Learning dependent sources using mixtures of Dirichlet: applications on hyperspectral unmixing

This paper is an elaboration of the DECA algorithm [1] to blindly unmix hyperspectral data. The underlying mixing model is linear, meaning that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. The proposed method, as DECA, is tailored to highly mixed mixtures in which the geometric based approaches fail to identify the simplex of minimum volume enclosing the observed spectral vectors. We resort then to a statitistical framework, where the abundance fractions are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely non-negativity and constant sum. With respect to DECA, we introduce two improvements: 1) the number of Dirichlet modes are inferred based on the minimum description length (MDL) principle; 2) The generalized expectation maximization (GEM) algorithm we adopt to infer the model parameters is improved by using alternating minimization and augmented Lagrangian methods to compute the mixing matrix. The effectiveness of the proposed algorithm is illustrated with simulated and read data

Classificação não-supervisionada de dados hiperespectrais usando análise em componentes independentes

No passado recente foram desenvolvidas v árias t écnicas para classi ca ção de dados hiperspectrais. Uma abordagem tí pica consiste em considerar que cada pixel e uma mistura linear das reflectancias espectrais dos elementos presentes na c élula de resolu ção, adicionada de ru ído. Para classifi car e estimar os elementos presentes numa imagem hiperespectral, v ários problemas se colocam: Dimensionalidade dos dados, desconhecimento dos elementos presentes e a variabilidade da reflectância destes. Recentemente foi proposta a An álise em Componentes Independentes,para separa ção de misturas lineares. Nesta comunica ção apresenta-se uma metodologia baseada na An álise em Componentes Independentes para detec ção dos elementos presentes em imagens hiperespectrais e estima ção das suas quantidades. Apresentam-se resultados desta metodologia com dados simulados e com dados hiperespectrais reais, ilustrando a potencialidade da t écnica

Estimação do subespaço de sinal em dados hiperespectrais

A redução de dimensionalidade é uma tarefa crucial no processamento e análise de dados hiperespectrais. Esta comunicação propõe um método de estimação do subespaço de sinal baseado no erro quadrático médio. O método consiste em primeiro estimar as matrizes de correlação do sinal e do ruído e em segundo seleccionar o conjunto de vectores próprios que melhor representa o subespaço de sinal. O eficiência deste método é ilustrada em imagens hiperespectrais sintéticas e reais

An overview on hyperspectral unmixing: Geometrical, statistical, and sparse regression based approaches

Hyperspectral instruments acquire electromagnetic energy scattered within their ground instantaneous field view in hun-dreds of spectral channels with high spectral resolution. Very often, however, owing to low spatial resolution of the scan-ner or to the presence of intimate mixtures (mixing of the materials at a very small scale) in the scene, the spectral vec-tors (collection of signals acquired at different spectral bands from a given pixel) acquired by the hyperspectral scanners are actually mixtures of the spectral signatures of the materials present in the scene. Given a set of mixed spectral vectors, spectral mixture analysis (or spectral unmixing) aims at estimating the number of reference materials, also called endmembers, their spectral signatures, and their fractional abundances. Spectral unmix

Hyperspectral unmixing based on mixtures of Dirichlet components

This paper introduces a new unsupervised hyperspectral unmixing method conceived to linear but highly mixed hyperspectral data sets, in which the simplex of minimum volume, usually estimated by the purely geometrically based algorithms, is far way from the true simplex associated with the endmembers. The proposed method, an extension of our previous studies, resorts to the statistical framework. The abundance fraction prior is a mixture of Dirichlet densities, thus automatically enforcing the constraints on the abundance fractions imposed by the acquisition process, namely, nonnegativity and sum-to-one. A cyclic minimization algorithm is developed where the following are observed: 1) The number of Dirichlet modes is inferred based on the minimum description length principle; 2) a generalized expectation maximization algorithm is derived to infer the model parameters; and 3) a sequence of augmented Lagrangian-based optimizations is used to compute the signatures of the endmembers. Experiments on simulated and real data are presented to show the effectiveness of the proposed algorithm in unmixing problems beyond the reach of the geometrically based state-of-the-art competitors