Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name "Plug-and-Play ADMM". Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since Plug-and-Play ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for common Gaussian and Poissonian image restoration problems.
In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixed point convergence. We show that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on super-resolution and single-photon imaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in each problem type, and demonstrate promising experimental results of the algorithm.
In plug-and-play image restoration, the regularization is performed using powerful denoisers such as nonlocal means (NLM) or BM3D. This is done within the framework of alternating direction method of multipliers (ADMM), where the regularization step is formally replaced by an off-the-shelf denoiser. Each plug-and-play iteration involves the inversion of the forward model followed by a denoising step. In this paper, we present a couple of ideas for improving the efficiency of the inversion and denoising steps. First, we propose to use linearized ADMM, which generally allows us to perform the in…
Since the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used in various image processing studies. Nonetheless, nuclear norm based convex surrogate of the rank function usually over-shrinks the rank components and makes different components equally, and thus may produce a result far from the optimum. To alleviate the above-mentioned limitations of the nuclear norm, in this paper we propose a new method for image restoration via the non-convex weighted Lp nuclear norm minimization (NCW-NNM), which is able to more …
Plug-and-Play optimization recently emerged as a powerful technique for solving inverse problems by plugging a denoiser into a classical optimization algorithm. The denoiser accounts for the regularization and therefore implicitly determines the prior knowledge on the data, hence replacing typical handcrafted priors. In this paper, we extend the concept of plug-and-play optimization to use denoisers that can be parameterized for non-constant noise variance. In that aim, we introduce a preconditioning of the ADMM algorithm, which mathematically justifies the use of such an adjustable denoiser. …
This paper studies a type of image priors that are constructed implicitly through the alternating direction method of multiplier (ADMM) algorithm, called the algorithm-induced prior. Different from classical image priors which are defined before running the reconstruction algorithm, algorithm-induced priors are defined by the denoising procedure used to replace one of the two modules in the ADMM algorithm. Since such prior is not explicitly defined, analyzing the performance has been difficult in the past. Focusing on the class of symmetric smoothing filters, this paper presents an explicit ex…
The Plug-and-Play (PnP) ADMM algorithm is a powerful image restoration framework that allows advanced image denoising priors to be integrated into physical forward models to generate high quality image restoration results. However, despite the enormous number of applications and several theoretical studies trying to prove the convergence by leveraging tools in convex analysis, very little is known about why the algorithm is doing so well. The goal of this paper is to fill the gap by discussing the performance of PnP ADMM. By restricting the denoisers to the class of graph filters under a linea…
In most state-of-the-art image restoration methods, the sum of a data-fidelity and a regularization term is optimized using an iterative algorithm such as ADMM (alternating direction method of multipliers). In recent years, the possibility of using denoisers for regularization has been explored in several works. A popular approach is to formally replace the proximal operator within the ADMM framework with some powerful denoiser. However, since most state-of-the-art denoisers cannot be posed as a proximal operator, one cannot guarantee the convergence of these so-called plug-and-play (PnP) algo…
Models including two $L^1$ -norm terms have been widely used in image restoration. In this paper we first propose the alternating direction method of multipliers (ADMM) to solve this class of models. Based on ADMM, we then propose the proximal point method (PPM), which is more efficient than ADMM. Following the operator theory, we also give the convergence analysis of the proposed methods. Furthermore, we use the proposed methods to solve a class of hybrid models combining the ROF model with the LLT model. Some numerical results demonstrate the viability and efficiency of the proposed methods.
ETH Zürich（苏黎世联邦理工学院）；KU Leuven（鲁汶大学）；Harbin Institute of Technology（哈尔滨工业大学）；The Hong Kong Polytechnic University（香港理工大学）
Recent works on plug-and-play image restoration have shown that a denoiser can implicitly serve as the image prior for model-based methods to solve many inverse problems. Such a property induces considerable advantages for plug-and-play image restoration (e.g., integrating the flexibility of model-based method and effectiveness of learning-based methods) when the denoiser is discriminatively learned via deep convolutional neural network (CNN) with large modeling capacity. However, while deeper and larger CNN models are rapidly gaining popularity, existing plug-and-play image restoration hinder…
Due to the development of deep learning-based denoisers, the plug-and-play strategy has achieved great success in image restoration problems. However, existing plug-and-play image restoration methods are designed for non-blind Gaussian denoising such as zhang et al (2022), the performance of which visibly deteriorate for unknown noises. To push the limits of plug-and-play image restoration, we propose a novel framework with blind Gaussian prior, which can deal with more complicated image restoration problems in the real world. More specifically, we build up a new image restoration model by reg…
Nanyang Technological University（南洋理工大学）；Michigan State University（密歇根州立大学）
Image restoration schemes based on the pre-trained deep models have received great attention due to their unique flexibility for solving various inverse problems. In particular, the Plug-and-Play (PnP) framework is a popular and powerful tool that can integrate an off-the-shelf deep denoiser for different image restoration tasks with known observation models. However, obtaining the observation model that exactly matches the actual one can be challenging in practice. Thus, the PnP schemes with conventional deep denoisers may fail to generate satisfying results in some real-world image restorati…
This paper proposes using a Gaussian mixture model as a prior, for solving two image inverse problems, namely image deblurring and compressive imaging. We capitalize on the fact that variable splitting algorithms, like ADMM, are able to decouple the handling of the observation operator from that of the regularizer, and plug a state-of-the-art algorithm into the pure denoising step. Furthermore, we show that, when applied to a specific type of image, a Gaussian mixture model trained from an database of images of the same type is able to outperform current state-of-the-art methods.
