Integrating Spatial Information in the Normalized P-Linear Algorithm for Nonlinear Hyperspectral Unmixing

To efficiently model high-order nonlinear material mixtures in complex scenery, more and more complex spectral mixing models have been developed, so that over-fitting phenomena more often occur during the unmixing process. Therefore, the accurate and robust inversion of material abundances is a challenging task, especially for low signal-to-noise ratio (SNR) data. In this paper, this task is achieved by inverting the parameters using a hierarchical Bayesian model based on the P-linear mixing model (PLMM). Moreover, spatial information is integrated in the inversion process by considering that similar pixels share the same prior information. Thanks to the fact that PLMM can be translated into a linear model using endmembers and their powers, unmixing is performed by solving a convex optimization problem. Results obtained from synthetic and real data show that the proposed algorithm improves the accuracy of abundance estimation and efficiently reduces over-fitting effects in low SNR data.