Linear spectral unmixing with generalized constraint for hyperspectral imagery

Linear mixture model (LMM) has been widely used in hyperspectral image unmixing under the assumption that the mixed spectrum is performed in a linear manner. In order to obtain accurate amounts of material abundance, two constrains are usually imposed on LMM, which are abundance non-negative constraint (ANC) and abundance sum-to-one constraint (ASC). Although LMM with full constraint shows bunches of advantages in application, it is not so effective in complicated ground scene, for it couldn´t simulate nonlinear factors and might distort the unmixed abundances under nonlinear interferences. In this paper, we propose a generalized constraint model by slacking the sum to one constraint of fractional abundances, which can tolerate spectral-amplitude variation caused by undulated terrain. The experiment results indicate that the proposed method outperforms LMM with full constraint significantly in terms of unmixing accuracy of specific land-covers, such as shadows caused by sheltering.