Plug-and-Play Image Restoration with Flow Matching: A Continuous Viewpoint
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA（犹他大学数学系）；Los Alamos National Laboratory, Los Alamos, USA（洛斯阿拉莫斯国家实验室）；Department of Mathematics, University of California, Los Angeles, USA（加州大学洛杉矶分校数学系）
Centre Suisse d’Electronique et de Microtechnique (CSEM)（瑞士电子与微技术中心（CSEM））；School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院（EPFL）计算机与通信科学学院）
Plug-and-play denoisers can be used to perform generic image restoration tasks independent of the degradation type. These methods build on the fact that the Maximum a Posteriori (MAP) optimization can be solved using smaller sub-problems, including a MAP denoising optimization. We present the first end-to-end approach to MAP estimation for image denoising using deep neural networks. We show that our method is guaranteed to minimize the MAP denoising objective, which is then used in an optimization algorithm for generic image restoration. We provide theoretical analysis of our approach and show…
Deep-learning-based hyperspectral image (HSI) restoration methods have gained great popularity for their remarkable performance but often demand expensive network retraining whenever the specifics of task changes. In this paper, we propose to restore HSIs in a unified approach with an effective plug-and-play method, which can jointly retain the flexibility of optimization-based methods and utilize the powerful representation capability of deep neural networks. Specifically, we first develop a new deep HSI denoiser leveraging gated recurrent convolution units, short- and long-term skip connecti…
This paper presents a novel method for restoring digital videos via a Deep Plug-and-Play (PnP) approach. Under a Bayesian formalism, the method consists in using a deep convolutional denoising network in place of the proximal operator of the prior in an alternating optimization scheme. We distinguish ourselves from prior PnP work by directly applying that method to restore a digital video from a degraded video observation. This way, a network trained once for denoising can be repurposed for other video restoration tasks. Our experiments in video deblurring, super-resolution, and interpolation …
State-of-the-art algorithms for imaging inverse problems (namely deblurring and reconstruction) are typically iterative, involving a denoising operation as one of its steps. Using a state-of-the-art denoising method in this context is not trivial, and is the focus of current work. Recently, we have proposed to use a class-adapted denoiser (patch-based using Gaussian mixture models) in a so-called plug-and-play scheme, wherein a state-of-the-art denoiser is plugged into an iterative algorithm, leading to results that outperform the best general-purpose algorithms, when applied to an image of a …
Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico（高等技术学院）
The recently proposed plug-and-play (PnP) framework allows leveraging recent developments in image denoising to tackle other, more involved, imaging inverse problems. In a PnP method, a black-box denoiser is plugged into an iterative algorithm, taking the place of a formal denoising step that corresponds to the proximity operator of some convex regularizer. While this approach offers flexibility and excellent performance, convergence of the resulting algorithm may be hard to analyze, as most state-of-the-art denoisers lack an explicit underlying objective function. In this paper, we propose a …
The Plug-and-Play (PnP) framework makes it possible to integrate advanced image denoising priors into optimization algorithms, to efficiently solve a variety of image restoration tasks generally formulated as Maximum A Posteriori (MAP) estimation problems. The Plug-and-Play alternating direction method of multipliers (ADMM) and the Regularization by Denoising (RED) algorithms are two examples of such methods that made a breakthrough in image restoration. However, while the former method only applies to proximal algorithms, it has recently been shown that there exists no regularization that exp…
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) to further improve image reconstruction. The motivating application is compressive sensing (CS), and a deep convolutional architecture is adopted to approximate the expensive matrix inversion in CS applications. An iterative algorithm based on this low-rank tensor factorization s…
Plug-and-Play (PnP) methods solve ill-posed inverse problems through iterative proximal algorithms by replacing a proximal operator by a denoising operation. When applied with deep neural network denoisers, these methods have shown state-of-the-art visual performance for image restoration problems. However, their theoretical convergence analysis is still incomplete. Most of the existing convergence results consider nonexpansive denoisers, which is non-realistic, or limit their analysis to strongly convex data-fidelity terms in the inverse problem to solve. Recently, it was proposed to train th…
