A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems
This work addresses practical challenges in inverse imaging for researchers and practitioners, though it appears incremental as it builds on existing Plug-and-Play frameworks.
The paper tackles the difficulty of applying Plug-and-Play methods with theoretically guaranteed step sizes and their limitation to Gaussian noise by proposing an adaptive algorithm based on split convex feasibility problems, which outperforms state-of-the-art methods like RED and RED-PRO in image deblurring, super-resolution, and compressed sensing MRI experiments.
In recent years Plug-and-Play (PnP) methods have achieved state-of-the-art performance in inverse imaging problems by replacing proximal operators with denoisers. Based on the proximal gradient method, some theoretical results of PnP have appeared, where appropriate step size is crucial for convergence analysis. However, in practical applications, applying PnP methods with theoretically guaranteed step sizes is difficult, and these algorithms are limited to Gaussian noise. In this paper,from a perspective of split convex feasibility problems (SCFP), an adaptive PnP algorithm with Projected Landweber Operator (PnP-PLO) is proposed to address these issues. Numerical experiments on image deblurring, super-resolution, and compressed sensing MRI experiments illustrate that PnP-PLO with theoretical guarantees outperforms state-of-the-art methods such as RED and RED-PRO.