Hyperspectral image reconstruction based on low-rank coefficient tensor and global prior

Compressive sensing (CS) has been employed to compress and store hyperspectral images (HSI) to transfer extensive data efficiently, and obtaining high-quality reconstructed images is crucial for subsequent applications. Model-based methods usually capture the priors of HSI, including sparsity, global and nonlocal low-rankness, nonlocal self-similarity and global correlation. However, it is challenging to reasonably integrate different regularizations in a united framework and exploit various priors mentioned to reconstruct high-quality images. In this paper, a tensor optimization model based on the low-rank coefficient tensor and global prior (LRCTGP) is proposed for HSI reconstruction. Complementary regularization terms are integrated into a united framework and effectively promote the reconstruction results. First, we apply the mode- n tensor-matrix product to decompose the original HSI rather than employing the regularization to capture the spectral low-rankness and simultaneously constrain the original and feature HSI. Then, tensor ring decomposition is employed to constrain the coefficient tensor with fewer bands, which is more efficient in the low-rank approximation and has smaller calculation costs than applying it to the original HSI. Moreover, integrating BM3D as a regularizer is more efficient than other patch-based models. Finally, considering the smoothness and global correlation, spatial-spectral total variation (SSTV) is applied to compensate for the shortcomings after decomposing the original and feature HSI, which complements the overall structure and details of reconstructed images and improves the reconstruction quality. Alternating direction method of multipliers (ADMM) is used to optimize the proposed model. Experimental results of the LRCTGP model on different HSI datasets are better than existing state-of-the-art approaches, which proves the superiority.