Hypersharpening by Joint-Criterion Nonnegative Matrix Factorization

Hypersharpening aims at combining an observable low-spatial resolution hyperspectral image with a high-spatial resolution remote sensing image, in particular a multispectral one, to generate an unobservable image with the high spectral resolution of the former and the high spatial resolution of the latter. In this paper, two such new fusion methods are proposed. These methods, related to linear spectral unmixing techniques, and based on nonnegative matrix factorization (NMF), optimize a new joint criterion and extend the recently proposed joint NMF (JNMF) method. The first approach, called gradient-based joint-criterion NMF (Grd-JCNMF), is a gradient-based method. The second one, called multiplicative JCNMF (Mult-JCNMF), uses new designed multiplicative update rules. These two JCNMF approaches are applied to synthetic and semireal data, and their effectiveness, in spatial and spectral domains, is evaluated with commonly used performance criteria. Experimental results show that the proposed JCNMF methods yield sharpened hyperspectral data with good spectral and spatial fidelities. The obtained results are compared with the performance of two NMF-based methods and one approach based on a sparse representation. These results show that the proposed methods significantly outperform the well-known coupled NMF sharpening method for most performance figures. Also, the proposed Mult-JCNMF method provides the results that are similar to those obtained by JNMF, with a lower computational cost. Compared with the tested sparse-representation-based approach, the proposed methods give better results. Moreover, the proposed Grd-JCNMF method considerably surpasses all other tested methods.