3D geometrical total variation regularized low-rank matrix factorization for hyperspectral image denoising

Abstract

The total variation (TV) regularization has been widely used in hyperspectral image (HSI) denoising owing to its powerful capabilities in terms of structure preservation. However, existing TV terms ignore the geometrical structures, such as edges and textures, in HSIs. To this end, we present a novel 3D geometrical total variation (3D GTV) regularizer to capture the local information in HSIs. 3D GTV can preserve the spatial and spectral information in 3D cubes effectively due to the introduction of geometrical structures. By incorporating this term, a 3D GTV regularized low-rank matrix factorization (3DGTVLR) method is proposed for the noise removal of noisy HSIs. In the proposed method, different norms are adopted to model the structures in 3D cubes. More specifically, the L1 norm is employed to enhance the structural information in the 3D cubes containing edges or textures, while the L2 norm is considered to ensure the information in flat 3D cubes. The local structures in HSIs are represented more compatibly by the combination of L1 and L2 norms. Then, we derive an efficient algorithm based on the alternating direction method of multipliers (ADMM) to solve the optimization problem. Experiments are performed on synthetic and real HSI datasets and the effectiveness of the proposed method is demonstrated when compared with the state-of-the-art methods. Our code is available at https://github.com/RSMagneto/3DGTVLR.