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In this study we investigate the approximation of the solutions of certain elliptic boundary value problems by the Method of Fundamental Solutions (MFS). In particular, we study the case in which the number of singularities (sources) exceeds the number of boundary (collocation) points. Two algorithms are proposed for the calculation of optimal solutions. An efficient numerical algorithm for the Dirichlet problem for Laplace's equation in the disk is described. Numerical experiments for a variety of geometries in two and three dimensions are presented. © 2009 IMACS. 60 4 337 357 Cited By :3

Let us consider a parameter estimation for linear model where the ensemble of N sensors acquire enough measurements to estimate the set of p-parameters θ = [θ 1 , …, θ p ]T, but the set of T measurements acquired by each sensor is not enough and the estimation problem is under-determined (T < p < NT). Rather than collecting all the NT measurements into a common fusion center as for a centralized estimate, in this paper we investigate the use of consensus methods to let each sensor to reach the same estimate without the need to exchange the measurements. More specifically, based on the local regressor model, each node solves locally an under-determined least-norm and the set of estimated parameters are exchanged with the neighbours jointly with the subspace corresponding righ eigenvectors. The weighted consensus iterations tailored for these settings refine these estimates up to the consensus. For a network of connected nodes, the method attains the Cramer Rao bounds as for a centralized estimate within a small set of iterations. Practical implications range from interference/spectrum analysis in cognitive radio systems or 3D shape reconstructions from multiple views.

International audience; We have recently proposed a second-order method for the blind identification of underdetermined mixtures that relies on the constrained factor (CONFAC) decomposition. It consists in storing successive second-order derivatives of the cumulant generating function (CGF) of the observations computed at different points of the observation space in a third-order tensor following a CONFAC model. In this work, we extend this approach to the case of third-order derivatives by resorting to a fourth-order CONFAC decomposition. We show how different third-order derivative types can be combined into a single fourth-order CONFAC tensor model with the goal of increasing the diversity of observations, so that higher under-determinacy levels can be handled. Computer simulation results illustrate the performance of a CONFAC-based blind identification algorithm compared to some competing methods.

We report on the synthesis of thin films of ZnCo 2O 4 and ZnMn 2O 4 spinels, as well as pure Co 3O 4 and Mn 3O 4 spinels, by means of electrodeposition. Spinel thin films have been analyzed by energy dispersive spectroscopy, X-ray diffraction, and Raman spectroscopy. We show that under determined deposition conditions the initial wurtzite structure of Co- and Mn-doped ZnO develops into spinel structures when the Co and Mn concentration in the films is above the solubility limit of these ions in the typical ZnO-wurtzite structure. © 2012 Elsevier Ltd. All rights reserved., This work was supported by Spanish Government through MICINN grants MAT2009-14625-C03-03, MAT2010-21270-C04-04 and MALTA CSD2007-0045. Financial support by the European Commission through NanoCIS project (PIRSES-GA-2010-269279) is gratefully acknowledged. Finally, we also want to acknowledge the support of Vicerrectorado de Investigacion y Desarrollo de la Universitat Politecnica de Valencia through projects UPV2011-0914 PAID-05-11 and UPV2011-0966 PAID-06-11.

