Local Spectral Similarity Preserving Regularized Robust Sparse Hyperspectral Unmixing

Spatial context has been demonstrated to be effective to constrain sparse unmixing (SU) of hyperspectral images. However, the existing algorithms employed simple spatial information without keeping spectral fidelity. By considering the fact that adjacent pixels own not only the endmembers with same variations but also approximated fractional abundances, in this paper, local spectral similarity preserving (LSSP) constraint is proposed to preserve spectral similarity in a local area during robust sparse unmixing (RSU). Specially, four LSSP constraints are constructed using different-norm-constrained pixel-level difference over abundance-level difference in a local area. Moreover, a convex optimization algorithm is proposed to solve the proposed LSSP-constrained RSU (LSSP-RSU). Experimental results on both synthetic and real hyperspectral data demonstrate that the developed algorithms yield better values of the signal-to-reconstruction error (SRE). Especially, when using <inline-formula> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> norm of pixel-level difference to weight the <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> norm of abundance-level difference, the proposed LSSP-RSU algorithm can achieve superior unmixing performance.