Collaborative Unmixing Hyperspectral Imagery via Nonnegative Matrix Factorization

We propose a method of hyperspectral unmixing for the linear mixing model (LMM) while both the spectral signatures of endmembers and their fractional abundances are unknown. The proposed algorithm employs the non-negative matrix factorization (NMF) method as well as simultaneous (collaborative) sparse regression model. We formulate the NMF problem along with an averaging over the l(2)-norm of the fractional abundances so-called l(2), q-norm term. We show that this problem can be efficiently solved by using the Karush-Kuhn-Tucker (KKT) conditions. Our simulations show that the proposed algorithm outperforms the state-of-the-art methods in terms of spectral angle distance (SAD) and abundance angle distance (AAD).