Hyperspectral Unmixing via Nonnegative Matrix Factorization With Handcrafted and Learned Priors

Abstract

Nowadays, nonnegative matrix factorization (NMF)-based methods have been widely applied to blind spectral unmixing. Introducing proper regularizers to NMF is crucial for mathematically constraining the solutions and physically exploiting spectral and spatial properties of images. Generally, properly handcrafted regularizers and solving the associated complex optimization problem are nontrivial tasks. In our work, we propose an NMF-based unmixing framework which jointly uses a learned regularizer from data and a handcrafted regularizer. To be specific, we plug learned priors of abundances where the associated subproblem can be addressed using various image denoisers, and we consider an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm as an example to illustrate the way of integrating handcrafted regularizers. The proposed framework is flexible and extendable. Both synthetic data and real airborne data are conducted to confirm the effectiveness of our method.