation of each source more sparse, while preserving its audio quality. This method is based on an iterative decrease of the distance between the distribution of the signal and a target sparse distribution, under a perceptual constraint. We aim to show that the proposed approach is robust to audio coding and that the use of the sparsified signals improves the source separation, in comparison with the original sources. In this work, the analysis is made only in instantaneous mixtures and focused on voice sources.

Proposal and Analysis of a FitzHugh-Nagumo Neuronal Circuit

Abstract In this work, we present an original implementation of a circuit to perform the analog simulation of the FitzHugh-Nagumo neuron model. The proposed circuit is tested for different stimulation patterns and provides results very similar to those derived from a more widespread digital computation approach, with a significantly better performance in terms of processing time and a noticeable robustness to parameter modification. Moreover, the results also reveal the possibility of chaotic behavior for distinct experimental setups, which may be essential for the process of learning and perception in biological systems.

Application of Robust Principal Component Analysis to Seismic Data Processing

The Singular Value Decomposition (SVD) is a useful tool in seismic data processing and has been applied in many problems. In the past several years, there is a growing interest in the application of extensions of the ordinary SVD to treat seismic data. For instance, recent works have shown that the combination of SVD with an Independent Component Analysis (ICA) approach can provide interesting results in problems such as wavefield separation. In this work, we investigate the application of new decomposition framework, known as robust principal component analysis (PCA). This method, which can also be seen as an extension of the SVD approach, searches for a data representation composed of a sparse term and a low-rank term. We show by means of simulations that such a feature lead to better results than those obtained by the SVD and SVD-ICA approaches in the task of separating hyperbolic events from horizontal ones in noisy data. Moreover, the robust PCA decomposition provided a good trade-off between computational complexity and precision in the separation of two close events.

An MSE-based theoretical limit to the performance of linear source extraction and equalization methods in undermodeled scenarios

This paper presents a simple and, to a certain extent, surprising result for Source Separation in an underdetermined scenario: without loss of generality, under the restriction that all sources have unit power, the sum of the residual mean-squared errors (MMSE) obtained after the estimation of all the sources is given by the difference between the number of sources and the number of sensors. This result can be extended to the case of single-input single-output (SISO) equalization, in which the obtained limit depends on the relationship between the length of the channel and equalizer impulse responses.