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 accurately enforce the image structural sparsity and self-similarity simultaneously. To make the proposed model tractable and robust, the alternative direction multiplier method (ADMM) is adopted to solve the associated non-convex minimization problem. Experimental results on various types of image restoration problems, including image deblurring, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed method outperforms many current state-of-the-art methods in both the objective and the perceptual qualities.
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 …
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…
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…
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. …
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.
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…
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.
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…
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…
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…
Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico, University of Lisbon（里斯本大学高等技术学院）
This paper introduces a new approach to patch-based image restoration based on external datasets and importance sampling. The Minimum Mean Squared Error (MMSE) estimate of the image patches, the computation of which requires solving a multidimensional (typically intractable) integral, is approximated using samples from an external dataset. The new method, which can be interpreted as a generalization of the external non-local means (NLM), uses self-normalized importance sampling to efficiently approximate the MMSE estimates. The use of self-normalized importance sampling endows the proposed met…
FAIR: Frequency-aware Image Restoration for Industrial Visual Anomaly Detection
State Key Laboratory for Manufacturing System Engineering, Xi’an Jiaotong University（西安交通大学制造系统工程国家重点实验室）；International Joint Research Laboratory for Micro/Nano Manufacturing and Measurement Technologies, Xi’an Jiaotong University（西安交通大学微纳制造与测量技术国际联合研究实验室）；Anhui Province Key Laboratory of Machine Vision Inspection, Yangtze River Delta HIT Robot Technology Research Institute（长三角哈工大机器人技术研究院安徽省机器视觉检测重点实验室）
Dual High-Order Total Variation Model for Underwater Image Restoration
College of Computer Science and Technology, Qingdao University（青岛大学计算机科学与技术学院）；Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, the School of Automation and Electrical Engineering, University of Science and Technology Beijing（北京科技大学自动化与电气工程学院 工业过程知识自动化教育部重点实验室）
Many image restoration techniques are highly dependent on the degradation used during training, and their performance declines significantly when applied to slightly different input. Blind and universal techniques attempt to mitigate this by producing a trained model that can adapt to varying conditions. However, blind techniques to date require prior knowledge of the degradation process, and assumptions regarding its parameter-space. In this paper we present the Self-Normalization Side-Chain (SCNC), a novel approach to blind universal restoration in which no prior knowledge of the degradation…
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…
In this paper, we explore the role of Instance Normalization in low-level vision tasks. Specifically, we present a novel block: Half Instance Normalization Block (HIN Block), to boost the performance of image restoration networks. Based on HIN Block, we design a simple and powerful multi-stage network named HINet, which consists of two subnetworks. With the help of HIN Block, HINet surpasses the state-of-the-art (SOTA) on various image restoration tasks. For image denoising, we exceed it 0.11dB and 0.28 dB in PSNR on SIDD dataset, with only 7.5% and 30% of its multiplier-accumulator operations…
University of Electronic Science and Technology of China（电子科技大学）
The wavelet frame systems have been widely investigated and applied for image restoration and many other image processing problems over the past decades, attributing to their good capability of sparsely approximating piece-wise smooth functions such as images. Most wavelet frame based models exploit the $l_1$ norm of frame coefficients for a sparsity constraint in the past. The authors in \cite{ZhangY2013, Dong2013} proposed an $l_0$ minimization model, where the $l_0$ norm of wavelet frame coefficients is penalized instead, and have demonstrated that significant improvements can be achieved c…
Unsupervised lesion detection is a challenging problem that requires accurately estimating normative distributions of healthy anatomy and detecting lesions as outliers without training examples. Recently, this problem has received increased attention from the research community following the advances in unsupervised learning with deep learning. Such advances allow the estimation of high-dimensional distributions, such as normative distributions, with higher accuracy than previous methods.The main approach of the recently proposed methods is to learn a latent-variable model parameterized with n…
