Plug-and-play (PnP) method is a recent paradigm for image regularization, where the proximal operator (associated with some given regularizer) in an iterative algorithm is replaced with a powerful denoiser. Algorithmically, this involves repeated inversion (of the forward model) and denoising until convergence. Remarkably, PnP regularization produces promising results for several restoration applications. However, a fundamental question in this regard is the theoretical convergence of the PnP iterations, since the algorithm is not strictly derived from an optimization framework. This question has been investigated in recent works, but there are still many unresolved problems. For example, it is not known if convergence can be guaranteed if we use generic kernel denoisers (e.g. nonlocal means) within the ISTA framework (PnP-ISTA). We prove that, under reasonable assumptions, fixed-point convergence of PnP-ISTA is indeed guaranteed for linear inverse problems such as deblurring, inpainting and superresolution (the assumptions are verifiable for inpainting). We compare our theoretical findings with existing results, validate them numerically, and explain their practical relevance.
Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stati…
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. …
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…
University of California, Los Angeles（加州大学洛杉矶分校）；Texas A&M University（得克萨斯农工大学）
Plug-and-play (PnP) is a non-convex framework that integrates modern denoising priors, such as BM3D or deep learning-based denoisers, into ADMM or other proximal algorithms. An advantage of PnP is that one can use pre-trained denoisers when there is not sufficient data for end-to-end training. Although PnP has been recently studied extensively with great empirical success, theoretical analysis addressing even the most basic question of convergence has been insufficient. In this paper, we theoretically establish convergence of PnP-FBS and PnP-ADMM, without using diminishing stepsizes, under a c…
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…
Washington University in St. Louis（圣路易斯华盛顿大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Plug-and-play priors (PnP) is a powerful framework for regularizing imaging inverse problems by using advanced denoisers within an iterative algorithm. Recent experimental evidence suggests that PnP algorithms achieve state-of-the-art performance in a range of imaging applications. In this paper, we introduce a new online PnP algorithm based on the iterative shrinkage/thresholding algorithm (ISTA). The proposed algorithm uses only a subset of measurements at every iteration, which makes it scalable to very large datasets. We present a new theoretical convergence analysis, for both batch and on…
University of Bath（巴斯大学）；Technical University of Munich（慕尼黑工业大学）；GE Healthcare（通用电气医疗集团）；Technische Hochschule Ingolstadt（英戈尔施塔特应用技术大学）
Current spatiotemporal deep learning approaches to Magnetic Resonance Fingerprinting (MRF) build artefact-removal models customised to a particular k-space subsampling pattern which is used for fast (compressed) acquisition. This may not be useful when the acquisition process is unknown during training of the deep learning model and/or changes during testing time. This paper proposes an iterative deep learning plug-and-play reconstruction approach to MRF which is adaptive to the forward acquisition process. Spatiotemporal image priors are learned by an image denoiser i.e. a Convolutional Neura…
A standard model for image reconstruction involves the minimization of a data-fidelity term along with a regularizer, where the optimization is performed using proximal algorithms such as ISTA and ADMM. In plug-and-play (PnP) regularization, the proximal operator (associated with the regularizer) in ISTA and ADMM is replaced by a powerful image denoiser. Although PnP regularization works surprisingly well in practice, its theoretical convergence -- whether convergence of the PnP iterates is guaranteed and if they minimize some objective function -- is not completely understood even for simple …
Plug-and-Play methods constitute a class of iterative algorithms for imaging problems where regularization is performed by an off-the-shelf denoiser. Although Plug-and-Play methods can lead to tremendous visual performance for various image problems, the few existing convergence guarantees are based on unrealistic (or suboptimal) hypotheses on the denoiser, or limited to strongly convex data terms. In this work, we propose a new type of Plug-and-Play methods, based on half-quadratic splitting, for which the denoiser is realized as a gradient descent step on a functional parameterized by a deep…
