Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase-like artifacts. Usually, the high-order total variation (HTV) regularizer is an good option except its over-smoothing property. In this work, we study a minimization problem where the objective includes an usual $l_2$ data-fidelity term and an overlapping group sparsity total variation regularizer which can avoid staircase effect and allow edges preserving in the restored image. We also proposed a fast algorithm for solving the corresponding minimization problem and compare our method with the state-of-the-art TV based methods and HTV based method. The numerical experiments illustrate the efficiency and effectiveness of the proposed method in terms of PSNR, relative error and computing time.
Optimal Transport Based Unsupervised Restoration Learning Exploiting Degradation Sparsity
School of Information Science and Electronic Engineering, Shanghai Jiao Tong University, China（信息科学与电子工程学院，上海交通大学）；School of Communication Engineering, Hangzhou Dianzi University, Hangzhou, China（通信工程学院，杭州电子科技大学）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Northeastern University（东北大学）；ByteDance（字节跳动）
Inspired by the robustness and efficiency of sparse representation in sparse coding based image restoration models, we investigate the sparsity of neurons in deep networks. Our method structurally enforces sparsity constraints upon hidden neurons. The sparsity constraints are favorable for gradient-based learning algorithms and attachable to convolution layers in various networks. Sparsity in neurons enables computation saving by only operating on non-zero components without hurting accuracy. Meanwhile, our method can magnify representation dimensionality and model capacity with negligible add…
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…
In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field is moving towards trainable models, inspired from deep learning. Deep image prior (DIP) is a recent regularization framework that uses a convolutional neural network (CNN) architecture without data-driven training. This paper extends the DIP framework by combining it with the traditional TV regularization. We show that the inclusion of TV leads to considerabl…
University of Electronic Science and Technology of China（电子科技大学）；Chongqing College of Electronic Engineering（重庆电子工程职业学院）；Minnan Normal University（闽南师范大学）
Because of the limitations of the infrared imaging principle and the properties of infrared imaging systems, infrared images have some drawbacks, including a lack of details, indistinct edges, and a large amount of salt-andpepper noise. To improve the sparse characteristics of the image while maintaining the image edges and weakening staircase artifacts, this paper proposes a method that uses the Lp quasinorm instead of the L1 norm and for infrared image deblurring with an overlapping group sparse total variation method. The Lp quasinorm introduces another degree of freedom, better describes i…
Xidian University（西安电子科技大学）；West Virginia University（西弗吉尼亚大学）
State-of-the-art approaches toward image restoration can be classified into model-based and learning-based. The former - best represented by sparse coding techniques - strive to exploit intrinsic prior knowledge about the unknown high-resolution images; while the latter - popularized by recently developed deep learning techniques - leverage external image prior from some training dataset. It is natural to explore their middle ground and pursue a hybrid image prior capable of achieving the best in both worlds. In this paper, we propose a systematic approach of achieving this goal called Structu…
Non-local self-similarity and sparsity principles have proven to be powerful priors for natural image modeling. We propose a novel differentiable relaxation of joint sparsity that exploits both principles and leads to a general framework for image restoration which is (1) trainable end to end, (2) fully interpretable, and (3) much more compact than competing deep learning architectures. We apply this approach to denoising, jpeg deblocking, and demosaicking, and show that, with as few as 100K parameters, its performance on several standard benchmarks is on par or better than state-of-the-art me…
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）
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…
Small compression noises, despite being transparent to human eyes, can adversely affect the results of many image restoration processes, if left unaccounted for. Especially, compression noises are highly detrimental to inverse operators of high-boosting (sharpening) nature, such as deblurring and superresolution against a convolution kernel. By incorporating the non-linear DCT quantization mechanism into the formulation for image restoration, we propose a new sparsity-based convex programming approach for joint compression noise removal and image restoration. Experimental results demonstrate s…
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…
