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Snapshot hyperspectral imaging can capture the 3D hyperspectral image (HSI)with a single 2D measurement and has attracted increasing attention recently.Recovering the underlying HSI from the compressive measurement is an ill-posedproblem and exploiting the image prior is essential for solving this ill-posedproblem. However, existing reconstruction methods always start from modelingimage prior with the 1D vector or 2D matrix and cannot fully exploit thestructurally spectral-spatial nature in 3D HSI, thus leading to a poorfidelity. In this paper, we propose an effective high-order tensor optimizationbased method to boost the reconstruction fidelity for snapshot hyperspectralimaging. We first build high-order tensors by exploiting the spatial-spectralcorrelation in HSI. Then, we propose a weight high-order singular valueregularization (WHOSVR) based low-rank tensor recovery model to characterizethe structure prior of HSI. By integrating the structure prior in WHOSVR withthe system imaging process, we develop an optimization framework for HSIreconstruction, which is finally solved via the alternating minimizationalgorithm. Extensive experiments implemented on two representative systemsdemonstrate that our method outperforms state-of-the-art methods.

Snapshot Hyperspectral Imaging Based on Weighted High-order Singular Value Regularization