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193
Hyperspectral Remote Sensing Data Analysis and Future Challenges
"... Abstract—Hyperspectral remote sensing ..."
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Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery
, 2012
"... This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial func ..."
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Cited by 24 (13 self)
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This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model.The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.
Enhancing hyperspectral image unmixing with spatial correlations
, 2011
"... This paper describes a new algorithm for hyperspectral image unmixing. Most unmixing algorithms proposed in the literature do not take into account the possible spatial correlations between the pixels. In this paper, a Bayesian model is introduced to exploit these correlations. The image to be unmi ..."
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Cited by 23 (13 self)
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This paper describes a new algorithm for hyperspectral image unmixing. Most unmixing algorithms proposed in the literature do not take into account the possible spatial correlations between the pixels. In this paper, a Bayesian model is introduced to exploit these correlations. The image to be unmixed is assumed to be partitioned into regions (or classes) where the statistical properties of the abundance coefficients are homogeneous. A Markov random field, is then proposed to model the spatial dependencies between the pixels within any class. Conditionally upon a given class, each pixel is modeled by using the classical linear mixing model with additive white Gaussian noise. For this model, the posterior distributions of the unknown parameters and hyperparameters allow the parameters of interest to be inferred. These parameters include the abundances for each pixel, the means and variances of the abundances for each class, as well as a classification map indicating the classes of all pixels in the image. To overcome the complexity of the posterior distribution, we consider a Markov chain Monte Carlo method that generates samples asymptotically distributed according to the posterior. The generated samples are then used for parameter and hyperparameter estimation. The accuracy of the proposed algorithms is illustrated on synthetic and real data.
A simplex volume maximization framework for hyperspectral endmember extraction
 IEEE Trans. Geosci. Remote Sens
, 2011
"... Abstract—In the late 1990s, Winter proposed an endmember extraction belief that has much impact on endmember extraction techniques in hyperspectral remote sensing. The idea is to find a maximumvolume simplex whose vertices are drawn from the pixel vectors. Winter’s belief has stimulated much intere ..."
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Cited by 22 (10 self)
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Abstract—In the late 1990s, Winter proposed an endmember extraction belief that has much impact on endmember extraction techniques in hyperspectral remote sensing. The idea is to find a maximumvolume simplex whose vertices are drawn from the pixel vectors. Winter’s belief has stimulated much interest, resulting in many different variations of pixel search algorithms, widely known as NFINDR, being proposed. In this paper, we take a continuous optimization perspective to revisit Winter’s belief, where the aim is to provide an alternative framework of formulating and understanding Winter’s belief in a systematic manner. We first prove that, fundamentally, the existence of pure pixels is not only sufficient for the Winter problem to perfectly identify the groundtruth endmembers but also necessary. Then, under the umbrella of the Winter problem, we derive two methods using two different optimization strategies. One is by alternating optimization. The resulting algorithm turns out to be an NFINDR variant, but, with the proposed formulation, we can pin down some of its convergence characteristics. Another is by successive optimization; interestingly, the resulting algorithm is found to exhibit some similarity to vertex component analysis. Hence, the framework provides linkage and alternative interpretations to these existing algorithms. Furthermore, we propose a robust worst case generalization of the Winter problem for accounting for perturbed pixel effects in the noisy scenario. An algorithm combining alternating optimization and projected subgradients is devised to deal with the problem. We use both simulations and real data experiments to demonstrate the viability and merits of the proposed algorithms. Index Terms—Alternating optimization, endmember extraction, hyperspectral imaging, projected subgradient method, robust optimization, simplex volume maximization, successive optimization. I.
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.
Implementation strategies for hyperspectral unmixing using Bayesian source separation
 IEEE Trans. Geosci. Remote Sens
, 2010
"... Abstract—Bayesian positive source separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical nonnegativity of spectra and abundances has to be ensured, such as in remote sensing. Moreover, it is sensible to impose a sumtoone (full additivity) constraint to ..."
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Cited by 16 (3 self)
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Abstract—Bayesian positive source separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical nonnegativity of spectra and abundances has to be ensured, such as in remote sensing. Moreover, it is sensible to impose a sumtoone (full additivity) constraint to the estimated source abundances in each pixel. Even though nonnegativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms has so far been limited by high computation time and large memory requirements due to the Markov chain Monte Carlo calculations. An implementation strategy that allows one to apply these algorithms on a full hyperspectral image, as it is typical in earth and planetary science, is introduced. The effects of pixel selection and the impact of such sampling on the relevance of the estimated component spectra and abundance maps, as well as on the computation times, are discussed. For that purpose, two different data sets have been used: a synthetic one and a real hyperspectral image from Mars. Index Terms—Bayesian estimation, computation time, hyperspectral imaging, implementation strategy, source separation.
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.
Hyperspectral Unmixing Algorithm via Dependent Component Analysis
"... Abstract—This paper introduces a new method to blindly unmix hyperspectral data, termed dependent component analysis (DECA). This method decomposes a hyperspectral images into a collection of reflectance (or radiance) spectra of the materials present in the scene (endmember signatures) and the corre ..."
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Abstract—This paper introduces a new method to blindly unmix hyperspectral data, termed dependent component analysis (DECA). This method decomposes a hyperspectral images into a collection of reflectance (or radiance) spectra of the materials present in the scene (endmember signatures) and the corresponding abundance fractions at each pixel. DECA assumes that each pixel is a linear mixture of the endmembers signatures weighted by the correspondent abundance fractions. These abudances are modeled as mixtures of Dirichlet densities, thus enforcing the constraints on abundance fractions imposed by the acquisition process, namely nonnegativity and constant sum. The mixing matrix is inferred by a generalized expectationmaximization (GEM) type algorithm. This method overcomes the limitations of unmixing methods based on Independent Component Analysis (ICA) and on geometrical based approaches. The effectiveness of the proposed method is illustrated using simulated data based on U.S.G.S. laboratory spectra and real hyperspectral data collected by the AVIRIS sensor over Cuprite, Nevada. I.