Triple-layer representation of low rank and group sparsity for hyperspectral image denoising

Hyperspectral image (HSI) denoising is an essential step in image processing. In the regularization-based approaches for this step, various kinds of prior information are investigated only in the original or one-layer transform domains of HSIs. To sufficiently explore deeper priors, we propose a novel triple-layer representation of low-rankness and group sparsity (TLLRGS) for HSI denoising. This method encodes the prior knowledge of HSIs with two low-rank layers and a single group-sparse layer. Specifically, the globally low rank in the original domain is measured by Tucker decomposition in the first layer. Then, the low rank in the gradient domain is captured via orthogonal transforms, which can be regarded as the second layer of our TLLRGS model. To describe the shared sparse pattern in the subspaces of gradient domains, we design an $l_{2,\gamma }$-norm with the parameter $\gamma$ in the third layer. Additionally, we introduce $l_1$-norm regularization for complex noise, especially sparse noise. To solve the TLLRGS model, we adopt an iterative approach based on the augmented Lagrange multiplier method. Finally, extensive experimental results involving complex noise removal demonstrate the superiority of the TLLRGS model over several state-of-the-art denoising methods.