An Extension of Slow Feature Analysis for Nonlinear Blind Source Separation

We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a reliability of more than $90$\%. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources

Precoder design for space-time coded systems over correlated Rayleigh fading channels using convex optimization

A class of computationally efficient linear precoders for space-time block coded multiple-input multiple-output wireless systems is derived based on the minimization of the exact symbol error rate (SER) and its upper bound. Both correlations at the transmitter and receiver are assumed to be present, and only statistical channel state information in the form of the transmit and receive correlation matrices is assumed to be available at the transmitter. The convexity of the design based on SER minimization is established and exploited. The advantage of the developed technique is its low complexity. We also find various relationships of the proposed designs to the existing precoding techniques, and derive very simple closed-form precoders for special cases such as two or three receive antennas and constant receive correlation. The numerical simulations illustrate the excellent SER performance of the proposed precoders

New Negentropy Optimization Schemes for Blind Signal Extraction of Complex Valued Sources

Blind signal extraction, a hot issue in the field of communication signal processing, aims to retrieve the sources through the optimization of contrast functions. Many contrasts based on higher-order statistics such as kurtosis, usually behave sensitive to outliers. Thus, to achieve robust results, nonlinear functions are utilized as contrasts to approximate the negentropy criterion, which is also a classical metric for non-Gaussianity. However, existing methods generally have a high computational cost, hence leading us to address the problem of efficient optimization of contrast function. More precisely, we design a novel “reference-based” contrast function based on negentropy approximations, and then propose a new family of algorithms (Alg.1 and Alg.2) to maximize it. Simulations confirm the convergence of our method to a separating solution, which is also analyzed in theory. We also validate the theoretic complexity analysis that Alg.2 has a much lower computational cost than Alg.1 and existing optimization methods based on negentropy criterion. Finally, experiments for the separation of single sideband signals illustrate that our method has good prospects in real-world applications

Acoustic Echo and Noise Cancellation System for Hand-Free Telecommunication using Variable Step Size Algorithms

In this paper, acoustic echo cancellation with doubletalk detection system is implemented for a hand-free telecommunication system using Matlab. Here adaptive noise canceller with blind source separation (ANC-BSS) system is proposed to remove both background noise and far-end speaker echo signal in presence of double-talk. During the absence of double-talk, far-end speaker echo signal is cancelled by adaptive echo canceller. Both adaptive noise canceller and adaptive echo canceller are implemented using LMS, NLMS, VSLMS and VSNLMS algorithms. The normalized cross-correlation method is used for double-talk detection. VSNLMS has shown its superiority over all other algorithms both for double-talk and in absence of double-talk. During the absence of double-talk it shows its superiority in terms of increment in ERLE and decrement in misalignment. In presence of double-talk, it shows improvement in SNR of near-end speaker signal

Underdetermined blind source separation based on Fuzzy C-Means and Semi-Nonnegative Matrix Factorization

Conventional blind source separation is based on over-determined with more sensors than sources but the underdetermined is a challenging case and more convenient to actual situation. Non-negative Matrix Factorization (NMF) has been widely applied to Blind Source Separation (BSS) problems. However, the separation results are sensitive to the initialization of parameters of NMF. Avoiding the subjectivity of choosing parameters, we used the Fuzzy C-Means (FCM) clustering technique to estimate the mixing matrix and to reduce the requirement for sparsity. Also, decreasing the constraints is regarded in this paper by using Semi-NMF. In this paper we propose a new two-step algorithm in order to solve the underdetermined blind source separation. We show how to combine the FCM clustering technique with the gradient-based NMF with the multi-layer technique. The simulation results show that our proposed algorithm can separate the source signals with high signal-to-noise ratio and quite low cost time compared with some algorithms

Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps

We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.Comment: 12 pages, 6 figure