Hyperspectral Image Compressive Sensing Reconstruction Using Subspace-Based Nonlocal Tensor Ring Decomposition

Hyperspectral image compressive sensing reconstruction (HSI-CSR) can largely reduce the high expense and low efficiency of transmitting HSI to ground stations by storing a few compressive measurements, but how to precisely reconstruct the HSI from a few compressive measurements is a challenging issue. It has been proven that considering the global spectral correlation, spatial structure, and nonlocal self-similarity priors of HSI can achieve satisfactory reconstruction performances. However, most of the existing methods cannot simultaneously capture the mentioned priors and directly design the regularization term to the HSI. In this article, we propose a novel subspace-based nonlocal tensor ring decomposition method (SNLTR) for HSI-CSR. Instead of designing the regularization of the low-rank approximation to the HSI, we assume that the HSI lies in a low-dimensional subspace. Moreover, to explore the nonlocal self-similarity and preserve the spatial structure of HSI, we introduce a nonlocal tensor ring decomposition strategy to constrain the related coefficient image, which can decrease the computational cost compared to the methods that directly employ the nonlocal regularization to HSI. Finally, a well-known alternating minimization method is designed to efficiently solve the proposed SNLTR. Extensive experimental results demonstrate that our SNLTR method can significantly outperform existing approaches for HSI-CSR.