A sparsity promoting bilinear unmixing model

An algorithm, Bilinear SPICE (BISPICE), for simultaneously estimating the number of endmembers, the endmembers, and proportions for a bilinear mixing model is derived and evaluated. BISPICE generalizes the SPICE algorithm for linear mixing. The proportion estimation steps of SPICE and BISPICE are similar. However, the endmember updates, one novel aspect of the work, are quite different. The SPICE objective function is quadratic in the endmembers. The BISPICE is a fourth degree polynomial. In SPICE, endmembers are updated simultaneously via a closed form. In BISPICE, each endmember must be updated with respect to all other endmembers. Empirically, BISPICE estimated endmembers and proportions more accurately then SPICE, even though the data fitting error was higher.