Hyper-Laplacian Regularized Nonlocal Low-rank Matrix Recovery for Hyperspectral Image Compressive Sensing Reconstruction

Sparsity prior is a powerful tool for compressive sensing reconstruction (CSR) of hyperspectral image (HSI). However, conventional HSI-CSR strategies are not tuned to extracting refine spatial and spectral sparsity prior. Moreover, these CSR techniques are weak in preserving edges and suppressing artifacts. To alleviate these issues, this paper represents a first effort to characterize the spatial and spectral knowledge using the structure-based sparsity prior. Specifically, we introduce the nonlocal low-rank matrix recovery model and the hyper-Laplacian prior to encode the spatial and spectral structured sparsity, respectively. The key advantage of the proposed method, termed as hyper-Laplacian regularized nonlocal low-rank matrix recovery (HyNLRMR), is to adopt insightful property, namely the nonlocal self-similarity across the spatial domain and the consistency along the spectral domain. Then, the alternative direction multiplier method (ADMM) is designed to effectively implement the proposed algorithm. Experimental results on various HSI datasets verify that the proposed algorithm can significantly outperform existing state-of-the-art HSI-CSR methods.