The source separation issue is addressed, in this PhD thesis, with an innovative point of view. This work joint associates two main domains in the signal processing area : digital watermarking and source separation which are most of the time considered unrelated. Our work aims at giving a "client-user" the possibility to separate different digital source signals that have been mixed together by the only use of their single mixture. To enable such a separation, a watermark is embedded by a "provider-user" into the signal before the mixture has been fixed on its digital support. This watermark which has to be imperceptibly inserted into the signal is made of several pieces of information from original signals. The message can be embedded either directly on source signals available to the "provider" before they are mixed or onto the mixture signal. This method is composed of two main parts, a coder where a "provider" can mix signals and embed the watermark, and a decoder where a client can control the separation based on the mixture signal study. In the present work, it was chosen to embed the watermark into the mixture signal. A typical application addressed by the proposed method is the process of Audio-CD polyphonic (stereo) music. The informed separation must enable a client to control several parameters (such as volume) of the different sources (instruments, voices) that compose the audio scene.; Nous abordons dans cette thèse le problème de la séparation de sources selon un angle novateur à de nombreux niveaux. Ces travaux associent deux domaines du traitement du signal jusqu'alors traités de manière disjointe, la séparation de source et le tatouage numérique. Le procédé mis en place au cours de ces travaux a pour but de permettre à un utilisateur "client" de séparer les différents signaux numériques sources composant un mélange audio à partir de ce seul mélange tatoué. Pour ce faire un marquage du signal est effectué par un utilisateur "fournisseur" avant la fixation du mélange sur son support numérique. Ce marquage consiste en l'insertion sur le signal lui-même d'informations utiles à la séparation, et ceci de façon imperceptible. Le tatouage peut, en principe, être inséré soit sur le mélange, soit sur les signaux sources, qui sont disponibles à l'utilisateur fournisseur. Deux systèmes composent donc ce procédé, un encodeur qui permet à l'utilisateur fournisseur de réaliser la phase de mélange et de marquage, et un décodeur qui permet à l'utilisateur client de contrôler la séparation à partir du mélange. Au cours de cette thèse, il est choisi de tatouer le signal de mélange. Une application cible particulièrement visée est le cas d'un mélange polyphonique (signal de musique) fixé sur un support CD audio. La séparation doit permettre à l'utilisateur client d'effectuer un certain nombre de contrôles (par exemple le volume sonore) sur les différentes composantes de la scène sonore (les différents instruments et voix).

The source separation issue is addressed, in this PhD thesis, with an innovative point of view. This work joint associates two main domains in the signal processing area : digital watermarking and source separation which are most of the time considered unrelated. Our work aims at giving a "client-user" the possibility to separate different digital source signals that have been mixed together by the only use of their single mixture. To enable such a separation, a watermark is embedded by a "provider-user" into the signal before the mixture has been fixed on its digital support. This watermark which has to be imperceptibly inserted into the signal is made of several pieces of information from original signals. The message can be embedded either directly on source signals available to the "provider" before they are mixed or onto the mixture signal. This method is composed of two main parts, a coder where a "provider" can mix signals and embed the watermark, and a decoder where a client can control the separation based on the mixture signal study. In the present work, it was chosen to embed the watermark into the mixture signal. A typical application addressed by the proposed method is the process of Audio-CD polyphonic (stereo) music. The informed separation must enable a client to control several parameters (such as volume) of the different sources (instruments, voices) that compose the audio scene., Nous abordons dans cette thèse le problème de la séparation de sources selon un angle novateur à de nombreux niveaux. Ces travaux associent deux domaines du traitement du signal jusqu'alors traités de manière disjointe, la séparation de source et le tatouage numérique. Le procédé mis en place au cours de ces travaux a pour but de permettre à un utilisateur "client" de séparer les différents signaux numériques sources composant un mélange audio à partir de ce seul mélange tatoué. Pour ce faire un marquage du signal est effectué par un utilisateur "fournisseur" avant la fixation du mélange sur son support numérique. Ce marquage consiste en l'insertion sur le signal lui-même d'informations utiles à la séparation, et ceci de façon imperceptible. Le tatouage peut, en principe, être inséré soit sur le mélange, soit sur les signaux sources, qui sont disponibles à l'utilisateur fournisseur. Deux systèmes composent donc ce procédé, un encodeur qui permet à l'utilisateur fournisseur de réaliser la phase de mélange et de marquage, et un décodeur qui permet à l'utilisateur client de contrôler la séparation à partir du mélange. Au cours de cette thèse, il est choisi de tatouer le signal de mélange. Une application cible particulièrement visée est le cas d'un mélange polyphonique (signal de musique) fixé sur un support CD audio. La séparation doit permettre à l'utilisateur client d'effectuer un certain nombre de contrôles (par exemple le volume sonore) sur les différentes composantes de la scène sonore (les différents instruments et voix).

