Log-Euclidean Kernel-Based Joint Sparse Representation for Hyperspectral Image Classification

Abstract

Motivated by the superior performance of region covariance descriptor, we use covariance matrices as new features to replace the original spectral pixel features, and employ a Log-Euclidean metric to characterize the geodesic distance between symmetric positive definite (SPD) covariance matrices. Based on the covariance features and Log-Euclidean metric, we propose a Log-Euclidean kernel-based joint sparse representation (LogEKJSR) model for the classification of hyperspectral images (HSIs). In the implementation of LogEKJSR, we first reduce the dimensionality of HSI by employing extended multiattribute profile (EMAP) transformations, and then extract the region covariance matrix features associated with each pixel on the EMAPs. The EMAP can model homogeneity and texture structure of HSI by aggregating multiple morphological attribute profiles, the covariance matrix feature contains both local spectral correlation and spatial structure information, and the Log-Euclidean kernel is a matrix-to-matrix similarity metric rather than vector-to-vector similarity metric. Finally, a LogEKJSR model is obtained by replacing the traditional kernel in the KJSR with the Log-Euclidean kernel. Experimental results on three benchmark hyperspectral data sets demonstrate that our proposed LogEKJSR is more effective than existing JSR, KJSR, and support vector machine methods.