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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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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.
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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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.
MUSICCSR: Hyperspectral Unmixing via 1 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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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.