Repeated constrained sparse coding with partial dictionaries for hyperspectral unmixing

Abstract

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 end-members. 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, Repeated-CSC (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.