From the Gradient-Step Denoiser to the Proximal Denoiser and their associated convergent Plug-and-Play algorithms

The main problem addressed in this paper is the development of efficient algorithms for solving imaging inverse problems. These problems involve recovering a clean image from a noisy observation, and they are commonly encountered in various fields such as computer vision, medical imaging, and remote sensing. The goal is to design algorithms that can effectively remove noise from the observed image and recover the original clean image.

The key innovation of this work is the introduction of two types of denoisers: the Gradient-Step Denoiser (Dσ) and the Proximal Denoiser. These denoisers are designed to mimic the behavior of gradient descent and proximity operators, respectively, and are trained to preserve state-of-the-art denoising capabilities. The authors propose a Plug-and-Play (PnP) framework that uses these denoisers to solve imaging inverse problems. The PnP framework is a novel approach that combines the strengths of deep learning and traditional optimization methods.

The practical impact of this research is significant. The proposed PnP framework can be applied to various imaging inverse problems, such as image denoising, deblurring, and inpainting. The framework can also be extended to other domains, such as signal processing and machine learning. The use of deep learning-based denoisers and the PnP framework can lead to more accurate and efficient solutions to these problems, which can have a significant impact on various applications, such as medical imaging, remote sensing, and computer vision.

Imagine you are trying to find your way back to a familiar location in a foggy environment. The noisy observation is like the fog that obscures your view, and the clean image is like the familiar location that you are trying to reach. The denoiser is like a GPS system that helps you navigate through the fog and recover the location. The PnP framework is like a combination of GPS and a map that helps you navigate through the fog and reach the desired location efficiently. Just as a GPS system uses location data and maps to provide accurate directions, the PnP framework uses the denoiser and the PnP algorithm to provide accurate solutions to imaging inverse problems.