Jilin University（吉林大学）；University of Trento（特伦托大学）；ETH Zurich（苏黎世联邦理工学院）
Constructing high-quality character image datasets is challenging because real-world images are often affected by image degradation. There are limitations when applying current image restoration methods to such real-world character images, since (i) the categories of noise in character images are different from those in general images; (ii) real-world character images usually contain more complex image degradation, e.g., mixed noise at different noise levels. To address these problems, we propose a real-world character restoration network (RCRN) to effectively restore degraded character images…
Chinese University of Hongkong（香港中文大学）；University of Electronic Science and Technology of China（电子科技大学）
Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part respectively. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation…
University of Electronic Science and Technology of China（电子科技大学）；Nokia Bell Labs（诺基亚贝尔实验室）；Nanyang Technological University（南洋理工大学）；University of Macau（澳门大学）；Nanjing Institute of Technology（南京工程学院）
In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underlying low-rank matrix directly from the corrupted observations, we progressively approximate the underlying low-rank matrix via minimizing the rank residual. Through integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we apply it to image restoration tasks, inc…
University of Science and Technology of China（中国科学技术大学）；Hefei Comprehensive National Science Center（合肥综合性国家科学中心）；Huawei Cloud BU（华为云业务单元）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；University of Macau（澳门大学）；Shenzhen Institutes of Advanced Technology, CAS（中国科学院深圳先进技术研究院）
Learning a generalized prior for natural image restoration is an important yet challenging task. Early methods mostly involved handcrafted priors including normalized sparsity, l_0 gradients, dark channel priors, etc. Recently, deep neural networks have been used to learn various image priors but do not guarantee to generalize. In this paper, we propose a novel approach that embeds a task-agnostic prior into a transformer. Our approach, named Task-Agnostic Prior Embedding (TAPE), consists of two stages, namely, task-agnostic pre-training and task-specific fine-tuning, where the first stage emb…
Northwest A\&F University, College of Science, Yangling 712100, P.R. China
Several bandwise total variation (TV) regularized low-rank (LR)-based models have been proposed to remove mixed noise in hyperspectral images (HSIs). Conventionally, the rank of LR matrix is approximated using nuclear norm (NN). The NN is defined by adding all singular values together, which is essentially a $L_1$-norm of the singular values. It results in non-negligible approximation errors and thus the resulting matrix estimator can be significantly biased. Moreover, these bandwise TV-based methods exploit the spatial information in a separate manner. To cope with these problems, we propose …
Robust Low-light Scene Restoration via Illumination Transition
The Hong Kong University of Science and Technology（香港科学与技术大学）；The Hong Kong Polytechnic University（香港理工大学）；Nanjing University of Posts and Telecommunications（南京邮电大学）；University of Surrey（萨里大学）
Ultra-High-Definition Image Restoration: New Benchmarks and A Dual Interaction Prior-Driven Solution
Dalian University of Technology（大连理工大学）；Centre for Advances in Reliability and Safety（可靠性与安全先进中心）；Nanjing University of Science and Technology（南京理工大学）；Yale University（耶鲁大学）；Shenzhen Campus of Sun Yat-Sen University（中山大学深圳校区）；Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province（辽宁省计算数学与数据智能重点实验室）
University of Electronic Science and Technology of China（中国电子科技大学）
Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation and the low-rank matrix recovery problem is solved through minimization of the nuclear norm regularized problem. However, a major limitation of nuclear norm minimization is that all the sin…
Department of Computer Science（计算机科学系）；DisneyResearch|Studios（迪士尼研究院|工作室）；ETH Zurich（苏黎世联邦理工学院）
Image restoration has seen great progress in the last years thanks to the advances in deep neural networks. Most of these existing techniques are trained using full supervision with suitable image pairs to tackle a specific degradation. However, in a blind setting with unknown degradations this is not possible and a good prior remains crucial. Recently, neural network based approaches have been proposed to model such priors by leveraging either denoising autoencoders or the implicit regularization captured by the neural network structure itself. In contrast to this, we propose using normalizin…
