Hyperspectral Image Denoising Based on Non- convex Low-rank Regularization in Tensor Transform Domain

Hyperspectral image includes rich spectral and spatial information with strong correlations, which makes it granted that hyperspectral image is modeled as a low-rank third- order tensor. In terms of the low-rank representation of tensor, non-convex low-rank approximation is regarded as an effective method. In this paper, based on the tensor singular value decomposition in transformed domain, a non-convex low-rank representation of tensor is proposed. Firstly, the unitary transformation is carried out along each mode of the tensor, thus the corresponding transformed tensor nuclear norm is developed. Then, the newly defined tensor nuclear norm is relaxed by a non- convex Gamma function, which leads to a non-convex low-rank regularized hyperspectral denoising model. The alternating direction multiplier method (ADMM) is employed to solve the model. Compared with the existing methods, the proposed model can effectively remove Gaussian and impulse noises, and achieves better performance on spatial structure preservation and spectral fidelity.