Backtracking-Based Simultaneous Orthogonal Matching Pursuit for Sparse Unmixing of Hyperspectral Data

Sparse unmixing is a promising approach in a semisupervised fashion by assuming that the observed signatures of a hyperspectral image can be expressed in the form of linear combination of only a few spectral signatures (endmembers) in an available spectral library. Simultaneous orthogonal matching pursuit (SOMP) algorithm is a typical simultaneous greedy algorithm for sparse unmixing, which involves finding the optimal subset of signatures for the observed data from a spectral library. But the numbers of endmembers selected by SOMP are still larger than the actual number, and the nonexisting endmembers will have a negative effect on the estimation of the abundances corresponding to the actual endmembers. This paper presents a variant of SOMP, termed backtracking-based SOMP (BSOMP), for sparse unmixing of hyperspectral data. As an extension of SOMP, BSOMP incorporates a backtracking technique to detect the previous chosen endmembers' reliability and then deletes the unreliable endmembers. Through this modification, BSOMP can select the true endmembers more accurately than SOMP. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed algorithm.