This work designs an image restoration deep network relying on unfolded Chambolle-Pock primal-dual iterations. Each layer of our network is built from Chambolle-Pock iterations when specified for minimizing a sum of a $\ell_2$-norm data-term and an analysis sparse prior. The parameters of our network are the step-sizes of the Chambolle-Pock scheme and the linear operator involved in sparsity-based penalization, including implicitly the regularization parameter. A backpropagation procedure is fully described. Preliminary experiments illustrate the good behavior of such a deep primal-dual networ…
INRIA（法国国家信息与自动化研究所）；Département d’informatique de l’ENS（巴黎高等师范学院计算机系）；ENS（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL University（巴黎文理研究大学）
We present a novel approach to image restoration that leverages ideas from localized structured prediction and non-linear multi-task learning. We optimize a penalized energy function regularized by a sum of terms measuring the distance between patches to be restored and clean patches from an external database gathered beforehand. The resulting estimator comes with strong statistical guarantees leveraging local dependency properties of overlapping patches. We derive the corresponding algorithms for energies based on the mean-squared and Euclidean norm errors. Finally, we demonstrate the practic…
State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS), CASIA（多模态人工智能系统国家重点实验室（MAIS），中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（人工智能学院，中国科学院大学）；Ant Group（蚂蚁集团）；PeopleAI Inc.（PeopleAI公司）
Framelet-Based Blind Image Restoration with Minimax Concave Regularization
College of Artificial Intelligence and Big Data, Chongqing Polytechnic University of Electronic Technology, Chongqing,China（人工智能与大数据学院，重庆电子工程职业大学，重庆，中国）；Department of Engineering Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Ardabil, Iran（工程科学系，先进科技学院，莫哈格赫阿德布利大学，阿德布尔，伊朗）
CAS Key Laboratory of Technology in Geo-spatial Information Processing and Application System, University of Science and Technology of China（中国科学技术大学 中国科学院空间信息处理与应用系统技术重点实验室）
Hybrid-distorted image restoration (HD-IR) is dedicated to restore real distorted image that is degraded by multiple distortions. Existing HD-IR approaches usually ignore the inherent interference among hybrid distortions which compromises the restoration performance. To decompose such interference, we introduce the concept of Disentangled Feature Learning to achieve the feature-level divide-and-conquer of hybrid distortions. Specifically, we propose the feature disentanglement module (FDM) to distribute feature representations of different distortions into different channels by revising gain-…
College of Arts and Sciences, National University of Defense Technology（国防科技大学文理学院）
It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the constraint of the nuclear norm or limiting the dimension of the matrix factorization component. Recently, theoretical works suggest that deep linear neural network has an implicit bias towards low rank on matrix completion. However, low rank is not adequate to reflect the intrinsic characteristics of a natural image. Thus, algorithms with only the constraint of low…
Simon Fraser University（西蒙弗雷泽大学）；The University of Arizona（亚利桑那大学）
The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models, including balanced approach and analysis based approach, is due to their capability of sparsely approximating piecewise smooth functions like images. Motivated by the balanced approach and analysis based approach, we shall propose a wavelet frame based $\ell_0$ minimization model, where the $\ell_0$ "norm" of the frame coefficients is penalized. We adapt th…
Taiyuan University of Technology（太原理工大学）；Durham University（杜伦大学）
Texture is one of the most obvious characteristics in solar images and it is normally described by texture features. Because textures from solar images of the same wavelength are similar, we assume texture features of solar images are multi-fractals. Based on this assumption, we propose a pure data-based image restoration method: with several high resolution solar images as references, we use the Cycle-Consistent Adversarial Network to restore burred images of the same steady physical process, in the same wavelength obtained by the same telescope. We test our method with simulated and real obs…
Heriot-Watt University（赫瑞-瓦特大学）；University of Edinburgh（爱丁堡大学）
Optical endomicroscopy (OEM) is an emerging technology platform with preclinical and clinical imaging applications. Pulmonary OEM via fibre bundles has the potential to provide in vivo, in situ molecular signatures of disease such as infection and inflammation. However, enhancing the quality of data acquired by this technique for better visualization and subsequent analysis remains a challenging problem. Cross coupling between fiber cores and sparse sampling by imaging fiber bundles are the main reasons for image degradation, and poor detection performance (i.e., inflammation, bacteria, etc.).…