International audience; In this work we consider the problem of blind identification of underdetermined mixtures using the generating function of the observations. This approach had been successfully applied on real sources but had not been extended to the more attractive case of complex mixtures of complex sources. This is the main goal of the present study. By developing the core equation in the complex case, we arrive at a particular tensor stowage which involves an original tensor decomposition. Exploiting this decomposition, an algorithm is proposed to blindly estimate the mixing matrix. Three versions of this algorithm based on 2nd, 3rd and 4th-order derivatives of the generating function are evaluated on complex mixtures of 4-QAM and 8-PSK sources and compared to the 6-BIOME algorithm by means of simulation results.

Chapter 9.; We consider the linear statistical model x=As+b, where x denotes the P-dimensional vector of observations, s the N-dimensional source vector, A the PxN mixing matrix and b an additive noise, which stands for background noise as well as modeling errors. Matrix A is unknown deterministic, whereas s and b are random and also unobserved. All quantities involved are assumed to take their values in the real or complex field. It is assumed that components sn of vector s are statistically mutually independent, and that random vectors b and s are statistically independent. The particularity of this chapter is that the number of sources, N, is assumed to be strictly larger than the number of sensors, P. Even if the mixing matrix were known, it would in general be quite difficult to recover the sources. In fact the mixing matrix does not admit a left inverse, because the linear system is under-determined, which means that it has more unknowns than equations. The goal is to identify the mixing matrix A from the sole observation of realizations of vector x. Note that other approaches exist that do not assume statistical independence among sources. One can mention non negativity of sources and mixture (see Chapter 13), finite alphabet (see Chapters 6 and 12) with possibly a sparsity assumption on source values (see Chapter 10). This chapter is organized as follows. General assumptions are stated in Section 9.1. Necessary conditions under which the identification problem is well posed are pointed out in Section 9.2. Various ways of posing the problem in mathematical terms are described in Section 9.3. Then tensor tools are introduced in Section 9.4 in order to describe numerical algorithms in Section 9.5.

Textile dye wastewater contains salts and trace elements beside dyestuff and suspended solid ( SS) content. Textile dye wastewater may cause important environmental problems due to high dye contents, important amount of suspended solid content and high chemical oxygen demand ( COD). Dyestuff used in textile dyed is known to be removed in traditional aerobic treatment systems. Recently advanced oxidation processes (AOP) like Fenton process have been successfully used in treatment of industrial wastewater that contains non-biodegredable and toxic matters. Especially Fenton oxidation has been applied for textile dye processes and decolorization of wastewater that contains dye. In this study optimum values were determined for parameters such as pH, Fe(+2) and H(2)O(2), temperature, slow mixing time doses for decolorization by Fenton Process of C.I. Disperse Yellow 119 and Disperse Red 167, two of disperse dyes whose production are increasing more and more everyday and which are used more commonly and intensively for dying polyester fiber. We also evaluated the removal efficiency of color and COD at these optimum conditions. The overall color and COD removal efficiencies were 99.70% and 98.70% for Disperse Yellow 119 and 97.20% and 96.10% for Disperse Red 167 under determined conditions, respectively., Textile dye wastewater contains salts and trace elements beside dyestuff and suspended solid (SS) content. Textile dye wastewater may cause important environmental problems due to high dye contents, importantamount of suspended solid content and high chemical oxygen demand (COD). Dyestuff used in textiledyed isknown to be removed in traditional aerobic treatment systems. Recently advanced oxidation processes (AOP)like Fenton process have been successfully used in treatment of industrial wastewater that contains non-biodegradableand toxic matters.Especially Fenton oxidation has been applied for textiledyeprocessesanddecolorization of wastewater that contains dye.In this study optimum values were determined for parameterssuch as pH, Fe+2 and H2O2, temperature, slow mixing time doses for decolorization by Fenton Process of C.I.Disperse Yellow 119 and Disperse Red 167, two of disperse dyes whose production are increasing more andmore every day and which are used more commonly and intensively for dying polyester fiber. We also evaluatedthe removal efficiency of color and COD at these optimum conditions. The overall color and COD removalefficiencies were 99.7% and 98.7% for Disperse Yellow 119 and 97.2% and 96.1% for Disperse Red 167under determined conditions, respectively.