Adaptive Spatial Regularization Sparse Unmixing Strategy Based on Joint MAP for Hyperspectral Remote Sensing Imagery

Sparse unmixing, as a recently developed spectral unmixing approach, has been successfully applied based on the assumption that the observed image signatures can be expressed in an efficient linear sparse regression with the potentially very large endmember spectral library. To improve the unmixing accuracy, spatial information has been incorporated in the sparse unmixing formulation by adding an appropriate spatial regularization for the hyperspectral remote sensing imagery. However, for the traditional spatial regularization sparse unmixing (SRSU) algorithms, it is a difficult task to set appropriate user-defined regularization parameters in real applications, and this often has a high computational cost. To overcome the difficulty of the regularization parameter selection, the adaptive spatial regularization sparse unmixing (ASRSU) strategy based on the joint maximum a posteriori (JMAP) estimation technique is proposed in this paper. In ASRSU, the SRSU problem is formulated in the framework of JMAP with an appropriate prior model. ASRSU considers the regularization parameters and the abundances jointly by an alternating iterative process, and the relationships between the regularization parameters and the abundances are obtained from the JMAP model. Based on the ASRSU strategy, two ASRSU algorithms are presented: the adaptive total variation spatial regularization sparse unmixing algorithm and the adaptive nonlocal means filtering sparse unmixing algorithm. The experimental results demonstrate that the two proposed ASRSU algorithms based on JMAP can adaptively obtain optimal or near-optimal regularization parameters for the three simulated datasets and the two real hyperspectral remote sensing images.