Spectral Unmixing with Sparsity and Structuring Constraints

This paper addresses the linear spectral unmixing problem, by incorporating different constraints that may be of interest in order to cope with spectral variability: sparsity (few nonzero abundances), group exclusivity (at most one nonzero abundance within subgroups of endmembers) and significance (non-zero abundances must exceed a threshold). We show how such problems can be solved exactly with mixed-integer programming techniques. Numerical simulations show that solutions can be computed for problems of limited, yet realistic, complexity, with improved estimation performance over existing methods, but with higher computing time.