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Hyperspectral unmixing overview: Geometrical, statistical, and sparse regressionbased approaches
 IEEE J. SEL. TOPICS APPL. EARTH OBSERV. REMOTE SENS
, 2012
"... Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher sp ..."
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Cited by 103 (34 self)
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Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, illposed
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.
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: Geometrical, Statistical, and Sparse RegressionBased Approaches
, 2010
"... Hyperspectral instruments acquire electromagnetic energy scattered within their ground instantaneous field view in hundreds of spectral channels with high spectral resolution. Very often, however, owing to low spatial resolution of the scanner or to the presence of intimate mixtures (mixing of the m ..."
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Cited by 15 (4 self)
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Hyperspectral instruments acquire electromagnetic energy scattered within their ground instantaneous field view in hundreds of spectral channels with high spectral resolution. Very often, however, owing to low spatial resolution of the scanner or to the presence of intimate mixtures (mixing of the materials at a very small scale) in the scene, the spectral vectors (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 unmixing is, thus, a source separation problem where, under a linear mixing model, the sources are the fractional abundances and the endmember spectral signatures are the columns of the mixing matrix. As such, the independent component analysis (ICA) framework came naturally to mind to unmix spectral data. However, the ICA crux assumption of source statistical independence is not satisfied in spectral applications, since the sources are fractions and, thus, nonnegative and sum to one. As a consequence, ICAbased algorithms have severe limitations in the area of spectral unmixing, and this has fostered new unmixing research directions taking into account geometric and statistical characteristics of hyperspectral sources. This paper presents an overview of the principal research directions in hyperspectral unmixing. The presentations is organized into four main topics: i) mixing models, ii) signal subspace identification, iii) geometricalbased spectral unmixing, (iv) statisticalbased spectral unmixing, and (v) sparse regressionbased unmixing. In each topic, we describe what physical or mathematical problems are involved and summarize stateoftheart algorithms to address these problems.
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.
Collaborative Sparse Regression For Hyperspectral Unmixing
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2013
"... Sparse unmixing has been recently introduced in hyperspectral imaging as a framework to characterize mixed pixels. It assumes that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance (e.g., spectra collected on th ..."
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Cited by 11 (4 self)
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Sparse unmixing has been recently introduced in hyperspectral imaging as a framework to characterize mixed pixels. It assumes that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance (e.g., spectra collected on the ground by a field spectroradiometer). Unmixing then amounts to finding the optimal subset of signatures in a (potentially very large) spectral library that can best model each mixed pixel in the scene. In this paper, we present a refinement of the sparse unmixing methodology recently introduced which exploits the usual very low number of endmembers present in real images, out of a very large library. Specifically, we adopt the collaborative (also called “multitask” or “simultaneous”) sparse regression framework that improves the unmixing results by solving a joint sparse regression problem, where the sparsity is simultaneously imposed to all pixels in the data set. Our experimental results with both synthetic and real hyperspectral data sets show clearly the advantages obtained using the new joint sparse regression strategy, compared with the pixelwise independent approach.
Automated extraction of imagebased endmember bundles for improved spectral unmixing
 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
, 2012
"... Abstract—Spectral unmixing is an important task in hyperspectral data exploitation. It amounts to estimating the abundance of pure spectral constituents (endmembers) in each (possibly mixed) observation collected by the imaging instrument. In recent years, several endmember extraction algorithms (E ..."
