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41
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
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.
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.
A Compressive Sensing and Unmixing Scheme for Hyperspectral Data Processing
"... Hyperspectral data processing typically demands enormous computational resources in terms of storage, computation and I/O throughputs, especially when realtime processing is desired. In this paper, we investigate a lowcomplexity scheme for hyperspectral data compression and reconstruction. In this ..."
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Cited by 16 (2 self)
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Hyperspectral data processing typically demands enormous computational resources in terms of storage, computation and I/O throughputs, especially when realtime processing is desired. In this paper, we investigate a lowcomplexity scheme for hyperspectral data compression and reconstruction. In this scheme, compressed hyperspectral data are acquired directly by a device similar to the singlepixel camera [5] based on the principle of compressive sensing. To decode the compressed data, we propose a numerical procedure to directly compute the unmixed abundance fractions of given endmembers, completely bypassing highcomplexity tasks involving the hyperspectral data cube itself. The reconstruction model is to minimize the total variational of the abundance fractions subject to a preprocessed fidelity equation with a significantly reduced size, and other side constraints. An augmented Lagrangian type algorithm is developed to solve this model. We conduct extensive numerical experiments to demonstrate the feasibility and efficiency of the proposed approach, using both synthetic data and hardwaremeasured data. Experimental and computational evidences obtained from this study indicate that the proposed scheme has a high potential in realworld applications.
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.
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,
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.
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)
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.
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