Hyperspectral Image Restoration Using 3-D Hybrid Higher Degree Total Variation Regularized Nonconvex Local Low-Rank Tensor Recovery

The degradation of spaceborne hyperspectral images (HSIs) usually results from various types of noise. In this letter, we propose a 3-D hybrid higher degree total variation regularized nonconvex local low-rank tensor recovery ( ${\text {H}^{2}}$ DTV-NLRTR) model to restore the HSIs. Inspired by the good performance of the higher DTV penalty in image denoising, we first develop a 3-D hybrid higher degree total variation penalty term, which is able to capture the fine image details and edges along the spatial dimensions and spectral dimension. The tensor multi-Schatten- $p$ norm is chosen as the relaxation of the low-rank tensor constraint, which can not only separate the low-rank clean HSI patches from noisy images effectively but also improve the computational efficiency. The proposed ${\text {H}^{2}}$ DTV-NLRTR model can simultaneously characterize the spectral correlation and the spatial structure of the HSI dataset by incorporating the ${\text {H}^{2}}$ DTV penalty in the NLRTR problem. In addition, we adopt a fast iterative majorize-minimize algorithm to efficiently solve the corresponding optimization problem. The numerical experiments on both simulated and real HSI datasets demonstrate that the proposed algorithm provides consistently improved restoration results compared with the state-of-the-art algorithms.