Improving Sparse Noise Removal via L0-Norm Optimization for Hyperspectral Image Restoration

This letter presents a novel method for hyperspectral image (HSI) restoration, which aims to improve the removal effectiveness of the sparse noise. In contrast to the existing approaches that employ the $L_{1}$ -norm for tractable optimization, we apply the non-convex non-smooth $L_{0}$ -norm to measure the sparsity of the impulse noise, stripes, deadlines, and other outliers accurately. By combining the low-rank and total variation (TV) priors to exploit the intrinsic properties of the clean HSI and using the patch scheme to preserve local features, the $L_{0}$ -PLRTV restoration model is established. In order to deal with the optimization problem, we introduce an equivalent primal-dual formulation to reformulate the $L_{0}$ -norm term, and develop a minimization approach for the objective function based on the alternating iterative method. The simulated and real data experiments confirm that the proposed algorithm can effectively reduce the sparse noise in HSI.