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169
Bayesian estimation of linear mixtures using the normal compositional model
 IEEE Trans. Image Processing
, 2010
"... Abstract—This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of socalled endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model e ..."
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Cited by 20 (13 self)
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Abstract—This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of socalled endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous Nfinder (NFINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images. Index Terms—Bayesian inference, hyperspectral images, Monte Carlo methods, normal compositional model, spectral unmixing.
Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2012
"... Spectral unmixing aims at estimating the fractional abundances of pure spectral signatures (also called endmembers) in each mixed pixel collected by a remote sensing hyperspectral imaging instrument. In recent work, the linear spectral unmixing problem has been approached in semisupervised fashion a ..."
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Cited by 19 (5 self)
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Spectral unmixing aims at estimating the fractional abundances of pure spectral signatures (also called endmembers) in each mixed pixel collected by a remote sensing hyperspectral imaging instrument. In recent work, the linear spectral unmixing problem has been approached in semisupervised fashion as a sparse regression one, under the assumption that the observed image signatures can be expressed as linear combinations of pure spectra, known aprioriand available in a library. It happens, however, that sparse unmixing focuses on analyzing the hyperspectral data without incorporating spatial information. In this paper, we include the total variation (TV) regularization to the classical sparse regression formulation, thus exploiting the spatial– contextual information present in the hyperspectral images and developing a new algorithm called sparse unmixing via variable splitting augmented Lagrangian and TV. Our experimental results, conducted with both simulated and real hyperspectral data sets, indicate the potential of including spatial information (through the TV term) on sparse unmixing formulations for improved characterization of mixed pixels in hyperspectral imagery.
Hyperspectral unmixing based on mixtures of Dirichlet components
 IEEE Transactions on Geoscience and Remote Sensing
"... Abstract—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 e ..."
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Cited by 19 (5 self)
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Abstract—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 sumtoone. 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 Lagrangianbased 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 stateoftheart competitors. Index Terms—Augmented Lagrangian method of multipliers, blind hyperspectral unmixing, dependent components, generalized expectation maximization (GEM), minimum description length (MDL), mixtures of Dirichlet densities. I.
Kernel fully constrained least squares abundance estimates
 in Proc. IEEE Int. Conf. Geoscience and Remote Sensing (IGARSS
, 2007
"... Abstract — A critical step for fitting a linear mixing model to hyperspectral imagery is the estimation of the abundances. The abundances are the percentage of each endmember within a given pixel; therefore, they should be nonnegative and sum to one. With the advent of kernel based algorithms for h ..."
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Cited by 19 (1 self)
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Abstract — A critical step for fitting a linear mixing model to hyperspectral imagery is the estimation of the abundances. The abundances are the percentage of each endmember within a given pixel; therefore, they should be nonnegative and sum to one. With the advent of kernel based algorithms for hyperspectral imagery, kernel based abundance estimates have become necessary. This paper presents such an algorithm that estimates the abundances in the kernel feature space while maintaining the nonnegativity and sumtoone constraints. The usefulness of the algorithm is shown using the AVIRIS Cuprite, Nevada image. Keywordskernel functions, hyperspectral imagery, spectral unmixing, abundance estimates I.
Tensor Methods for Hyperspectral Data Analysis: A Space Object Material Identification Study
"... An important and well studied problem in hyperspectral image data applications is to identify materials present in the object or scene being imaged and to quantify their abundance in the mixture. Due to the increasing quantity of data usually encountered in hyperspectral datasets, effective data com ..."
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Cited by 16 (4 self)
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An important and well studied problem in hyperspectral image data applications is to identify materials present in the object or scene being imaged and to quantify their abundance in the mixture. Due to the increasing quantity of data usually encountered in hyperspectral datasets, effective data compression is also an important consideration. In this paper, we develop novel methods based on tensor analysis that focus on all three of these goals: material identification, material abundance estimation, and data compression. Test results are reported in all three perspectives. c ○ 2008 Optical Society of
Nonlinear Unmixing of Hyperspectral Data Based on a LinearMixture/NonlinearFluctuation Model
"... Abstract—Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. Although the linear mixture model has obvious practical advantages, there are many situations in which it may not be appropriate and could be advantageously replaced by a nonlinear one. In this paper, we ..."
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Cited by 15 (6 self)
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Abstract—Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. Although the linear mixture model has obvious practical advantages, there are many situations in which it may not be appropriate and could be advantageously replaced by a nonlinear one. In this paper, we formulate a new kernelbased paradigm that relies on the assumption that the mixing mechanism can be described by a linear mixture of endmember spectra, with additive nonlinear fluctuations defined in a reproducing kernel Hilbert space. This family of models has clear interpretation, and allows to take complex interactions of endmembers into account. Extensive experiment results, with both synthetic and real images, illustrate the generality and effectiveness of this scheme compared with stateoftheart methods. Index Terms — Hyperspectral imaging, multikernel learning, nonlinear spectral unmixing, support vector regression.
A signal processing perspective on hyperspectral unmixing: Insights from remote sensing
 IEEE Signal Processing Magazine
, 2014
"... Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing for hyperspectral remote sensing [1, 2]. Blind HU aims at identifying materials present in a captured scene, ..."
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Cited by 14 (7 self)
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Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing for hyperspectral remote sensing [1, 2]. Blind HU aims at identifying materials present in a captured scene,
Color display for hyperspectral imagery
 IEEE Trans. Geoscience and Remote Sensing
, 2008
"... Abstract—This paper investigates RGB color composition schemes for hyperspectral imagery display. A threechannel composite inevitably loses a significant amount of information contained in the original highdimensional data. The objective here is to display the useful information as distinctively ..."
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Cited by 14 (1 self)
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Abstract—This paper investigates RGB color composition schemes for hyperspectral imagery display. A threechannel composite inevitably loses a significant amount of information contained in the original highdimensional data. The objective here is to display the useful information as distinctively as possible for highclass separability. To achieve this objective, it is important to find an effective data processing step prior to color display. A series of supervised and unsupervised data transformation and classification algorithms are reviewed, implemented, and compared for this purpose. The resulting color displays are evaluated in terms of class separability using a statistical detector and perceptual color distance. We demonstrate that the use of the data processing step can significantly improve the quality of color display, whereas data classification generally outperforms data transformation, although the implementation is more complicated. Several instructive suggestions for practitioners are provided. Index Terms—Classification, color display, human visual perception, hyperspectral imaging, transformation, visualization. I.
Nonlinear Unmixing of Hyperspectral Images: Models and Algorithms
"... When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are mul ..."
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Cited by 13 (4 self)
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When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances in nonlinear unmixing modeling.
1 Hyperspectral Unmixing Via L1/2 Sparsityconstrained Nonnegative Matrix Factorization
"... Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material endmembers. As an important constra ..."
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Cited by 12 (2 self)
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Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material endmembers. As an important constraint for NMF, sparsity has been modeled making use of the L1 regularizer. Unfortunately, the L1 regularizer cannot enforce further sparsity when the full additivity constraint of material abundances is used, hence, limiting the practical efficacy of NMF methods in hyperspectral unmixing. In this paper, we extend the NMF method by incorporating the L1/2 sparsity constraint, which we name L1/2NMF. The L1/2 regularizer not only induces sparsity, but is also a better choice among Lq(0 < q < 1) regularizers. We propose an iterative estimation algorithm for L1/2NMF, which provides sparser and more accurate results than those delivered using the L1 norm. We illustrate the utility of our method on synthetic and real hyperspectral data and compare our results to those yielded by other stateoftheart methods.