Deep Learning for Linear Inverse Problems Using the Plug-and-Play Priors Framework

Abstract

Linear inverse problems appear in many applications, where different algorithms are typically employed to solve each inverse problem. Nowadays, the rapid development of deep learning (DL) provides a fresh perspective for solving the linear inverse problem: a number of well-designed network architectures results in state-of-the-art performance in many applications. In this overview paper, we present the combination of the DL and the Plug-and-Play priors (PPP) framework, showcasing how it allows solving various inverse problems by leveraging the impressive capabilities of existing DL based denoising algorithms. Open challenges and potential future directions along this line of research are also discussed.

Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --

“…The seminal Plug-and-Play Prior (PnP) work by Venkatakrishnan, Bouman and Wohlberg [295] was the first to provide such an answer 7 , followed and improved upon by RED (Regularization by Denoising) [231]. These and their various extensions and variations have created a vivid and stimulating sub-field of research in imaging sciences [28,139,283,34,268,41,192,280,5,49,55] in which denoisers play a central role. Below we describe PnP and RED in more detail, and then turn to describe another, perhaps better founded, bridge between denoisers and the energy function ρ(x) via the score function.…”

“…PnP and RED have drawn much interest in our community in the past several years. Followup work has been considering a theoretical analysis of the two methods [42,278,225,94,309,269], deployment of the proposed algorithms in various applications [263,28,139,49], creation of new variants of these two methods [283,279,268,280,267,123,56], and more. An appealing outlet of this work returns to the unfolding idea discussed in Section 5: PnP/RED can be used to define well-motivated architectures for solving general inverse problems, by unfolding the proposed algorithms, and then training the repeated denoiser to best serve a series of inverse problems jointly.…”

“…In parallel to the above and seemingly detached from the deep learning activity, image denoising has been also a topic of investigation and discoveries of a different flavor: Harnessing denoiser engines for other imaging tasks. This started with the surprising idea that a good performing denoiser can serve as a prior, offering a highly effective regularization to inverse problems [295,231,28,139,283,268,192,280,49,55]. This continued with the discovery that such denoisers can also be used for randomly synthesizing images by offering a practical sampling from the prior distribution of images, this way posing a potent competition to Generative Adversarial Networks (GANs) and other image generation methods [260,261,262,120,287,68,122,143,121].…”

Plug-and-Play Quantum Adaptive Denoiser for Deconvolving Poisson Noisy Images

“…More recently, alternative learning-based approaches were developed in the literature using the deep learning (convolutional neural network (CNN)) techniques for tackling inverse problems [45]- [49]. In a few years the implementation of these Deep-CNN networks has been introduced for image denoising problem [50], [51] and further extended to the PnP schemes [52]. These Deep-CNN networks give several advantages such as reconstruction accuracy and convergence speed [53].…”