Single-Shot Plug-and-Play Methods for Inverse Problems

TL;DR

This work integrates Single-Shot proximal denoisers into iterative methods, enabling training with single instances and proposes implicit neural priors based on a novel function that preserves relevant frequencies to capture fine details while avoiding the issue of vanishing gradients.

Abstract

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.

Figures (8)

• Figure 1: The pipeline of Single-Shot Plug-and-Play methods (SS-PnP). The 2 blocks indicate the 2 steps as in Algorithm \ref{['alg:main']}, and the indicates the fix in denoiser weight over the ADMM iterations, where there are $K$ iterations in total (i.e. $k \in \{0,1,...,K-1\}$).
• Figure 2: The comparative visualisation of super resolution with 2$\times$ upscaling task on "Dog" example among the 4 Single-Shot deep denoising priors (with ★ denotes our proposed prior) in Plug-and-Play framework. The zommed-in view is provided at the right hand side of each result.
• Figure 3: The visualisation comparison of super resolution with 4$\times$ upscaling task on "Fox" example between the 4 Single-Shot deep denoising priors performing within Plug-and-Play framework, with detailed comparison zoomed in. ★ denotes our prior.
• Figure 4: Visual comparison of the 4 deep denoising priors (include our proposed as ★) on deconvolution task in Single-Shot Plug-and-Play (SS-PnP) strategy for "Giraffe" example, with a zoomed-in region exhibiting intricate details.
• Figure 5: The comparative visualisation of joint deconvolution and demosaicing tasks on the "Fractal" example. The comparison is made across different denoising priors in Play-and-Play framworks, inclusing Single-Shot deep denoising priors (our proposed prior–★, Noise2Self-UNET, and Noise2Self-FFDNet), pre-trained deep denoising priors (Pretrained-UNet and Pretrained-FFDNet), and classical denoising priors (TV).

Theorems & Definitions (2)

• proof
• proof