Sparse hyperspectral unmixing with spatial discontinuity preservation

Sparse unmixing and sparse representation are known to be effective for improving the interpretation of remotely sensed hyperspectral images. Classic methods for incorporating spatial information into spectral unmixing assume that the abundances of the pixels are smooth and fall into a homogeneous region shared by the same endmembers and their corresponding fractional abundances. Sometimes this assumption does not hold in practice, as images contain abrupt changes in endmember abundances, i.e., abundance maps are often spatially heterogeneous. To address this limitation, in this work we propose a novel sparse unmixing framework with discontinuity preservation which aims at preserving the spatial heterogeneity present in abundance maps. In the proposed framework, the Sobel operator is used to characterize such discontinuities. Our experimental results, conducted using both simulated and real hyperspectral data sets, indicate that the introduction of a discontinuity preserving strategy on sparse unmixing formulations is beneficial to preserve the spatial heterogeneity present in the abundance maps. We exploit this information effectively to improve abundance estimation.