Provable deep video denoiser using spatial–temporal information for video snapshot compressive imaging: Algorithm and convergence analysis

Abstract

Video snapshot compressive imaging (SCI) is a new compressive imaging system that aims to recover multiple video frames from a single measurement. Recent plug-and-play (PnP) imaging methods have been used for solving SCI inverse problems by leveraging pre-trained deep Gaussian denoisers. Under the condition of diminishing noise levels, a necessary assumption for the fixed-point convergence of PnP imaging algorithms is that the plugged denoisers are bounded denoisers. However, it is difficult to prove that existing deep Gaussian denoisers meet this assumption due to the complex network architectures, limiting the convergence analysis of these algorithms. This paper aims to elaborate a bounded deep video denoiser to remedy such a gap. Concretely, we propose a denoiser using double tight frames dubbed as VDTF and plug it into the PnP framework to construct the PnP-VDTF algorithm. In VDTF, a constant network (CNet) is designed, wherein a Swin Transformer-based module and a 3D convolution module extract the spatial information of the global features and the temporal information of the input video, respectively. Theoretically, we provide a strict boundary proof of VDTF, and show that PnP-VDTF can generate fixed-point convergent trajectories. Experiments show that PnP-VDTF can achieve higher-quality reconstructions compared with benchmark SCI algorithms.