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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
Nonlinear unmixing of hyperspectral images using a generalized bilinear model
 IEEE Trans. Geosci. and Remote Sensing
"... Nonlinear models have recently shown interesting properties for spectral unmixing. This paper considers a generalized bilinear model recently introduced for unmixing hyperspectral images. Different algorithms are studied to estimate the parameters of this bilinear model. The positivity and sumtoon ..."
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Cited by 41 (21 self)
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Nonlinear models have recently shown interesting properties for spectral unmixing. This paper considers a generalized bilinear model recently introduced for unmixing hyperspectral images. Different algorithms are studied to estimate the parameters of this bilinear model. The positivity and sumtoone constraints for the abundances are ensured by the proposed algorithms. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data. Index Terms — hyperspectral imagery, spectral unmixing, bilinear model, Bayesian inference, MCMC methods, gradient descent algorithm, least square algorithm. 1.
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.
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: 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.
ChanceConstrained Robust MinimumVolume Enclosing Simplex Algorithm for Hyperspectral Unmixing
, 2011
"... Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging research problem in remote sensing arena. A branch of existing hyperspectral unmixing algorithms is based on Craig’s criterion, which states that the vertices of the minimumvolume simplex enclosing the hype ..."
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Cited by 12 (4 self)
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Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging research problem in remote sensing arena. A branch of existing hyperspectral unmixing algorithms is based on Craig’s criterion, which states that the vertices of the minimumvolume simplex enclosing the hyperspectral data should yield high fidelity estimates of the endmember signatures associated with the data cloud. Recently, we have developed a minimumvolume enclosing simplex (MVES) algorithm based on Craig’s criterion and validated that the MVES algorithm is very useful to unmix highly mixed hyperspectral data. However, the presence of noise in the observations expands the actual data cloud, and as a consequence, the endmember estimates obtained by applying Craigcriterionbased algorithms to the noisy data may no longer be in close proximity to the true endmember signatures. In this paper, we propose a robust MVES (RMVES)
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
Recent developments in endmember extraction and spectral unmixing
 of Advances in Signal Processing and Exploitation Techniques
, 2011
"... Abstract Spectral unmixing is an important task for remotely sensed hyperspectral data exploitation. The spectral signatures collected in natural environments are invariably a mixture of the pure signatures of the various materials found within the spatial extent of the ground instantaneous field ..."
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Cited by 5 (0 self)
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Abstract Spectral unmixing is an important task for remotely sensed hyperspectral data exploitation. The spectral signatures collected in natural environments are invariably a mixture of the pure signatures of the various materials found within the spatial extent of the ground instantaneous field view of the imaging instrument. Spectral unmixing aims at inferring such pure spectral signatures, called endmembers, and the material fractions, called fractional abundances, at each pixel of the scene. In this chapter, we provide an overview of existing techniques for spectral unmixing and endmember extraction, with particular attention paid to recent advances in the field such as the incorporation of spatial information into the endmember searching process, or the use of nonlinear mixture models for fractional abundance characterization. In order to substantiate the methods presented throughout the chapter, highly representative hyperspectral scenes obtained by different imaging spectrometers are used to provide a quantitative and comparative algorithm assessment. To address the computational requirements introduced by hyperspectral imaging algorithms, the chapter also
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.