Single-Shot Plug-and-Play Methods for Inverse Problems
This addresses the problem of data scarcity in inverse problems for researchers and practitioners, though it is incremental as it builds on existing PnP frameworks.
The paper tackles the data-intensive requirement of Plug-and-Play methods for inverse problems by introducing Single-Shot PnP methods that work with minimal data, achieving better approximations as demonstrated through experiments.
The utilisation of Plug-and-Play (PnP) priors in inverse problems has become increasingly prominent in recent years. This preference is based on the mathematical equivalence between the general proximal operator and the regularised denoiser, facilitating the adaptation of various off-the-shelf denoiser priors to a wide range of inverse problems. However, existing PnP models predominantly rely on pre-trained denoisers using large datasets. In this work, we introduce Single-Shot PnP methods (SS-PnP), shifting the focus to solving inverse problems with minimal data. First, we integrate Single-Shot proximal denoisers into iterative methods, enabling training with single instances. Second, we propose implicit neural priors based on a novel function that preserves relevant frequencies to capture fine details while avoiding the issue of vanishing gradients. We demonstrate, through extensive numerical and visual experiments, that our method leads to better approximations.