Plug-and-Play and Relay Regularizations on Noisy Low Rank Tensor Completion for Snapshot Multispectral Image Restoration

The spatial resolution of snapshot multispectral imaging is degraded owing to its spatio-spectral tradeoff. Restoring the resolution is considered as a noisy tensor completion problem and recent studies have jointly optimized the transformed tensor nuclear norm (tTNN) with regularization. However, existing work is limited and cause artifacts that stem from the periodic missing pattern and observation noise. To improve the restoration performance, we introduce two regularizations in a Plug-and-Play (PnP) manner. They still have their own drawbacks. We then further propose a Plug-and-Relay (PnR) technique to switch them at an appropriate timing. We experimentally show that PnP improves the completion accuracy compared with existing methods and that PnR could further improve the performance at a moderate computational cost.