Band-Wise Nonlinear Unmixing for Hyperspectral Imagery Using an Extended Multilinear Mixing Model

Most nonlinear mixture models and unmixing methods in the literature assume implicitly that the degrees of multiple scatterings at each band are the same. However, it is commonly against the practical situation that spectral mixing is intrinsically wavelength dependent, and the nonlinear intensity varies along with bands. In this paper, a band-wise nonlinear unmixing algorithm is proposed to circumvent this drawback. Pixel dependent probability parameters of the recent multilinear mixing model that represent different orders of nonlinear contributions are vectorized. Therefore, each band can get a scalar probability parameter which explicitly corresponds to the nonlinear intensity at that band. Before solving the extended model, abundances' sparsity and probability parameters' smoothness are exploited to build two physical constraints. After incorporating them into the objective function as regularization terms, the issue of local minima can be well alleviated to produce better solutions. Finally, alternating direction method of multipliers is applied to solve the constrained optimization problem and implement the nonlinear spectral unmixing. Experiments are further carried out with current model-based simulated data, physical-based synthetic data of virtual vegetated areas, and real hyperspectral remote sensing images, to provide a more reasonable validation for the developed model and algorithm. In comparison with state-of-the-art nonlinear unmixing methods, this method performs better in explaining the band dependent nonlinear mixing effect for improving the unmixing accuracy.