Hyperspectral Image Mixed Noise Removal Based on Multidirectional Low-Rank Modeling and Spatial–Spectral Total Variation

Abstract

Conventional low-rank (LR)-based hyperspectral image (HSI) denoising models generally convert high-dimensional data into 2-D matrices or just treat this type of data as 3-D tensors. However, these pure LR or tensor low-rank (TLR)-based methods lack flexibility for considering different correlation information from different HSI directions, which leads to the loss of comprehensive structure information and inherent spatial-spectral relationship. To overcome these shortcomings, we propose a novel multidirectional LR modeling and spatial-spectral total variation (MLR-SSTV) model for removing HSI mixed noise. By incorporating the weighted nuclear norm, we obtain the weighted sum of weighted nuclear norm minimization (WSWNNM) and the weighted sum of weighted tensor nuclear norm minimization (WSWTNNM) to estimate the more accurate LR tensor, especially, to remove the dead-line noise better. Gaussian noise is further denoised and the local spatial-spectral smoothness is preserved effectively by SSTV regularization. We develop an efficient algorithm for solving the derived optimization based on the alternating direction method of multipliers (ADMM). Extensive experiments on both synthetic data and real data demonstrate the superior performance of the proposed MLR-SSTV model for HSI mixed noise removal.