Méthodes de séparation aveugle de sources pour le démélange d'images de télédétection

Nous proposons dans le cadre de cette thèse, de nouvelles méthodes de séparation aveugle de mélanges linéaires instantanés pour des applications de télédétection. La première contribution est fondée sur la combinaison de deux grandes classes de méthodes de Séparation Aveugle de Sources (SAS) : l'Analyse en Composantes Indépendantes (ACI), et la Factorisation en Matrices Non-négatives (NMF). Nous montrons comment les contraintes physiques de notre problème peuvent être utilisées pour éliminer une partie des indéterminations liées à l'ACI et fournir une première approximation des spectres de endmembers et des fractions d'abondance associées. Ces approximations sont ensuite utilisées pour initialiser un algorithme de NMF, avec pour objectif de les améliorer. Les résultats obtenus avec notre méthode sont satisfaisants en comparaison avec les méthodes de la littérature utilisées dans les tests réalisés. La deuxième méthode proposée est fondée sur la parcimonie ainsi que sur des propriétés géométriques. Nous commençons par mettre en avant quelques propriétés facilitant la présentation des hypothèses considérées dans cette méthode, puis nous mettons en lumière les grandes lignes de cette dernière qui est basée sur la détermination des zones bi-sources contenues dans une image de télédétection, ceci à l'aide d'un critère de corrélation. A partir des intersections des droites générées par ces zones bi-sources, nous détaillons le moyen d'obtention des colonnes de la matrice de mélange et enfin des sources recherchées. Les résultats obtenus, en comparaison avec plusieurs méthodes de la littérature sont très encourageants puisque nous avons obtenu les meilleures performances.Within this thesis, we propose new blind source separation (BSS) methods intended for instantaneous linear mixtures, aimed at remote sensing applications. The first contribution is based on the combination of two broad classes of BSS methods : Independent Component Analysis (ICA), and Non-negative Matrix Factorization (NMF). We show how the physical constraints of our problem can be used to eliminate some of the indeterminacies related to ICA and provide a first approximation of endmembers spectra and associated sources. These approximations are then used to initialize an NMF algorithm with the goal of improving them. The results we reached are satisfactory as compared with the classical methods used in our undertaken tests. The second proposed method is based on sparsity as well as on geometrical properties. We begin by highlighting some properties facilitating the presentation of the hypotheses considered 153 in the method. We then provide the broad lines of this approach which is based on the determination of the two-source zones that are contained in a remote sensing image, with the help of a correlation criterion. From the intersections of the lines generated by these two-source zones, we detail how to obtain the columns of the mixing matrix and the sought sources. The obtained results are quite attractive as compared with those reached by several methods from literature

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

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

Blind Unmixing of Hyperspectral Remote Sensing Data: A New Geometrical Method Based on a Two-Source Sparsity Constraint

Blind source separation (or unmixing) methods process a set of mixed signals, which are typically linear memoryless combinations of source signals, so as to estimate these unknown source signals and/or combination coefficients. These methods have been extensively applied to hyperspectral images in the field of remote sensing, because the reflectance spectrum of each image pixel is often a mixture of elementary contributions, due to the limited spatial resolution of hyperspectral remote sensing sensors. Each spatial source signal then corresponds to a pure material, and its value in each pixel is equal to the “abundance fraction” of the corresponding Earth surface covered by that pure material. The mixing coefficients then form the pure material spectra. Various unmixing methods have been designed for this data model and the majority of them are either geometrical or statistical, or even based on sparse regressions. Various such unmixing techniques mainly consider assumptions that are related to the presence or absence of pure pixels (i.e., pixels which contain only one pure material). The case when, for each pure material, the image includes at least one pixel or zone which only contains that material yielded attractive unmixing methods, but corresponds to a stringent sparsity condition. We here aim at relaxing that condition, by only requesting a few tiny pixel zones to contain two pure materials. The proposed linear and geometrical sparse-based, blind (or unsupervised) unmixing method first automatically detects these zones. Each such zone defines a line in the data representation space. These lines are then estimated and clustered. The pairs of cluster centers, corresponding to lines, which have an intersection, yield the spectra of pure materials, forming the columns of the mixing matrix. Finally, the proposed method derives all abundance fractions, i.e., source signals, by using a least squares method with a non-negativity constraint. This method is applied to realistic synthetic images and is shown to outperform various methods from the literature. Indeed, and for the conducted experiments, when considering the pure material spectra extraction, the obtained improvements, for the considered spectral angle mapper performance criterion, vary between 0.02∘ and 12.43∘. For the abundance fractions estimation, the proposed technique is able to achieve a normalized mean square error lower than 0.01%, while the tested literature methods yield errors greater than 0.1%