Least-Squares Joint Diagonalization of a matrix set by a congruence transformation

The approximate joint diagonalization (AJD) is an important analytic tool at the base of numerous independent component analysis (ICA) and other blind source separation (BSS) methods, thus finding more and more applications in medical imaging analysis. In this work we present a new AJD algorithm named SDIAG (Spheric Diagonalization). It imposes no constraint either on the input matrices or on the joint diagonalizer to be estimated, thus it is very general. Whereas it is well grounded on the classical leastsquares criterion, a new normalization reveals a very simple form of the solution matrix. Numerical simulations shown that the algorithm, named SDIAG (spheric diagonalization), behaves well as compared to state-of-the art AJD algorithms.Comment: 2nd Singaporean-French IPAL Symposium, Singapour : Singapour (2009

A new stability results for the backward heat equation

In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved. This work extends to many earlier results in (f2,f3, hao1,Quan,tau1, tau2, Trong3,x1).Comment: 13 page

Séparation aveugle de mélange instantanée de sources à l'aide de fonctions séparatrices ajustées

Nous proposons un algorithme de séparation aveugle des mélanges instantanés de sources basé sur des fonctions séparatrices qui sont elle même ajustées à partir des sources venant d'être reconstruites. Nous montrons la stabilité de l'algorithme au voisinage de la vraie solution et, dans quelque cas simples, son instabilité au voisinage de la solution parasite. Cette bonne propriété de l'algorithme est confirmé dans nos simulations pour des situations plus complexes

Contrastes pour la séparation aveugle de sources

Une méthode générale pour construire de contrastes pour la séparation aveugles de mélanges instantanés de sources est introduit. Elle est basée sur une fonctionnelle super-additive de classe II appliquées aux lois des sources reconstituées. Des exemples de telles fonctionnelles sont donnés. Notre approche permet d'exploiter la dépendance temporelle des sources en se servant d'une fonctionnelle sur la loi conjointe du processus sources dans un intervalle de temps. Cela fournit de nombreux nouveaux exemples et nous affranchit de la contrainte que les sources soient non gaussiennes. Le cas des contrastes basés sur les cumulants nécessitant la contrainte d'orthogonalité est également abordé

Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems

This paper considers several filtering methods of stochastic nature based on Monte-Carlo drawings, in view of the sequential data assimilation in non linear models. They include some known methods such as the particle filter and the ensemble Kalman filters and some other introduced by us: the second order particle filters and the singular evolutive interpolated filter. The aim is to study their behaviour in the simple non linear chaotic Lorenz system, in the hope of getting some insight on more complex models. It is seen that these filters perform satisfactory but our filters have the clear advantage in term of cost. This is achieved through the concept of second order exact drawing and the selective error correction parallel to the tangent space of the attractor of the system (which is of low dimension- ). We have also introduced the use of the forgetting factor, which could enhance significantly the filter stability in this nonlinear context

ICA based algorithms for computing optimal 1-D linear block transforms in variable high-rate source coding

International audienceThe Karhunen-Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources. Furthermore, under the high-resolution quantization hypothesis, nearly everything is known about the performance of a transform coding system with entropy constrained scalar quantization and mean-square distortion. It is then straightforward to find a criterion that, when minimized, gives the optimal linear transform under the abovementioned conditions. However, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculus. In this paper, we present the abovementioned criterion as a contrast of independent component analysis modified by an additional term which is a penalty to non-orthogonality. Then we adapt the icainf algorithm by Pham in order to compute the transform minimizing the criterion either with no constraint or with the orthogonality constraint. Finally, experimental results show that the transforms we introduced can (1) outperform the KLT on synthetic signals, (2) achieve slightly better PSNR for high-rates and better visual quality (preservation of lines and contours) for medium-to-low rates than the KLT and 2-D DCT on grayscale natural images

Initialisation of Nonlinearities for PNL and Wiener systems Inversion

This paper proposes a very fast method for blindly initial- izing a nonlinear mapping which transforms a sum of random variables. The method provides a surprisingly good approximation even when the basic assumption is not fully satis¯ed. The method can been used success- fully for initializing nonlinearity in post-nonlinear mixtures or in Wiener system inversion, for improving algorithm speed and convergence

Inversió cega de funcions no-lineals mitjançant un procés de Gaussianització

En aquest treball es presenta un nou mètode per a la inversió cega de funcions no-lineals mitjançant la gaussianització del senyal observat. El mètode es basa en restituir el caràcter aproximadament gaussià que presenta un senyal filtrat, gràcies al teorema del límit central,que ha vist canviada la seva distribució per l’efecte d’una funció no-lineal. Inicialment, doncs,aquest mètode és útil per a la inversió de sistemes de Wiener, tot i que en els darrers experiments realitzats s’han obtingut resultats interessants en sistemes purament no-lineals. El treball presenta dues possibles parametritzacions, la primera basada en xarxes neurals i la segona en polinomis. En els dos casos s’aconsegueix invertir la funció desconeguda sense tenir cap coneixement a priori ni del senyal original, ni del filtre, ni de la funció no-lineal que volem invertir.Abstract In this work a new method for the blind inversion of nonlinear functions is presented, based on the gaussianization of the observed signal. The method restores the approximately gaussian character of the filtered signals, in accordance with the central limit theorem, that has been modified by a nonlinear distortion. Then, this method is appropriate for the inversion of Wiener systems, but in the latest experiments we have carried out, some interesting results have been obtained for a purely nonlinear system. This work develops two possible parameterizations. The first one is based on neural networks (multi-layer perceptron) and the second one uses a polynomial parameterization. In these two cases, we obtain the inverse function without having any a priori knowledge neither of the original signal, nor of the filter, nor of the nonlinear function.En este trabajo se presenta un nuevo método para la inversión ciega de funciones no-lineales mediante la gausianización de la señal observada. El método se basa en restituir el carácter aproximadamente gausiano que presenta una señal filtrada, gracias al teorema del límite central, que ha visto modificada su distribución por el efecto de una función no-lineal. Inicialmente este método es útil para la inversión de sistemas de Wiener, aún que en los últimos experimentos realizados se han obtenido resultados interesantes en sistemas puramente no-lineales. El trabajo presenta dos posibles parametrizaciones, la primera basada en redes neuronales y la segunda en polinomios. En los dos casos se consigue invertir la función desconocida sin tener ningún conocimiento a priori ni de la señal original, ni del filtro, ni de la función no-lineal a invertir