Nonnegative Matrix Factorization with Piecewise Smoothness Constraint for Hyperspectral Unmixing

Hyperspectral unmixing is a process to identify the constituent materials and estimate the corresponding fractions from the mixture. During the last few years, nonnegative matrix factorization (NMF), as a suitable candidate for the linear spectral. mixture model, has been applied to unmix hyperspectral data. Unfortunately, the nonconvexity of the objective function makes the solution non-unique, indicating that additional constraints on the nonegative components are needed for NMF applications. Therefore in this paper, piecewise smoothness constraint of spectral data (both temporal and spatial), which is an inherent characteristic of hyperspectral data, is introduced to NMF Vie regularization function from edge-preserving regularization is used to describe the smoothness constraint while preserving sharp variation in spectral data. The monotonic convergence of the algorithm is guaranteed by an alternating multiplicative updating process. Experimentations on real data are provided to illustrate the algorithm's performance.