Laboratoire AIM, CEA/DSM-CNRS-Universite Paris Diderot（AIM实验室，法国原子能和替代能源委员会/材料科学部-法国国家科学研究中心-巴黎狄德罗大学）；CEA Saclay（法国原子能和替代能源委员会萨克雷）；Institut d’Astrophysique de Paris（巴黎天体物理研究所）；CNRS（法国国家科学研究中心）；UPMC（皮埃尔和玛丽·居里大学）
Context: in large-scale spatial surveys, the Point Spread Function (PSF) varies across the instrument field of view (FOV). Local measurements of the PSFs are given by the isolated stars images. Yet, these estimates may not be directly usable for post-processings because of the observational noise and potentially the aliasing. Aims: given a set of aliased and noisy stars images from a telescope, we want to estimate well-resolved and noise-free PSFs at the observed stars positions, in particular, exploiting the spatial correlation of the PSFs across the FOV. Contributions: we introduce RCA (Reso…
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…
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 …
Nanyang Technological University（南洋理工大学）；Michigan State University（密歇根州立大学）
Constructing effective image priors is critical to solving ill-posed inverse problems in image processing and imaging. Recent works proposed to exploit image non-local similarity for inverse problems by grouping similar patches and demonstrated state-of-the-art results in many applications. However, compared to classic methods based on filtering or sparsity, most of the non-local algorithms are time-consuming, mainly due to the highly inefficient and redundant block matching step, where the distance between each pair of overlapping patches needs to be computed. In this work, we propose a novel…
Shanghai Jiao Tong University（上海交通大学）；ETH Zürich（苏黎世联邦理工学院）；Shanghai AI Laboratory（上海人工智能实验室）；The University of Sydney（悉尼大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；Westlake University（西湖大学）
Recently, Transformer-based image restoration networks have achieved promising improvements over convolutional neural networks due to parameter-independent global interactions. To lower computational cost, existing works generally limit self-attention computation within non-overlapping windows. However, each group of tokens are always from a dense area of the image. This is considered as a dense attention strategy since the interactions of tokens are restrained in dense regions. Obviously, this strategy could result in restricted receptive fields. To address this issue, we propose Attention Re…
Beyond Degradation Redundancy: Contrastive Prompt Learning for All-in-One Image Restoration
School of Computer Science and Technology, Harbin Institute of Technology（计算机科学与技术学院，哈尔滨工业大学）；School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen)（计算机科学与技术学院，哈尔滨工业大学（深圳））
DSwinIR: Rethinking Window-based Attention for Image Restoration
School of Computer Science and Technology, Harbin Institute of Technology（计算机科学与技术学院，哈尔滨工业大学）；School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen)（计算机科学与技术学院，哈尔滨工业大学（深圳））
Modeling statistics of image priors is useful for image super-resolution, but little attention has been paid from the massive works of deep learning-based methods. In this work, we propose a Bayesian image restoration framework, where natural image statistics are modeled with the combination of smoothness and sparsity priors. Concretely, firstly we consider an ideal image as the sum of a smoothness component and a sparsity residual, and model real image degradation including blurring, downscaling, and noise corruption. Then, we develop a variational Bayesian approach to infer their posteriors.…
University of Maryland, College Park（马里兰大学帕克分校）；Cornell University（康奈尔大学）
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels are non-zero, simple $l_1$-norm-based methods ignore potential correlations in the support between adjacent pixels. In a number of applications, one is interested in images that are not only sparse, but also have a support with smooth (or contiguous) boundaries. Existing algorithms that take into account such a support structure mostly rely on non-convex meth…
CoRE-UIR: Prior-guided common and residual experts for efficient all-in-one remote sensing image restoration
School of Geodesy and Geomatics, Wuhan University（武汉大学测绘学院）；School of Artificial Intelligence, Wuhan University（武汉大学人工智能学院）；State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University（武汉大学测绘遥感信息工程国家重点实验室）
A Convex Functional for Image Denoising based on Patches with Constrained Overlaps and its vectorial application to Low Dose Differential Phase Tomography
the Ludwig Maximilians University, Physics Departement, 85748 Garching, Germany（慕尼黑大学物理系）；Ludwig Maximilians University, Departement of Clinical Radiology,80336 Munich, Germany（慕尼黑大学临床放射学系）
Tsinghua University（清华大学）；Shanghai AI Laboratory（上海人工智能实验室）；ETH Zürich（苏黎世联邦理工学院）；ByteDance Inc（字节跳动公司）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
The high computational costs of video super-resolution (VSR) models hinder their deployment on resource-limited devices, (e.g., smartphones and drones). Existing VSR models contain considerable redundant filters, which drag down the inference efficiency. To prune these unimportant filters, we develop a structured pruning scheme called Structured Sparsity Learning (SSL) according to the properties of VSR. In SSL, we design pruning schemes for several key components in VSR models, including residual blocks, recurrent networks, and upsampling networks. Specifically, we develop a Residual Sparsity…
