Riemannian sparse coding for classification of PolSAR images

Hermitian positive definite (HPD) covariance matrices form one of the most widely-used data representations in PolSAR applications. However, most of these applications either use statistical distribution models on the PolSAR covariance matrices or polarimetric target decomposition. In this paper, we study HPD matrices for PolSAR image classification in the context of sparse coding. More specifically, the PolSAR HPD matrices are first represented as sparse linear combinations of elements from a dictionary, where each element itself is an HPD matrix and the representation loss is measured by the affine-invariant Riemannian metric. We then introduce a sparsity induced similarity measure between two HPD matrices. Finally, we propose a supervised classification scheme using support vector machines on the Riemannian sparse codes and an unsupervised classification scheme encompassing a sparsity induced similarity measure followed by spectral clustering. The proposed methods are validated on the NASA/JPL AIRSAR fully PolSAR data. The experimental results demonstrate the effectiveness of our methods.