Anisotropic Spatiotemporal Regularization in Compressive Video Recovery by Adaptively Modeling the Residual Errors as Correlated Noise

Many approaches to compressive video recovery proceed iteratively, treating the difference between the previous estimate and the ideal video as residual noise to be filtered. We go beyond the common white-noise modeling by adaptively modeling the residual as stationary spatiotemporally correlated noise. This adaptive noise model is updated at each iteration and is highly anisotropic in space and time; we leverage it with respect to the transform spectra of a motion-compensated video denoiser. Experimental results demonstrate that our proposed adaptive correlated noise model outperforms state-of-the-art methods both quantitatively and qualitatively.acceptedVersionPeer reviewe

Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition

The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixed-points of a deep neural network. We also present numerical results comparing the recovery performance of PnP/RED in compressive sensing against that of recent compressive sensing algorithms based on generative models. Our numerical results suggest that PnP with a pre-trained artifact removal network provides significantly better results compared to the existing state-of-the-art methods.Comment: 27 pages, 13 figure