Iterative denoising algorithms (IDAs) have been tremendously successful in a range of linear inverse problems arising in signal and image processing. The classic instance of this is the famous Iterative Soft-Thresholding Algorithm (ISTA), based on soft-thresholding of wavelet coefficients. More modern approaches to IDAs replace soft-thresholding with a black-box denoiser, such as BM3D or a learned deep neural network denoiser. These are often referred to as ``plug-and-play" (PnP) methods because, in principle, an off-the-shelf denoiser can be used for a variety of different inverse problems. T…
Magnetic Resonance Imaging (MRI) is a noninvasive imaging technique that provides excellent soft-tissue contrast without using ionizing radiation. MRI's clinical application may be limited by long data acquisition time; therefore, MR image reconstruction from highly under-sampled k-space data has been an active research area. Calibrationless MRI not only enables a higher acceleration rate but also increases flexibility for sampling pattern design. To leverage non-linear machine learning priors, we pair our High-dimensional Fast Convolutional Framework (HICU) with a plug-in denoiser and demonst…
Plug-and-play priors (PnP) is an image reconstruction framework that uses an image denoiser as an imaging prior. Unlike traditional regularized inversion, PnP does not require the prior to be expressible in the form of a regularization function. This flexibility enables PnP algorithms to exploit the most effective image denoisers, leading to their state-of-the-art performance in various imaging tasks. In this paper, we propose a new denoiser scaling technique to explicitly control the amount of PnP regularization. Traditionally, the performance of PnP algorithms is controlled via intrinsic par…
In plug-and-play (PnP) regularization, the knowledge of the forward model is combined with a powerful denoiser to obtain state-of-the-art image reconstructions. This is typically done by taking a proximal algorithm such as FISTA or ADMM, and formally replacing the proximal map associated with a regularizer by nonlocal means, BM3D or a CNN denoiser. Each iterate of the resulting PnP algorithm involves some kind of inversion of the forward model followed by denoiser-induced regularization. A natural question in this regard is that of optimality, namely, do the PnP iterations minimize some f+g, w…
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…
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…
A new Plug-and-Play (PnP) alternating direction of multipliers (ADMM) scheme is proposed in this paper, by embedding a recently introduced adaptive denoiser using the Schroedinger equation's solutions of quantum physics. The potential of the proposed model is studied for Poisson image deconvolution, which is a common problem occurring in number of imaging applications, such as limited photon acquisition or X-ray computed tomography. Numerical results show the efficiency and good adaptability of the proposed scheme compared to recent state-of-the-art techniques, for both high and low signal-to-…
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…
It's well-known that inverse problems are ill-posed and to solve them meaningfully, one has to employ regularization methods. Traditionally, popular regularization methods are the penalized Variational approaches. In recent years, the classical regularization approaches have been outclassed by the so-called plug-and-play (PnP) algorithms, which copy the proximal gradient minimization processes, such as ADMM or FISTA, but with any general denoiser. However, unlike the traditional proximal gradient methods, the theoretical underpinnings, convergence, and stability results have been insufficient …
Single-Shot Plug-and-Play Methods for Inverse Problems
University of Cambridge（剑桥大学）；Hong Kong Polytechnic University（香港理工大学）；The University of Hong Kong（香港大学）；Lingnan University（岭南大学）；Tsinghua University（清华大学）；City University of Hong Kong（香港城市大学）
Cardiac magnetic resonance imaging (CMR) is a noninvasive imaging modality that provides a comprehensive evaluation of the cardiovascular system. The clinical utility of CMR is hampered by long acquisition times, however. In this work, we propose and validate a plug-and-play (PnP) method for CMR reconstruction from undersampled multi-coil data. To fully exploit the rich image structure inherent in CMR, we pair the PnP framework with a deep learning (DL)-based denoiser that is trained using spatiotemporal patches from high-quality, breath-held cardiac cine images. The resulting "PnP-DL" method …
