Hyperspectral Image Denoising with Log-Based Robust PCA

It is a challenging task to remove heavy and mixed types of noise from Hyperspectral images (HSIs). In this paper, we propose a novel nonconvex approach to RPCA for HSI denoising, which adopts the log-determinant rank approximation and a novel ${\mathrm{\ell }}_{2,\log }$ norm, to restrict the low-rank or column-wise sparse properties for the component matrices, respectively.For the ${\mathrm{\ell }}_{2,\log }$-regularized shrinkage problem, we develop an efficient, closed-form solution, which is named ${\mathrm{\ell }}_{2,\log }$-shrinkage operator, which can be generally used in other problems. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.