Theoretical Studies and Algorithms Regarding the Solution of Non-invertible Nonlinear Source Separation

International audienceIn this paper, we analyse and solve a source separation problem based on a mixing model that is nonlinear and non-invertible at the space of mixtures. The model is relevant considering it may represent the data obtained from ion-selective electrode arrays. We apply a new approach for solving the problems of local stability of the recurrent network previously used in the literature, which allows for a wider range of source concentration. In order to achieve this, we utilize a second-order recurrent network which can be shown to be locally stable for all solutions. Using this new network and the priors that chemical sources are continuous and smooth, our proposal performs better than the previous approach

Application of Blind Source Separation Methods to Ion-Selective Electrode Arrays in Flow-Injection Analysis

International audienceAs shown recently, the interference problem typical of ion-selective electrodes can be dealt with via smart arrays adjusted by blind source separation methods. In this letter, we resume this study and show that such an approach can be applied even when faced with a limited number of samples acquired through flow-injection analysis

A Sparsity-Based Method for Blind Compensation of a Memoryless Nonlinear Distortion: Application to Ion-Selective Electrodes

International audience— In this paper, we propose a method for blind compensation of a memoryless nonlinear distortion. We assume as prior information that the desired signal admits a sparse representation in a transformed domain that should be known in advance. Then, given that a nonlinear distortion tends to generate signals that are less sparse than the desired one, our proposal is to build a compensating function model that gives rise to a maximally sparse signal. The implementation of this proposal has, as central elements, a criterion built upon an approximation of the 0-norm, the use of polynomial functions as compensating structures, and an optimization strategy based on sequential quadratic programming. We provide a theoretic analysis for an 0-norm criterion and results considering synthetic data. We also employ the method in an actual application related to chemical analysis via ion-selective electrode arrays

An overview of signal processing issues in chemical sensing

International audienceThis tutorial paper aims at summarizing some problems, ranging from analytical chemistry to novel chemical sensors, that can be addressed with classical or advanced methods of signal and image processing. We gather them under the denomination of "chemical sensing". It is meant to introduce the special session "Signal Processing for Chemical Sensing" with a large overview of issues which have been and remain to be addressed in this application domain, including chemical analysis leading to PARAFAC/tensor methods, hyper spectral imaging, ion-sensitive sensors, artificial nose, chromatography, mass spectrometry, etc. For enlarging and illustrating the points of view of this tutorial, the invited papers of the session consider other applications (NMR, Raman spectroscopy, recognition of explosive compounds, etc.) addressed by various methods, e.g. source separation, Bayesian, and exploiting typical chemical signal priors like positivity, linearity, unit-concentration or sparsity

Non-negative Independent Component Analysis Algorithm Based on 2D Givens Rotations and a Newton Optimization

ISBN 978-3-642-15994-7, SoftcoverInternational audienceIn this paper, we consider the Independent Component Analysis problem when the hidden sources are non-negative (Non-negative ICA). This problem is formulated as a non-linear cost function optimization over the special orthogonal matrix group SO(n). Using Givens rotations and Newton optimization, we developed an effective axis pair rotation method for Non-negative ICA. The performance of the proposed method is compared to those designed by Plumbley and simulations on synthetic data show the efficiency of the proposed algorithm

A Blind Source Separation Method for Chemical Sensor Arrays based on a Second-order mixing model

International audienceIn this paper we propose a blind source separation method to process the data acquired by an array of ion-selective electrodes in order to measure the ionic activity of different ions in an aqueous solution. While this problem has already been studied in the past, the method presented differs from the ones previously analyzed by approximating the mixing function by a second-degree polynomial, and using a method based on the differential of the mutual information to adjust the parameter values. Experimental results, both with synthetic and real data, suggest that the algorithm proposed is more accurate than the other models in the literature

Blind Source Separation of Overdetermined Linear-Quadratic Mixtures

ISBN 978-3-642-15994-7, SoftcoverInternational audienceThis work deals with the problem of source separation in overdetermined linear-quadratic (LQ) models. Although the mixing model in this situation can be inverted by linear structures, we show that some simple independent component analysis (ICA) strategies that are often employed in the linear case cannot be used with the studied model. Motivated by this fact, we consider the more complex yet more robust ICA framework based on the minimization of the mutual information. Special attention is given to the development of a solution that be as robust as possible to suboptimal convergences. This is achieved by defining a method composed of a global optimization step followed by a local search procedure. Simulations confirm the effectiveness of the proposal

Design and development of a multichannel potentiometer for monitoring an electrode array and its application in flow analysis

A versatile potentiometer that works with electrode arrays in flow injection and/or monosegmented flow systems is described. The potentiometer is controlled by a microcomputer that allows individual, sequential multiplexed or random accesses to eight electrodes while employing only one reference electrode. The instrument was demonstrated by monitoring an array of seven flow-through ion-selective electrodes for Ag+ and for three electrodes for Cl-, Ca2+ and K+. The figures of merit of the individual and multiplexed (summed) readings of the electrode array were compared. The absolute standard deviation of the measurements made by summing the potential of two or more electrodes was maintained constant, thus improving the precision of the measurements. This result shows that an attempt to combine the signals of the electrodes to produce a more intense signal in the Hadamard strategy is feasible and accompanied by a proportional improvement in the precision of individual measurements. The preliminary tests suggest that the system can allow for 270 determinations per hour, with a linear range from 1.0 × 10-2 to 1.0 × 10-4 mol l-1 for the three di¡erent analytes. Detection limits were estimated as 3.1 × 10-5, 3.0 × 10-6 and 1.0 × 10-5 mol l-1 for Cl-, Ca2+ and K+, respectively