Robust Joint Sparse Representation Based on Maximum Correntropy Criterion for Hyperspectral Image Classification

Joint sparse representation (JSR) has been a popular technique for hyperspectral image classification, where a testing pixel and its spatial neighbors are simultaneously approximated by a sparse linear combination of all training samples, and the testing pixel is classified based on the joint reconstruction residual of each class. Due to the least-squares representation of the approximation error, the JSR model is usually sensitive to outliers, such as background, noisy pixels, and outlying bands. In order to eliminate such effects, we propose three correntropy-based robust JSR (RJSR) models, i.e., RJSR for handling pixel noise, RJSR for handling band noise, and RJSR for handling both pixel and band noise. The proposed RJSR models replace the traditional square of the Euclidean distance with 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 nonconvex and nonlinear optimization problem into an iteratively reweighted JSR problem. As a result, the optimization of our models can handle the noise in neighboring pixels and the noise in spectral bands. It can adaptively assign small weights to noisy pixels or bands and put more emphasis on noise-free pixels or bands. The experimental results using real and simulated data demonstrate the effectiveness of our models in comparison with the related state-of-the-art JSR models.