Harbin Institute of Technology（哈尔滨工业大学）；The Hong Kong Polytechnic University（香港理工大学）；Peng Cheng Laboratory（鹏城实验室）；DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）
While deep neural networks (DNN) based single image super-resolution (SISR) methods are rapidly gaining popularity, they are mainly designed for the widely-used bicubic degradation, and there still remains the fundamental challenge for them to super-resolve low-resolution (LR) image with arbitrary blur kernels. In the meanwhile, plug-and-play image restoration has been recognized with high flexibility due to its modular structure for easy plug-in of denoiser priors. In this paper, we propose a principled formulation and framework by extending bicubic degradation based deep SISR with the help o…
BIR-Adapter: A parameter-efficient diffusion adapter for blind image restoration
Chair of Media Technology, Munich Institute of Robotics and Machine Intelligence（媒体技术教授会，慕尼黑机器人与机器智能研究所）；School of Computation, Information and Technology, Technical University of Munich（计算、信息与技术学院，慕尼黑技术大学）
Learning Adaptive Dynamical Features via Multi-$τ$ Liquid-Mamba for All-in-one Image Restoration
Department of Computer Science, Shanghai Jiao Tong University（上海交通大学计算机科学与技术系）；Department of Architecture and Design, Harbin Institute of Technology（哈尔滨工业大学建筑与设计系）
Multimodal Prompt Perceiver: Empower Adaptiveness, Generalizability and Fidelity for All-in-One Image Restoration
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；University of Science and Technology of China（中国科学技术大学）
CMAP, CNRS, École Polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院综合理工学院应用数学中心、法国国家科学研究中心）；University of Bologna（博洛尼亚大学）
In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anisotropic extension of the classical isotropic Total Variation (TV) regularizer. The proposed regularizer comes from the statistical assumption that the gradients of the target image distribute locally according to space-variant bivariate Laplacian distributions. The highly flexible variational structure of the corresponding regularizer encodes several free parameters which hold the potential for faithfully modelling the local geometry in the image and describing loca…
Nanyang Technological University（南洋理工大学）；University of Science and Technology of China（中国科学技术大学）；Nankai University（南开大学）
Image and video restoration has achieved a remarkable leap with the advent of deep learning. The success of deep learning paradigm lies in three key components: data, model, and loss. Currently, many efforts have been devoted to the first two while seldom study focuses on loss function. With the question ``are the de facto optimization functions e.g., $L_1$, $L_2$, and perceptual losses optimal?'', we explore the potential of loss and raise our belief ``learned loss function empowers the learning capability of neural networks for image and video restoration''. Concretely, we stand on the shoul…
Analysis and Benchmarking of Extending Blind Face Image Restoration to Videos
The University of Hong Kong（香港大学）；SenseTime Research（商汤科技研究院）；ARC Lab, Tencent PCG（腾讯平台与内容事业群ARC实验室）；The Guangdong University of Technology（广东工业大学）；Texas A&M University（德克萨斯农工大学）
In this work we propose an efficient stochastic plug-and-play (PnP) algorithm for imaging inverse problems. The PnP stochastic gradient descent methods have been recently proposed and shown improved performance in some imaging applications over standard deterministic PnP methods. However, current stochastic PnP methods need to frequently compute the image denoisers which can be computationally expensive. To overcome this limitation, we propose a new stochastic PnP-ADMM method which is based on introducing stochastic gradient descent inner-loops within an inexact ADMM framework. We provide the …
You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors
Department of Applied Mathematics and Theoretical Physics（应用数学与理论物理系）；University of Cambridge（剑桥大学）；Yau Mathematical Sciences Center（叶中伟数学科学中心）；Tsinghua University（清华大学）
提出 KAN-PnP 优化框架，将 KAN 作为去噪器融入即插即用范式解决单实例先验逆问题，证明了其 Lipschitz 连续性与收敛性，并在超分辨率等任务上以更少迭代实现高精度。
HIR-ALIGN: Enhancing Hyperspectral Image Restoration via Diffusion-Based Data Generation
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学学院）；School of Computer Science and Technology, Xi’an Jiaotong University（西安交通大学计算机科学与技术学院）；School of Mathematics and Statistics and the Ministry of Education Key Laboratory for Intelligent Networks and Network Security, Xi’an Jiaotong University（西安交通大学数学与统计学学院和教育部智能网络与网络安全重点实验室）；Pazhou Laboratory (Huangpu), Guangzhou（广州黄埔 Pazhou 实验室）