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Cited by 8 (3 self)
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Abstract—Spectral unmixing is an important task in hyperspectral data exploitation. It amounts to estimating the abundance of pure spectral constituents (endmembers) in each (possibly mixed) observation collected by the imaging instrument. In recent years, several endmember extraction algorithms (EEAs) have been proposed for automated endmember extraction from hyperspectral data sets. Traditionally, EEAs extract/select only one single standard endmember spectrum for each of the presented endmember classes or scene components. The use of fixed endmember spectra, however, is a simplification since in many cases the conditions of the scene components are spatially and temporally variable. As a result, variation in endmember spectral signatures is not always accounted for and, hence, spectral unmixing can lead to poor accuracy of the estimated endmember fractions. Here, we address this issue by developing a simple strategy to adapt available EEAs to select multiple endmembers (or bundles) per scene component. We run the EEAs in randomly selected subsets of the original hyperspectral image, and group the extracted samples of pure materials in a bundle using a clustering technique. The output is a spectral library of pure materials, extracted automatically from the input scene. The proposed technique is applied to several common EEAs and combined with an endmember variability reduction technique for unmixing purposes. Experiments with both simulated and real hyperspectral data sets indicate that the proposed strategy can significantly improve fractional abundance estimations by accounting for endmember variability in the original hyperspectral data. Index Terms—Endmember extraction algorithms (EEAs), endmember variability, hyperspectral imaging, multiple endmember spectral mixture analysis (MESMA), spectral mixture analysis (SMA). I.
A Sparse Regression Approach to Hyperspectral Unmixing
, 2011
"... Spectral unmixing is an important problem in hyperspectral data exploitation. It amounts at characterizing the mixed spectral signatures collected by an imaging instrument in the form of a combination of pure spectral constituents (endmembers), weighted by their correspondent abundance fractions. Li ..."
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Cited by 6 (0 self)
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Spectral unmixing is an important problem in hyperspectral data exploitation. It amounts at characterizing the mixed spectral signatures collected by an imaging instrument in the form of a combination of pure spectral constituents (endmembers), weighted by their correspondent abundance fractions. Linear spectral unmixing is a popular technique in the literature which assumes linear interactions between the endmembers, thus simplifying the characterization of the mixtures and approaching the problem from a general perspective independent of the physical properties of the observed materials. However, linear spectral unmixing suffers from several shortcomings. First, it is unlikely to find completely pure spectral endmembers in the image data due to spatial resolution and mixture phenomena. Second, the linear mixture model does not naturally include spatial information, which is an important source of information (together with spectral information) to solve the unmixing problem. In this thesis, we propose a completely new approach for spectral unmixing which makes use of spectral libraries of materials collected on the ground or in a laboratory, thus circumventing the problems associated to image endmember extraction. Due to the increasing availability and dimensionality of spectral libraries, this problem calls for efficient sparse regularizers. The resulting approach is called
Intercomparison and validation of techniques for spectral unmixing of hyperspectral images: A planetary case study
 IEEE Transactions on Geoscience and Remote Sensing
, 2011
"... Abstract—As the volume of hyperspectral data for planetary exploration increases, efficient yet accurate algorithms are decisive for their analysis. In this paper, the capability of spectral unmixing for analyzing hyperspectral images from Mars is investigated. For that purpose, we consider the Russ ..."
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Cited by 4 (1 self)
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Abstract—As the volume of hyperspectral data for planetary exploration increases, efficient yet accurate algorithms are decisive for their analysis. In this paper, the capability of spectral unmixing for analyzing hyperspectral images from Mars is investigated. For that purpose, we consider the Russell megadune observed by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) and the HighResolution Imaging Science Experiment (HiRISE) instruments. In late winter, this area of Mars is appropriate for testing linear unmixing techniques because of the geographical coexistence of seasonal CO2 ice and defrosting dusty features that is not resolved by CRISM. Linear unmixing is carried out on a selected CRISM image by seven stateoftheart approaches based on different principles. Three physically coherent sources with an increasing fingerprint of dust are recognized by the majority of the methods. Processing of HiRISE imagery allows the construction of a ground truth in the form of a reference abundance map related to the defrosting features. Validation of abundances estimated by spectral unmixing is carried out in an independent and quantitative manner by comparison with the ground truth. The quality of the results is estimated through the correlation coefficient and average error between the reconstructed and reference abundance maps. Intercomparison of the selected linear unmixing approaches is performed. Global and local comparisons show that misregistration inaccuracies between the HiRISE and CRISM images represent the major source of error. We also conclude that abundance maps provided by three methods out of seven are generally accurate, i.e., sufficient for a planetary interpretation.