Hyperspectral image restoration using low-rank representation on spectral difference image

This letter presents a novel mixed noise (i.e., Gaussian, impulse, stripe noises, or dead lines) reduction method for hyperspectral image (HSI) by utilizing low-rank representation (LRR) on spectral difference image. The proposed method is based on the assumption that all spectra in the spectral difference space of HSI lie in the same low-rank subspace. The LRR on the spectral difference space was exploited by nuclear norm of difference image along the spectral dimension. It showed great potential in removing structured sparse noise (e.g., stripes or dead lines located at the same place of each band) and heavy Gaussian noise. To simultaneously solve the proposed model and reduce computational load, alternating direction method of multipliers was utilized to achieve robust reconstruction. The experimental results on both simulated and real HSI data sets validated that the proposed method outperformed many state-of-the-art methods in terms of quantitative assessment and visual quality.