93 research outputs found
A Variable Splitting Augmented Lagrangian Approach to Linear Spectral Unmixing
This paper presents a new linear hyperspectral unmixing method of the minimum
volume class, termed \emph{simplex identification via split augmented
Lagrangian} (SISAL). Following Craig's seminal ideas, hyperspectral linear
unmixing amounts to finding the minimum volume simplex containing the
hyperspectral vectors. This is a nonconvex optimization problem with convex
constraints. In the proposed approach, the positivity constraints, forcing the
spectral vectors to belong to the convex hull of the endmember signatures, are
replaced by soft constraints. The obtained problem is solved by a sequence of
augmented Lagrangian optimizations. The resulting algorithm is very fast and
able so solve problems far beyond the reach of the current state-of-the art
algorithms. The effectiveness of SISAL is illustrated with simulated data.Comment: 4 pages, 2 figures. Submitted to "First IEEE GRSS Workshop on
Hyperspectral Image and Signal Processing, 2009
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
literature
Robust hyperspectral image classification with rejection fields
In this paper we present a novel method for robust hyperspectral image
classification using context and rejection. Hyperspectral image classification
is generally an ill-posed image problem where pixels may belong to unknown
classes, and obtaining representative and complete training sets is costly.
Furthermore, the need for high classification accuracies is frequently greater
than the need to classify the entire image.
We approach this problem with a robust classification method that combines
classification with context with classification with rejection. A rejection
field that will guide the rejection is derived from the classification with
contextual information obtained by using the SegSALSA algorithm. We validate
our method in real hyperspectral data and show that the performance gains
obtained from the rejection fields are equivalent to an increase the dimension
of the training sets.Comment: This paper was submitted to IEEE WHISPERS 2015: 7th Workshop on
Hyperspectral Image and Signal Processing: Evolution on Remote Sensing. 5
pages, 1 figure, 2 table
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 tà 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 Ãdo. 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 ruÃdo 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
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