  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-posed
problem and exploiting the image prior is essential for solving this ill-posed
problem. However, existing reconstruction methods always start from modeling
image prior with the 1D vector or 2D matrix and cannot fully exploit the
structurally spectral-spatial nature in 3D HSI, thus leading to a poor
fidelity. In this paper, we propose an effective high-order tensor optimization
based method to boost the reconstruction fidelity for snapshot hyperspectral
imaging. We first build high-order tensors by exploiting the spatial-spectral
correlation in HSI. Then, we propose a weight high-order singular value
regularization (WHOSVR) based low-rank tensor recovery model to characterize
the structure prior of HSI. By integrating the structure prior in WHOSVR with
the system imaging process, we develop an optimization framework for HSI
reconstruction, which is finally solved via the alternating minimization
algorithm. Extensive experiments implemented on two representative systems
demonstrate that our method outperforms state-of-the-art methods.