Patch-based low rank is an important prior assumption for image processing. Moreover, according to our calculation, the optimization of l0 norm corresponds to the maximum likelihood estimation under random-valued impulse noise. In this article, we thus combine exact rank and l0 norm for removing the noise. It is solved formally using the alternating direction method of multipliers (ADMM), with our previous patch-based weighted filter (PWMF) producing initial images. Since this model is not convex, we consider it as a Plug-and-Play ADMM, and do not discuss theoretical convergence properties. Ex…
Unified Image Restoration and Enhancement: Degradation Calibrated Cycle Reconstruction Diffusion Model
College of Computer Science and Engineering, Chongqing University of Technology（重庆理工大学计算机科学与工程学院）；School of Science, Engineering and Environment, University of Salford（索尔福德大学科学、工程与环境学院）；College of Computer Science, Chongqing University（重庆大学计算机学院）
National Laboratory of Pattern Recognition, CASIA（中国科学院自动化研究所模式识别国家重点实验室）；Center for Excellence in Brain Science and Intelligence Technology, CAS（中国科学院脑科学与智能技术卓越创新中心）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）
Blind face restoration (BFR) is a challenging problem because of the uncertainty of the degradation patterns. This paper proposes a Restoration with Memorized Modulation (RMM) framework for universal BFR in diverse degraded scenes and heterogeneous domains. We apply random noise as well as unsupervised wavelet memory to adaptively modulate the face-enhancement generator, considering attentional denormalization in both layer and instance levels. Specifically, in the training stage, the low-level spatial feature embedding, the wavelet memory embedding obtained by wavelet transformation of the hi…
Image restoration is a typical ill-posed problem, and it contains various tasks. In the medical imaging field, an ill-posed image interrupts diagnosis and even following image processing. Both traditional iterative and up-to-date deep networks have attracted much attention and obtained a significant improvement in reconstructing satisfying images. This study combines their advantages into one unified mathematical model and proposes a general image restoration strategy to deal with such problems. This strategy consists of two modules. First, a novel generative adversarial net(GAN) with WGAN-GP …
Monitoring Pasture Restoration from Satellite Image Time Series: Caveats and Opportunities
Lund University（隆德大学）；RISE Research Institutes of Sweden（瑞典RISE研究院）；Climate AI Nordics（北欧气候人工智能中心）；Swedish Centre for Impacts of Climate Extremes (CLIMES)（瑞典气候极端影响中心（CLIMES））
CADD: Context aware disease deviations via restoration of brain images using normative conditional diffusion models
Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School（阿提诺拉A.马丁纳生物医学成像中心，麻省总医院和哈佛医学院）；Hawkes Institute, University College London（霍克斯研究所，伦敦大学学院）；Mecha Health（Mecha健康）；Computer Science & Artificial Intelligence Lab, Massachusetts Institute of Technology（计算机科学与人工智能实验室，麻省理工学院）；Department of Radiology, the University of Tokyo（东京大学放射科）；Medical Engineering, Chiba University（千叶大学医学工程）；Department of Computational Diagnostic Radiology and Preventive Medicine, the University of Tokyo Hospital（东京大学医院计算诊断放射学与预防医学科）
URA-Net: Uncertainty-Integrated Anomaly Perception and Restoration Attention Network for Unsupervised Anomaly Detection
State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University（精密测量技术与仪器国家重点实验室，清华大学精密仪器系）；State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology（智能制造装备与技术国家重点实验室，华中科技大学）；School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院）
Ruhr University Bochum（波鸿鲁尔大学）；Technical University Berlin（柏林工业大学）；Technical University of Munich（慕尼黑工业大学）
We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-input and multiple-output (MIMO) wireless radar. Here, the strong clutter due to the reflection of the layered structure's surface often makes the detection of the defects challenging. Thus, sophisticated signal separation methods are required for improved defect detection. In many scenarios, the number of defects that we are interested in is limited and the signaling response of the layered structure can be modeled as a low-rank structure. Therefore, we propose …
This paper considers the problem of signal denoising using a sparse tight-frame analysis prior. The L1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the underlying signal. To more accurately estimate non-zero values, we propose the use of a non-convex regularizer, chosen so as to ensure convexity of the objective function. The convexity of the objective function is ensured by constraining the parameter of the non-convex penalty. We use ADMM to obtain a solution and show how to guarantee that ADMM converges to the glo…
