Iván Durán-Díaz

Blind Separation of Dependent Sources With a Bounded Component Analysis Deflationary Algorithm

The problem of blind source separation of complex-valued sources from a linear mixture is addressed. We propose a deflationary algorithm for the sequential recovery of a set of communication signals, where each source is extracted by performing a Bounded Component Analysis of the linear mixture. The contribution of each recovered source to the observations is removed by minimizing its convex perimeter, without using second-order statistics. This implies to run a gradient descent algorithm several times. In order to accelerate the convergence, we have derived a fast step size that exploits the second-order information of the cost function by means of the augmented Hessian matrix. Computer simulations show that the proposed method is able to blindly separate even dependent sources, as long as they satisfy the BCA separability conditions. Also, the speed of convergence of this novel step size is compared with other classical approaches.

Cyclic maximization of non-Gaussianity for blind signal extraction of complex-valued sources

This article presents a new algorithm for the blind extraction of communications sources (complex-valued sources) through the maximization of negentropy approximations based on nonlinearities. A criterion based on the square modulus of a nonlinearity of the output is used. We decouple the arguments of the criterion so that the algorithm maximizes it cyclically with respect to each argument by means of the Cauchy-Schwarz inequality. A proof of the ascent of the objective function after each iteration is also provided. Numerical simulations corroborate the good performance of the proposed algorithm in comparison with the existing methods.

A contrast function based on generalized divergences for solving the permutation problem in convolved speech mixtures

In this paper, we propose a method for solving the permutation problem that is inherent in the separation of convolved mixtures of speech signals in the time-frequency domain. The proposed method obtains the solution through maximization of a contrast function that exploits the similarity of the temporal envelope of the speech spectrum. For this purpose, the contrast calculation uses a global measure of similarity based on the recently developed family of generalized Alpha-Beta divergences, which depend on two tuning parameters, alpha and beta. This parameterization is exploited to best measure the similarity of the speech spectrum and to obtain solutions that are robust against noise and outliers. The ability of this contrast function to solve the permutation problem is supported by a theoretical study that shows that for a simple time-frequency speech model, the contrast value reaches its maximum when the estimated components are properly aligned. Several performance studies demonstrate that the proposed method maintains a high level of permutation correction accuracy in a wide variety of acoustic environments. Moreover, it produces better results than other state-of-the-art methods for solving permutations in highly reverberant environments.

Fast communication: Criterion for signal extraction in underdetermined mixtures of bounded support

This work studies the problem of recovering a complex signal (source) from an underdetermined linear mixture of bounded sources. We assume some a priori information of the desired signal in the form of a training sequence and complete absence of knowledge from the other sources, except for their bounded character. The main contribution of this letter is the proposal of a bounded component analysis of the training error that tries to condense the relevant information of the observations in a linear estimate of the desired signal. This subspace can be later used for subsequent refined estimation of the signal of interest. Simulations corroborate the good performance of the proposed method in high SNR scenarios.

A Joint Optimization Criterion for Blind DS-CDMA Detection

This paper addresses the problem of the blind detection of a desired user in an asynchronous DS-CDMA communications system with multipath propagation channels. Starting from the inverse filter criterion introduced by Tugnait and Li in 2001, we propose to tackle the problem in the context of the blind signal extraction methods for ICA. In order to improve the performance of the detector, we present a criterion based on the joint optimization of several higher-order statistics of the outputs. An algorithm that optimizes the proposed criterion is described, and its improved performance and robustness with respect to the near-far problem are corroborated through simulations. Additionally, a simulation using measurements on a real software-radio platform at 5 GHz has also been performed.

The Minimum Risk Principle That Underlies the Criteria of Bounded Component Analysis

This paper studies the problem of the blind extraction of a subset of bounded component signals from the observations of a linear mixture. In the first part of this paper, we analyze the geometric assumptions of the observations that characterize the problem, and their implications on the mixing matrix and latent sources. In the second part, we solve the problem by adopting the principle of minimizing the risk, which refers to the encoding complexity of the observations in the worst admissible situation. This principle provides an underlying justification of several bounded component analysis (BCA) criteria, including the minimum normalized volume criterion of the estimated sources or the maximum negentropy-likelihood criterion with a uniform reference model for the estimated sources. This unifying framework can explain the differences between the criteria in accordance with their considered hypotheses for the model of the observations. This paper is first presented for the case of the extraction of a complex and multidimensional source, and later is particularized for the case of the extraction of subsets of 1-D complex sources. The results also hold true in the case of real signals, where the obtained criteria for the extraction of a set of 1-D sources usually coincide with the existing BCA criteria.

Initialization method for speech separation algorithms that work in the time-frequency domain

This article addresses the problem of the unsupervised separation of speech signals in realistic scenarios. An initialization procedure is proposed for independent component analysis (ICA) algorithms that work in the time-frequency domain and require the prewhitening of the observations. It is shown that the proposed method drastically reduces the permuted solutions in that domain and helps to reduce the execution time of the algorithms. Simulations confirm these advantages for several ICA instantaneous algorithms and the effectiveness of the proposed technique in emulated reverberant environments.

Solving permutations in frequency-domain for blind separation of an arbitrary number of speech sources

Blind separation of speech sources in reverberant environments is usually performed in the time-frequency domain, which gives rise to the permutation problem: the different ordering of estimated sources for different frequency components. A two-stage method to solve permutations with an arbitrary number of sources is proposed. The suggested procedure is based on the spectral consistency of the sources. At the first stage frequency bins are compared with each other, while at the second stage the neighboring frequencies are emphasized. Experiments for perfect separation situations and for live recordings show that the proposed method improves the results of existing approaches.

A two-stage Independent Component Analysis-based method for blind detection in CDMA systems

We propose an ICA-based method for blind detection of users in asynchronous DS-CDMA communications systems with multipaths channels with the only knowledge of the desired user@?s code. The method can handle both the uplink and the downlink situations, since it does not require the synchronism between users. We convert the received cyclostationary signal into an observations vector that follows the ICA model with instantaneous mixture. The selection of the estimated source is carried out by means of the desired user@?s code. Unlike previous works, we avoid to project the results after each iteration. Instead, we introduce a preprocessing based on a linear transformation of the data that enforces the extraction vector to lie in the desired user@?s subspace. The detection is done in two stages. The second stage is a fine tuning in which the constraint is removed from the data in order to obtain more accurate results. Computer simulations show that the proposed method compares favorably with other well-known methods, in terms of mean-square error (MSE) of the output, symbol error rate and robustness against the near-far problem.

Convergence study of a Bounded Component Analysis algorithm

This work presents the convergence study of a component analysis algorithm that is designed for extracting a source from a linear mixture of bounded sources. The algorithm implements the parsimonious criterion of finding the linear projection of observations whose convex support has the minimum normalised perimeter. In a noiseless situation, our stability analysis provides recommendations for setting the step size of the algorithm. These recommendations are designed to guarantee the global monotonic convergence to the source that is closest to the algorithms initialisation (in a given sense) while at the same time maintaining a fast local convergence rate in the neighborhood of this solution. In the absence of noise, these theoretical results have been corroborated by means of computer simulations. Furthermore, we have shown that in noisy mixtures, the performance of the algorithms is improved by eliminating the bias that noise creates. HighlightsWe analyse the convergence of a Bounded Component Analysis algorithm.A suitable set of coefficients determine the behaviour of the iterations.We propose practical step sizes to guarantee the stability and other conditions.We provide a modification to improve the algorithm in the presence of noise.To guarantee the stability, we use a step size usually slower than the N-R one.