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Hyperspectral unmixing overview: Geometrical, statistical, and sparse regressionbased approaches
 IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens
, 2012
"... Abstract—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). H ..."
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Cited by 104 (34 self)
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Abstract—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
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 (10 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.
Repeated constrained sparse coding with partial dictionaries for hyperspectral unmixing
"... Hyperspectral images obtained from remote sensing platforms have limited spatial resolution. Thus, each spectra measured at a pixel is usually a mixture of many pure spectral signatures (endmembers) corresponding to different materials on the ground. Hyperspectral unmixing aims at separating these m ..."
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Cited by 3 (1 self)
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Hyperspectral images obtained from remote sensing platforms have limited spatial resolution. Thus, each spectra measured at a pixel is usually a mixture of many pure spectral signatures (endmembers) corresponding to different materials on the ground. Hyperspectral unmixing aims at separating these mixed spectra into its constituent endmembers. We formulate hyperspectral unmixing as a constrained sparse coding (CSC) problem where unmixing is performed with the help of a library of pure spectral signatures under positivity and summation constraints. We propose two different methods that perform CSC repeatedly over the hyperspectral data. However, the first method, RepeatedCSC (RCSC), systematically neglects a few spectral bands of the data each time it performs the sparse coding. Whereas the second method, Repeated Spectral Derivative (RSD), takes the spectral derivative of the data before the sparse coding stage. The spectral derivative is taken such that it is not operated on a few selected bands. Experiments on simulated and real hyperspectral data and comparison with existing state of the art show that the proposed methods achieve significantly higher accuracy. Our results demonstrate the overall robustness of RCSC to noise and better performance of RSD at high signal to noise ratio.
Hyperspectral Unmixing: Geometrical, Statistical, and Sparse RegressionBased Approaches
"... 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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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.
Surveying, Mapping and Remote Sensing
"... Abstract—Hyperspectral imagery unmixing model based on sparse regression uses the existing endmembers ’ library as priori information. Usually, the existing endmembers’ library contains almost all kinds of ground objects. Even though sparse regressionbased imagery unmixing method added sparse const ..."
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Abstract—Hyperspectral imagery unmixing model based on sparse regression uses the existing endmembers ’ library as priori information. Usually, the existing endmembers’ library contains almost all kinds of ground objects. Even though sparse regressionbased imagery unmixing method added sparse constraint to the original unmxing model, the solution is still far away as sparse as real scenario. Therefore, we propose a hyperspectral imagery further unmixing method based on the analysis of variance. In this method, fractional abundances unmixed by sparse regressionbased approach are analyzed with ttest. If the fractional abundances are not significant enough, the corresponding endmembers will be removed and a new optimal endmember subset will be extracted. Then the unmixing process was redid with acquired optimal endmember subset and the final result will be acquired. The experimental results indicate that the proposed method could acquire sparser solution, which is closer to the real sparsity of abundance, both in simulate scenario and real scenario. Furthermore, the precision of the endmember recognition of proposed method is more than 97%, which is a pretty good result. KeywordsHyperspectral imagery; Linear unmixing; Sparse regression; Analysis of variance I.