Results 1  10
of
103
Vertex component analysis: A fast algorithm to unmix hyperspectral data
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2005
"... Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for ..."
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Cited by 193 (16 self)
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Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: 1) the endmembers are the vertices of a simplex and 2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with stateoftheart methods, with a computational complexity between one and two orders of magnitude lower than the best available method.
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
Dimensionality reduction and classification of hyperspectral image data using sequences of extended morphological transformations
 IEEE Trans. Geosci. Remote Sens
, 2005
"... Abstract—This paper describes sequences of extended morphological transformations for filtering and classification of highdimensional remotely sensed hyperspectral datasets. The proposed approaches are based on the generalization of concepts from mathematical morphology theory to multichannel imag ..."
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Cited by 62 (27 self)
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Abstract—This paper describes sequences of extended morphological transformations for filtering and classification of highdimensional remotely sensed hyperspectral datasets. The proposed approaches are based on the generalization of concepts from mathematical morphology theory to multichannel imagery. A new vector organization scheme is described, and fundamental morphological vector operations are defined by extension. Extended morphological transformations, characterized by simultaneously considering the spatial and spectral information contained in hyperspectral datasets, are applied to agricultural and urban classification problems where efficacy in discriminating between subtly different ground covers is required. The methods are tested using real hyperspectral imagery collected by the
MINIMUM VOLUME SIMPLEX ANALYSIS: A FAST ALGORITHM TO UNMIX HYPERSPECTRAL DATA
"... This paper presents a new method of minimum volume class for hyperspectral unmixing, termed minimum volume simplex analysis (MVSA). The underlying mixing model is linear; i.e., the mixed hyperspectral vectors are modeled by a linear mixture of the endmember signatures weighted by the correspondent a ..."
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Cited by 55 (11 self)
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This paper presents a new method of minimum volume class for hyperspectral unmixing, termed minimum volume simplex analysis (MVSA). The underlying mixing model is linear; i.e., the mixed hyperspectral vectors are modeled by a linear mixture of the endmember signatures weighted by the correspondent abundance fractions. MVSA approaches hyperspectral unmixing by fitting a minimum volume simplex to the hyperspectral data, constraining the abundance fractions to belong to the probability simplex. The resulting optimization problem is solved by implementing a sequence of quadratically constrained subproblems. In a final step, the hard constraint on the abundance fractions is replaced with a hinge type loss function to account for outliers and noise. We illustrate the stateoftheart performance of the MVSA algorithm in unmixing simulated data sets. We are mainly concerning with the realistic scenario in which the pure pixel assumption (i.e., there exists at least one pure pixel per endmember) is not fulfilled. In these conditions, the MVSA yields much better performance than the pure pixel based algorithms. Index Terms — Hyperspectral unmixing, Minimum volume simplex, Source separation.
Sparse unmixing of hyperspectral data
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2011
"... Linear spectral unmixing is a popular tool in remotely sensed hyperspectral data interpretation. It aims at estimating the fractional abundances of pure spectral signatures (also called as endmembers) in each mixed pixel collected by an imaging spectrometer. In many situations, the identification o ..."
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Cited by 51 (15 self)
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Linear spectral unmixing is a popular tool in remotely sensed hyperspectral data interpretation. It aims at estimating the fractional abundances of pure spectral signatures (also called as endmembers) in each mixed pixel collected by an imaging spectrometer. In many situations, the identification of the endmember signatures in the original data set may be challenging due to insufficient spatial resolution, mixtures happening at different scales, and unavailability of completely pure spectral signatures in the scene. However, the unmixing problem can also be approached in semisupervised fashion, i.e., by assuming 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
A variable splitting augmented Lagrangian approach to linear spectral unmixing
 In First IEEE Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing
, 2009
"... This paper presents a new linear hyperspectral unmixing method of the minimum volume class, termed 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 ..."
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Cited by 41 (8 self)
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This paper presents a new linear hyperspectral unmixing method of the minimum volume class, termed 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 stateofthe art algorithms. The effectiveness of SISAL is illustrated with simulated data. Index Terms — Hyperspectral unmixing, Minimum volume simplex, Variable Splitting augmented Lagrangian, nonsmooth optimization.