HAT: Hybrid Attention Transformer for Image Restoration
State Key Laboratory of Internet of Things for Smart City, University of Macau（澳门大学物联网智能城市国家重点实验室）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；ARC Lab, Tencent PCG（腾讯PCG ARC实验室）
MicroDiffuse3D: A Foundation Model for 3D Microscopy Imaging Restoration
Paul G. Allen School of Computer Science and Engineering, University of Washington, Seattle, WA, USA（保罗·G·艾伦计算机科学与工程学院，华盛顿大学，西雅图，华盛顿州，美国）；Department of Chemistry, University of Washington, Seattle, WA, USA（化学系，华盛顿大学，西雅图，华盛顿州，美国）
Image Restoration Learning via Noisy Supervision in the Fourier Domain
Department of Electrical and Electronic Engineering, The University of Hong Kong（香港大学电子与电气工程系）；Key Laboratory of Image Processing and Intelligent Control, Ministry of Education（教育部图像处理与智能控制重点实验室；华中科技大学人工智能与自动化学院）；School of Artificial Intelligence and Automation, Huazhong University of Science and Technology
Harbin Institute of Technology（哈尔滨工业大学）；Peking University（北京大学）
Traditional patch-based sparse representation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational complexity in dictionary learning. Second, each patch is considered independently in dictionary learning and sparse coding, which ignores the relationship among patches, resulting in inaccurate sparse coding coefficients. In this paper, instead of using patch as the basic unit of sparse representation, we exploit the concept of group as the basic unit of sparse representation, which is composed of nonlocal p…
Advanced Communication Research Institute (ACRI)（先进通信研究所）；Sharif University of Technology（谢里夫理工大学）
In this paper, we propose a method for image block loss restoration based on the notion of sparse representation. We use the sparsity pattern as side information to efficiently restore block losses by iteratively imposing the constraints of spatial and transform domains on the corrupted image. Two novel features, including a pre-interpolation and a criterion for stopping the iterations, are proposed to improve the performance. Also, to deal with practical applications, we develop a technique to transmit the side information along with the image. In this technique, we first compress the side in…
In this paper, we solve blind image deconvolution problem that is to remove blurs form a signal degraded image without any knowledge of the blur kernel. Since the problem is ill-posed, an image prior plays a significant role in accurate blind deconvolution. Traditional image prior assumes coefficients in filtered domains are sparse. However, it is assumed here that there exist additional structures over the sparse coefficients. Accordingly, we propose new problem formulation for the blind image deconvolution, which utilizes the structural information by coupling Student's-t image prior with ov…
Xidian University（西安电子科技大学）；The Hong Kong Polytechnic University（香港理工大学）；McMaster University（麦克马斯特大学）
As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques, and the fact that natural images are intrinsically sparse in some domain. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases f…
Sparse decomposition has been widely used for different applications, such as source separation, image classification and image denoising. This paper presents a new algorithm for segmentation of an image into background and foreground text and graphics using sparse decomposition. First, the background is represented using a suitable smooth model, which is a linear combination of a few smoothly varying basis functions, and the foreground text and graphics are modeled as a sparse component overlaid on the smooth background. Then the background and foreground are separated using a sparse decompos…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properti…
From Fog Chamber to Aircraft Window: Pixel-Registered Imaging and Synthetic Fine-Tuning Enable Cross-Domain Defogging
Department of Electrical and Computer Engineering, University of Utah（犹他大学电气与计算机工程系）；U.S. Naval Research Laboratory Remote Sensing Division（美国海军研究实验室远程传感部门）
Graduate School at Shenzhen, Tsinghua University（清华大学深圳研究生院）；BioSyM IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre（新加坡-麻省理工研究与技术联盟BioSyM研究组）
We propose a three-dimensional nonlinear diffusion method to implement the similar autofocusing function of multiple micro-objects and simultaneously remove the defocused images, which can distinguish the locations of certain sized scattering particles that are overlapping along z-axis. It is applied to all of the reconstruction slices that are generated from the captured hologram after each back propagation. For certain small sized particles, the maxima of maximum gradient magnitude of each reconstruction slice appears at the ground truth z position after applying the proposed scheme when the…
