A Robust PCA Approach With Noise Structure Learning and Spatial–Spectral Low-Rank Modeling for Hyperspectral Image Restoration

Hyperspectral images (HSIs), during the acquisition process, are often corrupted by a mixture of several types of noises, including Gaussian noise, impulsive noise, dead lines, stripes, and many others. These mixed noises not only severely degrade the visual quality of HSIs, but also limit the related subsequent applications. In this paper, we propose a novel robust principal component analysis approach for mixed noise removal by fully identifying the intrinsic structures of the mixed noise and clean HSI. Specifically, for the noise modeling, considering that the mixed noise consists of the dense Gaussian noise and sparse noise, and even the noise densities in different bands are disparate, we introduce a series of Gaussian–Laplace mixture distributions with the band-adaptive scale parameters to estimate the mixed noise. For the image modeling, since there exist rich correlations among the spectral bands and many self-similarities over the image blocks, we initialize a spatial–spectral low-rank characterization of the image. Furthermore, we impose the anisotropic spatial–spectral total variation regularization on the image to enhance the robustness of our approach. Then, by combining the expectation–maximization algorithm and the alternative direction method of multiplier, we develop an efficient algorithm for the resulting optimization problem. Extensive experimental results on the simulated and real datasets demonstrate that the proposed method is superior over the existing state-of-the-art ones.