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 for these PnP-algorithms. Hence, the results obtained from these algorithms, though empirically outstanding, can't always be completely trusted, as they may contain certain instabilities or (hallucinated) features arising from the denoiser, especially when using a pre-trained learned denoiser. In fact, in this paper, we show that a PnP-algorithm can induce hallucinated features, when using a pre-trained deep-learning-based (DnCNN) denoiser. We show that such instabilities are quite different than the instabilities inherent to an ill-posed problem. We also present methods to subdue these instabilities and significantly improve the recoveries. We compare the advantages and disadvantages of a learned denoiser over a classical denoiser (here, BM3D), as well as, the effectiveness of the FISTA-PnP algorithm vs. the ADMM-PnP algorithm. In addition, we also provide an algorithm to combine these two denoisers, the learned and the classical, in a weighted fashion to produce even better results. We conclude with numerical results which validate the developed theories.
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…
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 …
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…
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 Ohio State University（俄亥俄州立大学）；The University of Maryland（马里兰大学）
To solve inverse problems, plug-and-play (PnP) methods replace the proximal step in a convex optimization algorithm with a call to an application-specific denoiser, often implemented using a deep neural network (DNN). Although such methods yield accurate solutions, they can be improved. For example, denoisers are usually designed/trained to remove white Gaussian noise, but the denoiser input error in PnP algorithms is usually far from white or Gaussian. Approximate message passing (AMP) methods provide white and Gaussian denoiser input error, but only when the forward operator is sufficiently …
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…
Beyond MMSE: Enhancing PnP Restoration with ProxiMAP
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Inria（法国国家科学研究中心）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔理工大学）；LJK（实验室）；MaLGa Centre（MaLGa中心）；DIBRIS（DIBRIS研究所）；Università di Genova（热那亚大学）；MMS（MMS机构）；Italian Institute of Technology（意大利理工学院）
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…
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…
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）
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. …
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 …
Blur and noise corrupting Computed Tomography (CT) images can hide or distort small but important details, negatively affecting the diagnosis. In this paper, we present a novel gradient-based Plug-and-Play algorithm, constructed on the Half-Quadratic Splitting scheme, and we apply it to restore CT images. In particular, we consider different schemes encompassing external and internal denoisers as priors, defined on the image gradient domain. The internal prior is based on the Total Variation functional. The external denoiser is implemented by a deep Convolutional Neural Network (CNN) trained o…
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…
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…
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…
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。
We introduce a novel energy formulation for Plug- and-Play (PnP) image recovery. Traditional PnP methods that use a convolutional neural network (CNN) do not have an energy based formulation. The primary focus of this work is to introduce an energy-based PnP formulation, which relies on a CNN that learns the log of the image prior from training data. The score function is evaluated as the gradient of the energy model, which resembles a UNET with shared encoder and decoder weights. The proposed score function is thus constrained to a conservative vector field, which is the key difference with c…
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…
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 …
Snapshot compressive imaging (SCI) aims to capture the high-dimensional (usually 3D) images using a 2D sensor (detector) in a single snapshot. Though enjoying the advantages of low-bandwidth, low-power and low-cost, applying SCI to large-scale problems (HD or UHD videos) in our daily life is still challenging. The bottleneck lies in the reconstruction algorithms; they are either too slow (iterative optimization algorithms) or not flexible to the encoding process (deep learning based end-to-end networks). In this paper, we develop fast and flexible algorithms for SCI based on the plug-and-play …
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）
The Plug-and-Play (PnP) framework was recently introduced for low-dose CT reconstruction to leverage the interpretability and the flexibility of model-based methods to incorporate various plugins, such as trained deep learning (DL) neural networks. However, the benefits of PnP vs. state-of-the-art DL methods have not been clearly demonstrated. In this work, we proposed an improved PnP framework to address the previous limitations and develop clinical-relevant segmentation metrics for quantitative result assessment. Compared with the DL alone methods, our proposed PnP framework was slightly inf…
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 …
Data61, CSIRO (The Commonwealth Scientific and Industrial Research Organisation)（澳大利亚联邦科学与工业研究组织 Data61）；School of Engineering, Australian National University（澳大利亚国立大学工程学院）；School of Computing, Australian National University（澳大利亚国立大学计算机学院）
With the help of the deep learning paradigm, many point cloud networks have been invented for visual analysis. However, there is great potential for development of these networks since the given information of point cloud data has not been fully exploited. To improve the effectiveness of existing networks in analyzing point cloud data, we propose a plug-and-play module, PnP-3D, aiming to refine the fundamental point cloud feature representations by involving more local context and global bilinear response from explicit 3D space and implicit feature space. To thoroughly evaluate our approach, w…
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…
National Tsin Hua University（国立清华大学）；NEC Labs America（NEC美国实验室）；National Chiao Tung University（国立交通大学）
We propose a novel plug-and-play (PnP) module for improving depth prediction with taking arbitrary patterns of sparse depths as input. Given any pre-trained depth prediction model, our PnP module updates the intermediate feature map such that the model outputs new depths consistent with the given sparse depths. Our method requires no additional training and can be applied to practical applications such as leveraging both RGB and sparse LiDAR points to robustly estimate dense depth map. Our approach achieves consistent improvements on various state-of-the-art methods on indoor (i.e., NYU-v2) an…
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…
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…
In this work we propose a new paradigm for designing fast plug-and-play (PnP) algorithms using dimensionality reduction techniques. Unlike existing approaches which utilize stochastic gradient iterations for acceleration, we propose novel multi-stage sketched gradient iterations which first perform downsampling dimensionality reduction in the image space, and then efficiently approximate the true gradient using the sketched gradient in the low-dimensional space. This sketched gradient scheme can also be naturally combined with PnP-SGD methods for further improvement on computational complexity…
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）
Washington University in St. Louis（圣路易斯华盛顿大学）；University of California, Riverside（加州大学河滨分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixed-points of a deep neural network. We also pre…
Inverse problem regularization with hierarchical variational autoencoders
Univ. Bordeaux（波尔多大学）；CNRS（法国国家科学研究中心）；Bordeaux INP（波尔多国立综合理工学院）；IMB（数学与计算机科学研究所）；Ubisoft La Forge（育碧拉福奇工作室）；Université Paris Cité（巴黎城市大学）；MAP5（数学与应用概率科学研究所）
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…
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…
Visual question answering (VQA) is a hallmark of vision and language reasoning and a challenging task under the zero-shot setting. We propose Plug-and-Play VQA (PNP-VQA), a modular framework for zero-shot VQA. In contrast to most existing works, which require substantial adaptation of pretrained language models (PLMs) for the vision modality, PNP-VQA requires no additional training of the PLMs. Instead, we propose to use natural language and network interpretation as an intermediate representation that glues pretrained models together. We first generate question-guided informative image captio…
Technion Israel Institute of Technology（以色列理工学院）；Google Research（谷歌研究院）
Inverse problems in image processing are typically cast as optimization tasks, consisting of data-fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED). While both have shown state-of-the-art results in various recovery tasks, their theoretical justification is incomplete. In this paper, we aim to bridge between RED and PnP, enriching the understanding of both frameworks. Towards that end, we reformulate RED as a convex op…
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 …
The Ohio State University（俄亥俄州立大学）；Purdue University（普渡大学）
Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., CT or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling and thus drives the need for accurate, efficient reconstruction methods from undersampled datasets. In this article, we describe the use of "plug-and-play" (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then…
