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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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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
MUSICCSR: Hyperspectral Unmixing via Multiple Signal Classification and Collaborative Sparse Regression
"... Spectral unmixing aims at finding the spectrally pure constituent materials (also called endmembers) and their respective fractional abundances in each pixel of a hyperspectral image scene. In recent years, sparse unmixing has been widely used as a reliable spectral unmixing methodology. In this app ..."
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Cited by 3 (2 self)
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Spectral unmixing aims at finding the spectrally pure constituent materials (also called endmembers) and their respective fractional abundances in each pixel of a hyperspectral image scene. In recent years, sparse unmixing has been widely used as a reliable spectral unmixing methodology. In this approach, the observed spectral vectors are expressed as linear combinations of spectral signatures assumed to be known a priori and present in a large collection, termed spectral library or dictionary, usually acquired in laboratory. Sparse unmixing has attracted much attention as it sidesteps two common limitations of classic spectral unmixing approaches: the lack of pure pixels in hyperspectral scenes and the need to estimate the number of endmembers in a given scene, which are very difficult tasks. However, the high mutual coherence of spectral libraries, jointly with their evergrowing dimensionality, strongly limits the operational applicability of sparse unmixing. In this paper, we introduce a twostep algorithm aimed at mitigating the aforementioned limitations. The algorithm exploits the usual low dimensionality of the hyperspectral data sets. The first step, similar to the multiple signal classification (MUSIC) array signal processing algorithm, identifies a subset of the library elements which contains the endmember signatures. Because this subset has cardinality much smaller than the initial number of library elements, the sparse regression we are led to is much more wellconditioned than the initial one using the complete library. The second step applies collaborative sparse regression (CSR), which is a form of structured sparse regression, exploiting the fact that only a few spectral signatures in the library are active. The effectiveness of the proposed approach, termed MUSICCSR, is extensively validated using both simulated and real hyperspectral data sets.
Dictionary pruning in sparse unmixing of hyperspectral data
 4th IEEE GRSS Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS
, 2012
"... Spectral unmixing is an important technique for remotely sensed hyperspectral data exploitation. When hyperspectral unmixing relies on the use of spectral libraries (dictionaries of pure spectra), the sparse regression problem to be solved is severely illconditioned and timeconsuming. This is due, ..."
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Cited by 1 (1 self)
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Spectral unmixing is an important technique for remotely sensed hyperspectral data exploitation. When hyperspectral unmixing relies on the use of spectral libraries (dictionaries of pure spectra), the sparse regression problem to be solved is severely illconditioned and timeconsuming. This is due, on the one hand, to the presence of very similar signatures in the library and, on the other, to the existence in the library of spectral signatures that do not contribute to the observed mixtures. In practice, spectral libraries are highly coherent, which adds yet another complication. In this regard, the identification of a subset of signatures from the library which truly contribute to the observed mixtures has the potential to improve the conditioning of the problem and to considerably decrease the running time of the sparse unmixing algorithm. This paper proposes a methodology for obtaining such a dictionary pruning. The efficiency of the method is assessed using both simulated and real hyperspectral data. 1.