Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation

This paper concerns underdetermined linear instantaneous and convolutive blind source separation (BSS), i.e., the case when the number of observed mixed signals is lower than the number of sources.We propose partial BSS methods, which separate supposedly nonstationary sources of interest (while keeping residual components for the other, supposedly stationary, "noise" sources). These methods are based on the general differential BSS concept that we introduced before. In the instantaneous case, the approach proposed in this paper consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures). In the convolutive case, we extend our recent time-domain fast fixed-point C-FICA algorithm to underdetermined mixtures. Both proposed approaches thus keep the attractive features of the FastICA and C-FICA methods. Our approaches are based on differential sphering processes, followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper. Experimental tests show that these differential algorithms are much more robust to noise sources than the standard FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for linear instantaneous and convolutive underdetermined mixture

Modified Independent Component Analysis for Initializing Non-negative Matrix Factorization : An approach to Hyperspectral Image Unmixing (ECMS 2013)

International audienceHyperspectral unmixing consists of identifying, from mixed pixel spectra, a set of pure constituent spectra (endmembers) in a scene and a set of abundance fractions for each pixel. Most linear blind source separation (BSS) techniques are based on Independent Component Analysis (ICA) or Non-Negative Matrix Factorization (NMF). Using only one of these techniques does not resolve the unmixing problem because of, respectively, the statistical dependence between the abundance fractions of the different constituents and the non-uniqueness of the NMF results. To overcome this issue, we propose an unsupervised unmixing approach called ModifICA-NMF (which stands for modified version of ICA followed by NMF). Consider the ideal case of a hyperspectral image combining (M-1) statistically independent source images, and an Mth image depending on them due to the sum-to-one constraint. Our modified ICA first estimates these (M-1) sources and associated mixing coefficients, then derives the remaining source and coefficients, while it also removes the BSS scale indeterminacy. In real conditions, the above (M-1) sources may be somewhat dependent. Our modified ICA method then only yields approximate data. These are then used as the initial values of an NMF method, which refines them. Our tests show that this joint modifICA-NMF approach significantly outperforms the considered classical methods

Modified Independent Component Analysis for Initializing Non-negative Matrix Factorization : An approach to Hyperspectral Image Unmixing (WHISPERS 2013)

National audienceIn this paper, we propose an unsupervised unmixing approach for hyperspectral images, consisting of a modified version of ICA, followed by NMF. In the ideal case of a hyperspectral image combining (C−1) statistically independent source images , and a C th image which is dependent on them due to the sum-to-one constraint, our modified ICA first estimates these (C −1) sources and associated mixing coefficients, and then derives the remaining source and coefficients, while also removing the BSS scale indeterminacy. In real conditions, the above (C−1) sources may be somewhat dependent. Our modified ICA method then only yields approximate data. These are then used as the initial values of an NMF method, which refines them. Our tests show that this joint modifICA-NMF approach significantly outperforms the considered classical methods

Un algorithme rapide à identification polynomiale multivariable pour la séparation aveugle d'images

Cet article a pour objet la séparation rapide de mélanges linéaires instantanés dans le cas d'observations contenant un grand nombre d'échantillons. Cette configuration est fréquente notamment en séparation d'images en raison de l'augmentation actuelle du nombre de pixels des capteurs de types CCD ou CMOS. Nous présentons ici un algorithme de type point fixe inspiré de FastICA, qui, grâce à une première étape d'identification polynomiale, permet d'éviter le calcul de statistiques à chaque itération de l'algorithme d'optimisation sous contrainte du kurtosis