Regionbased spatial preprocessing for endmember extraction and spectral unmixing
 IEEE Geosci. Remote Sens. Lett
, 2011
"... In this paper, we develop a new spatial preprocessing strategy which can be applied prior to a spectralbased endmember extraction process for unmixing of hyperspectral data. Our proposed approach directs the endmember searching process to regions which are both spectrally pure and spatially homoge ..."
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Cited by 35 (11 self)
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In this paper, we develop a new spatial preprocessing strategy which can be applied prior to a spectralbased endmember extraction process for unmixing of hyperspectral data. Our proposed approach directs the endmember searching process to regions which are both spectrally pure and spatially homogeneous in the scene. Our experimental results, conducted using simulated hyperspectral data sets with known endmembers and fractional abundances, reveal that the proposed approach can successfully integrate the spatial and spectral information in the search for more relevant endmembers. Index Terms — Spectral unmixing, endmember extraction, spatialspectral integration.
ALTERNATING DIRECTION ALGORITHMS FOR CONSTRAINED SPARSE REGRESSION: APPLICATION TO HYPERSPECTRAL UNMIXING
"... Convex optimization problems are common in hyperspectral unmixing. Examples are the constrained least squares (CLS) problem used to compute the fractional abundances in a linear mixture of known spectra, the constrained basis pursuit (CBP) to find sparse (i.e., with a small number of terms) linear m ..."
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Cited by 33 (11 self)
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Convex optimization problems are common in hyperspectral unmixing. Examples are the constrained least squares (CLS) problem used to compute the fractional abundances in a linear mixture of known spectra, the constrained basis pursuit (CBP) to find sparse (i.e., with a small number of terms) linear mixtures of spectra, selected from large libraries, and the constrained basis pursuit denoising (CBPDN), which is a generalization of BP to admit modeling errors. In this paper, we introduce two new algorithms to efficiently solve these optimization problems, based on the alternating direction method of multipliers, a method from the augmented Lagrangian family. The algorithms are termed SUnSAL (sparse unmixing by variable splitting and augmented Lagrangian) and CSUnSAL (constrained SUnSAL). CSUnSAL solves the CBP and CBPDN problems, while SUnSAL solves CLS as well as a more general version thereof, called constrained sparse regression (CSR). CSUnSAL and SUnSAL are shown to outperform offtheshelf methods in terms of speed and accuracy. 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.
Learning sparse codes for hyperspectral imagery
 IEEE Journal of Selected Topics in Signal Processing
, 2011
"... The spectral features in hyperspectral imagery (HSI) contain significant structure that, if properly characterized could enable more efficient data acquisition and improved data analysis. Because most pixels contain reflectances of just a few materials, we propose that a sparse coding model is well ..."
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Cited by 19 (2 self)
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The spectral features in hyperspectral imagery (HSI) contain significant structure that, if properly characterized could enable more efficient data acquisition and improved data analysis. Because most pixels contain reflectances of just a few materials, we propose that a sparse coding model is wellmatched to HSI data. Sparsity models consider each pixel as a combination of just a few elements from a larger dictionary, and this approach has proven effective in a wide range of applications. Furthermore, previous work has shown that optimal sparse coding dictionaries can be learned from a dataset with no other a priori information (in contrast to many HSI “endmember ” discovery algorithms that assume the presence of pure spectra or side information). We modified an existing unsupervised learning approach and applied it to HSI data (with significant ground truth labeling) to learn an optimal sparse coding dictionary. Using this learned dictionary, we demonstrate three main findings: i) the sparse coding model learns spectral signatures of materials in the scene and locally approximates nonlinear manifolds for individual materials, ii) this learned dictionary can be used to infer HSIresolution data with very high accuracy from simulated imagery collected at multispectrallevel resolution, and iii) this learned dictionary improves the performance of a supervised classification algorithm, both in terms of the classifier complexity and generalization from very small training sets.