Bilayer Muti-Modal Low-Rank Prior for Snapshot Compressive Imaging

Snapshot Compressive Imaging (SCI) systems allow multiple frames to be mapped to a single measurement frame, enabling the capture of high-dimensional signals with low-dimensional sensors. For reconstructing multiple frames from a single snapshot, we employ a powerful concept called non-local self-similarity (NLS). Nevertheless, existing NLS based iterative optimization algorithms are too slow. To address the issue, we propose a novel model to re- construct the multiple frames from compressed measurements. We firstly apply a non-local operation to the measurement and construct a 4-D tensor from it. Then, we propose a bilayer low-rankness mea- sure to represent the high-dimensional low-rank structure of the 4- D tensor in multiple orientations. A block successive upper-bound minimization algorithm is designed to solve the resulting optimization problem. Subsequence convergence of our algorithm can be established under some mild conditions