Unsupervised Classification of Polarimetric SAR Images via Riemannian Sparse Coding

Unsupervised classification plays an important role in understanding polarimetric synthetic aperture radar (PolSAR) images. One of the typical representations of PolSAR data is in the form of Hermitian positive definite (HPD) covariance matrices. Most algorithms for unsupervised classification using this representation either use statistical distribution models or adopt polarimetric target decompositions. In this paper, we propose an unsupervised classification method by introducing a sparsity-based similarity measure on HPD matrices. Specifically, we first use a novel Riemannian sparse coding scheme for representing each HPD covariance matrix as sparse linear combinations of other HPD matrices, where the sparse reconstruction loss is defined by the Riemannian geodesic distance between HPD matrices. The coefficient vectors generated by this step reflect the neighborhood structure of HPD matrices embedded in the Euclidean space and hence can be used to define a similarity measure. We apply the scheme for PolSAR data, in which we first oversegment the images into superpixels, followed by representing each superpixel by an HPD matrix. These HPD matrices are then sparse coded, and the resulting sparse coefficient vectors are then clustered by spectral clustering using the neighborhood matrix generated by our similarity measure. The experimental results on different fully PolSAR images demonstrate the superior performance of the proposed classification approach against the state-of-the-art approaches.