Pixel-Wise Linear/Nonlinear Nonnegative Matrix Factorization for Unmixing of Hyperspectral Data

Nonlinear spectral unmixing is a challenging and important task in hyperspectral image analysis. The kernel-based bi-objective non-negative matrix factorization (Bi-NMF) has shown its usefulness in nonlinear unmixing; However, it suffers several issues that prohibit its practical application. In this work, we propose an unsupervised nonlinear unmixing method that overcomes these weaknesses. Specifically, the new method introduces into each pixel a parameter that adjusts the nonlinearity therein. These parameters are jointly optimized with endmembers and abundances, using a carefully designed objective function by multiplicative update rules. Experiments on synthetic and real datasets confirm the effectiveness of the proposed method.