Orthogonal Subspace Unmixing to Address Spectral Variability for Hyperspectral Image

Hyperspectral unmixing aims at estimating pure spectral signatures and their proportions in each pixel. In practice, the atmospheric effects, intrinsic variation of the spectral signatures of the materials, illumination, and topographic changes cause what is known as spectral variability resulting in significant estimation errors being propagated throughout the unmixing task. To this end, we developed a new method, called the orthogonal subspace unmixing (OSU), to address spectral variability by utilizing the orthogonal subspace projection. The proposed OSU method jointly performs orthogonal subspace learning and the unmixing process to find a more suitable subspace for unmixing. The orthogonal subspace projection encourages the representation held in the subspace to be more distinct from each other to remove the complex spectral variability in the subspace. Furthermore, an alternating minimization (AM) was designed to solve the resulting optimization problem. An efficient and convergent symmetric Gauss–Seidel alternating direction method of multipliers (sGS-ADMM), essentially a special case of the semiproximal alternating direction method of multipliers (SPADMM), was developed to solve the subproblem. Experiments conducted on one synthetic data and two real data demonstrate the effectiveness and superiority of the proposed framework in mitigating the effects of spectral variability with respect to classical linear unmixing methods or variability accounting approaches.