Blind Sparse Nonlinear Hyperspectral Unmixing Using an <inline-formula> <tex-math notation="LaTeX">$\ell_{q}$ </tex-math> </inline-formula> Penalty

Abstract

Blind hyperspectral unmixing (HU) is the task of jointly estimating the spectral signatures of materials and abundances in hyperspectral images. Most unmixing algorithms assume the linear mixture model, however, nonlinear models have recently gained interest, as they represent more complicated scenes. This letter proposes two blind nonlinear HU algorithms. The former algorithm assumes that the spectra are mixed according to the generalized bilinear model, while the latter assumes an extension to this model, called the Fan model. Both the algorithms use the $\boldsymbol \ell _{ \boldsymbol q}$ regularizer to promote sparse abundances and solve the minimization problems using cyclic descent. The algorithms are evaluated and compared with other unmixing algorithms using both simulated and real data.