Provable General Bounded Denoisers for Snapshot Compressive Imaging With Convergence Guarantee

In the snapshot compressive imaging (SCI) field, how to explore priors for recovering the original high-dimensional data from its lower-dimensional measurements is a challenge. Recent plug-and-play efforts plugged by deep denoisers have achieved superior performance, and their convergences have been guaranteed under the assumption of bounded denoisers and the condition of diminishing noise levels. However, it is difficult to explicitly prove the bounded properties of existing deep denoisers due to complex network architectures. To address these issues, we propose a novel provable and trainable bounded denoiser using dual tight frames and spatial-variation thresholds. Furthermore, we combine the proposed trainable bounded denoiser with the well-known block matching 3D filtering (BM3D) denoiser for building a plug-and-play SCI framework. Precisely, we formulate a convergent plug-and-play SCI algorithm that can exploit complementary denoiser priors, and plug the two denoisers into it. We explicitly prove that these two denoisers are general bounded denoisers, and further show the convergence of the proposed SCI algorithm. Both simulation (video compressive imaging and hyperspectral compressive imaging) and real data results show that the proposed algorithm can achieve higher-quality reconstructions compared with benchmark SCI algorithms.