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…
Beijing Institute of Technology（北京理工大学）；University of Cambridge（剑桥大学）
Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based denoisers. However, a key problem of PnP based approaches is that they require manual parameter tweaking. It is necessary to obtain high-quality results across the high discrepancy in terms of imaging conditions and varying scene content. In this work, we present a tuning-free PnP proximal algorithm, which can automatically determine the internal parameters includin…
East China Normal University（华东师范大学）；The University of Hong Kong（香港大学）
Aiming at high-dimensional (HD) data acquisition and analysis, snapshot compressive imaging (SCI) obtains the 2D compressed measurement of HD data with optical imaging systems and reconstructs HD data using compressive sensing algorithms. While the Plug-and-Play (PnP) framework offers an emerging solution to SCI reconstruction, its intrinsic denoising process is still a challenging problem. Unfortunately, existing denoisers in the PnP framework either suffer limited performance or require extensive training data. In this paper, we propose an efficient and effective shallow-learning-based algor…
UCA（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；INRIA（法国国家信息与自动化研究所）；University of Bath（巴斯大学）
The spatial resolution of images of living samples obtained by fluorescence microscopes is physically limited due to the diffraction of visible light, which makes the study of entities of size less than the diffraction barrier (around 200 nm in the x-y plane) very challenging. To overcome this limitation, several deconvolution and super-resolution techniques have been proposed. Within the framework of inverse problems, modern approaches in fluorescence microscopy reconstruct a super-resolved image from a temporal stack of frames by carefully designing suitable hand-crafted sparsity-promoting r…
Single-photon lidar has emerged as a prime candidate technology for depth imaging through challenging environments. Until now, a major limitation has been the significant amount of time required for the analysis of the recorded data. Here we show a new computational framework for real-time three-dimensional (3D) scene reconstruction from single-photon data. By combining statistical models with highly scalable computational tools from the computer graphics community, we demonstrate 3D reconstruction of complex outdoor scenes with processing times of the order of 20 ms, where the lidar data was …
Analysis and Synthesis Denoisers for Forward-Backward Plug-and-Play Algorithms
Laboratoire Interdisciplinaire des Sciences du Numériques, Inria, Université Paris-Saclay, CNRS, Gif-sur-Yvette, France（跨学科数字科学实验室，法国国家信息与自动化研究所，巴黎-萨克雷大学，法国国家科学研究中心，法国吉夫-sur-伊夫特）；Inria, Université Paris-Saclay, CEA, Palaiseau, France（法国国家信息与自动化研究所，巴黎-萨克雷大学，法国原子能委员会，法国帕莱索）；School of Mathematics and Computer Sciences and School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK（数学与计算机科学学院和工程与物理科学学院，赫里奥特-瓦特大学，英国爱丁堡）；Maxwell Institute for Mathematical Sciences, Edinburgh, UK（数学科学麦克斯韦研究所，英国爱丁堡）
Score-Based Turbo Message Passing for Plug-and-Play Compressive Image Recovery
Department of Information Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR（信息工程系，香港中文大学（深圳校区））；National Key Lab. of Wireless Commun., Uni. of Electronic Sci. and Tech. of China, Chengdu, China（无线通信国家重点实验室，电子科技大学，成都，中国）
Recent work has shown the effectiveness of the plug-and-play priors (PnP) framework for regularized image reconstruction. However, the performance of PnP depends on the quality of the denoisers used as priors. In this letter, we design a novel PnP denoising prior, called multiple self-similarity net (MSSN), based on the recurrent neural network (RNN) with self-similarity matching using multi-head attention mechanism. Unlike traditional neural net denoisers, MSSN exploits different types of relationships among non-local and repeating features to remove the noise in the input image. We numerical…
This paper introduces a new Plug-and-Play (PnP) alternating direction of multipliers (ADMM) scheme based on a recently proposed denoiser using the Schroedinger equation's solutions of quantum physics. The efficiency of the proposed algorithm is evaluated for Poisson image deconvolution, which is very common for imaging applications, such as, for example, limited photon acquisition. Numerical results show the superiority of the proposed scheme compared to recent state-of-the-art techniques, for both low and high signal-to-noise-ratio scenarios. This performance gain is mostly explained by the f…
