Correntropy-based robust joint sparse representation for hyperspectral image classification

In the joint sparse representation (JSR) model, a test pixel and its spatial neighbors are simultaneously approximated by a sparse linear combination of all training samples, and then the test pixel is classified based on the joint reconstruction residual of each class. Due to the least-squares representation of reconstruction residual, the JSR model is usually sensitive to outliers, such as background and noisy pixels. In order to eliminate the effect of noisy and outliers, we propose a robust correntropy-based JSR (CJSR) model for the hyperspectral image classification. It replaces the traditional square of the Euclidean distance to the correntropy-based metric in measuring the joint approximation error. To solve the correntropy-based joint sparsity model, a half-quadratic optimization technique is developed to convert the original non-convex and nonlinear optimization problem into an iteratively reweighted JSR problem. As a result, the optimization of our model can handle the noise in the spatial neighborhood of each test pixel. It can adaptively assign small weights to noisy pixels and put more emphasis on noise-free pixels. Experiments demonstrate the effectiveness of our model in comparison to the related state-of-the-art sparsity models.