Futuristic Greedy Approach to Sparse Unmixing of Hyperspectral Data

Spectra measured at a single pixel of a remotely sensed hyperspectral image is usually a mixture of multiple spectral signatures (endmembers) corresponding to different materials on the ground. Sparse unmixing assumes that a mixed pixel is a sparse linear combination of different spectra already available in a spectral library. It uses sparse approximation (SA) techniques to solve the hyperspectral unmixing problem. Among these techniques, greedy algorithms suite well to sparse unmixing. However, their accuracy is immensely compromised by the high correlation of the spectra of different materials. This paper proposes a novel greedy algorithm, called OMP-Star, that shows robustness against the high correlation of spectral signatures. We preprocess the signals with spectral derivatives before they are used by the algorithm. To approximate the mixed pixel spectra, the algorithm employs a futuristic greedy approach that, if necessary, considers its future iterations before identifying an endmember. We also extend OMP-Star to exploit the nonnegativity of spectral mixing. Experiments on simulated and real hyperspectral data show that the proposed algorithms outperform the state-of-the-art greedy algorithms. Moreover, the proposed approach achieves results comparable to convex relaxation-based SA techniques, while maintaining the advantages of greedy approaches.