In Plug-and-Play (PnP) algorithms, an off-the-shelf denoiser is used for image regularization. PnP yields state-of-the-art results, but its theoretical aspects are not well understood. This work considers the question: Similar to classical compressed sensing (CS), can we theoretically recover the ground-truth via PnP under suitable conditions on the denoiser and the sensing matrix? One hurdle is that since PnP is an algorithmic framework, its solution need not be the minimizer of some objective function. It was recently shown that a convex regularizer $Φ$ can be associated with a class of line…
Plug-and-play (PnP) methods that employ application-specific denoisers have been proposed to solve inverse problems, including MRI reconstruction. However, training application-specific denoisers is not feasible for many applications due to the lack of training data. In this work, we propose a PnP-inspired recovery method that does not require data beyond the single, incomplete set of measurements. The proposed method, called recovery with a self-calibrated denoiser (ReSiDe), trains the denoiser from the patches of the image being recovered. The denoiser training and a call to the denoising su…
City University of Hong Kong（香港城市大学）；The Chinese University of Hong Kong（香港中文大学）；Hong Kong Centre for Cerebro-Cardiovascular Health Engineering（香港脑心血管健康工程中心）；University of Hong Kong（香港大学）
Spherical image processing has been widely applied in many important fields, such as omnidirectional vision for autonomous cars, global climate modelling, and medical imaging. It is non-trivial to extend an algorithm developed for flat images to the spherical ones. In this work, we focus on the challenging task of spherical image inpainting with deep learning-based regularizer. Instead of a naive application of existing models for planar images, we employ a fast directional spherical Haar framelet transform and develop a novel optimization framework based on a sparsity assumption of the framel…
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…
We introduce a new class of iterative image reconstruction algorithms for radio interferometry, at the interface of convex optimization and deep learning, inspired by plug-and-play methods. The approach consists in learning a prior image model by training a deep neural network (DNN) as a denoiser, and substituting it for the handcrafted proximal regularization operator of an optimization algorithm. The proposed AIRI (``AI for Regularization in radio-interferometric Imaging'') framework, for imaging complex intensity structure with diffuse and faint emission from visibility data, inherits the r…
Beijing Institute of Technology（北京理工大学）；University of Cambridge（剑桥大学）；Shanghai Jiao Tong University（上海交通大学）；Beijing Normal University（北京师范大学）
Plug-and-Play (PnP) is a non-convex optimization framework that combines proximal algorithms, for example, the alternating direction method of multipliers (ADMM), with advanced denoising priors. Over the past few years, great empirical success has been obtained by PnP algorithms, especially for the ones that integrate deep learning-based denoisers. However, a key challenge of PnP approaches is the need for manual parameter tweaking as it is essential to obtain high-quality results across the high discrepancy in imaging conditions and varying scene content. In this work, we present a class of t…
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…
Harvard Medical School（哈佛医学院）；Boston Children’s Hospital（波士顿儿童医院）
Fast data acquisition in Magnetic Resonance Imaging (MRI) is vastly in demand and scan time directly depends on the number of acquired k-space samples. Conventional MRI reconstruction methods for fast MRI acquisition mostly relied on different regularizers which represent analytical models of sparsity. However, recent data-driven methods based on deep learning has resulted in promising improvements in image reconstruction algorithms. In this paper, we propose a deep plug-and-play prior framework for parallel MRI reconstruction problems which utilize a deep neural network (DNN) as an advanced d…
We consider the problem of estimating a vector from its noisy measurements using a prior specified only through a denoising function. Recent work on plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the state-of-the-art performance of estimators under such priors in a range of imaging tasks. In this work, we develop a new block coordinate RED algorithm that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables. We theoretically analyze the convergence of the algorithm and discuss its relationship to the trad…