Polytechnic Institute of New York University（纽约大学理工学院）
This paper addresses signal denoising when large-amplitude coefficients form clusters (groups). The L1-norm and other separable sparsity models do not capture the tendency of coefficients to cluster (group sparsity). This work develops an algorithm, called 'overlapping group shrinkage' (OGS), based on the minimization of a convex cost function involving a group-sparsity promoting penalty function. The groups are fully overlapping so the denoising method is translation-invariant and blocking artifacts are avoided. Based on the principle of majorization-minimization (MM), we derive a simple iter…
École de technologie supérieure（高等技术学院）；McGill University（麦吉尔大学）
Diffusion magnetic resonance imaging, a non-invasive tool to infer white matter fiber connections, produces a large number of streamlines containing a wealth of information on structural connectivity. The size of these tractography outputs makes further analyses complex, creating a need for methods to group streamlines into meaningful bundles. In this work, we address this by proposing a set of kernel dictionary learning and sparsity priors based methods. Proposed frameworks include L-0 norm, group sparsity, as well as manifold regularization prior. The proposed methods allow streamlines to be…
Beckman Institute, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校贝克曼研究所）；University of Science and Technology of China（中国科学技术大学）
In this paper, we design a Deep Dual-Domain ($\mathbf{D^3}$) based fast restoration model to remove artifacts of JPEG compressed images. It leverages the large learning capacity of deep networks, as well as the problem-specific expertise that was hardly incorporated in the past design of deep architectures. For the latter, we take into consideration both the prior knowledge of the JPEG compression scheme, and the successful practice of the sparsity-based dual-domain approach. We further design the One-Step Sparse Inference (1-SI) module, as an efficient and light-weighted feed-forward approxim…
University of Texas at Arlington（德克萨斯大学阿灵顿分校）；Library of Congress（美国国会图书馆）；University of Electronic Science and Technology of China（电子科技大学）
In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed algorithm is based on the iterative reweighted least squares (IRLS) model, which is further accelerated by the preconditioned conjugate gradient method. The convergence rate of the proposed algorithm is almost the same as that of the traditional IRLS algorithms, that is, exponentially fast. Moreover, with the specifically devised preconditioner, the computation…
The most widely used form of convolutional sparse coding uses an $\ell_1$ regularization term. While this approach has been successful in a variety of applications, a limitation of the $\ell_1$ penalty is that it is homogeneous across the spatial and filter index dimensions of the sparse representation array, so that sparsity cannot be separately controlled across these dimensions. The present paper considers the consequences of replacing the $\ell_1$ penalty with a mixed group norm, motivated by recent theoretical results for convolutional sparse representations. Algorithms are developed for …
The Chinese University of Hong Kong（香港中文大学）；Imsight Medical Technology, Co., Ltd.（视见医疗科技有限公司）；Imperial College London（帝国理工学院）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）
Cell instance segmentation in Pap smear image remains challenging due to the wide existence of occlusion among translucent cytoplasm in cell clumps. Conventional methods heavily rely on accurate nuclei detection results and are easily disturbed by miscellaneous objects. In this paper, we propose a novel Instance Relation Network (IRNet) for robust overlapping cell segmentation by exploring instance relation interaction. Specifically, we propose the Instance Relation Module to construct the cell association matrix for transferring information among individual cell-instance features. With the co…
Polytechnic Institute of New York University（纽约大学理工学院）
Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a non-convex regularization term chosen such that the total cost function (consisting of data consistency and regularization terms) is convex. Therefore, sparsity is more strongly promoted than in the standard convex formulation, but without sacrificing the attractive aspects of conv…
Generalized Low-Rank Matrix Completion Model with Overlapping Group Error Representation
School of Mathematics and Statistics, Hubei Minzu University（湖北民族大学数学与统计学院）；School of Mathematics and Statistics, Southwest University（西南大学数学与统计学院）；School of Mathematics and Statistics, Chongqing University（重庆大学数学与统计学院）
Nonlocal self-similarity and group sparsity have been widely utilized in image compressive sensing (CS). However, when the sampling rate is low, the internal prior information of degraded images may be not enough for accurate restoration, resulting in loss of image edges and details. In this paper, we propose a joint group and residual sparse coding method for CS image recovery (JGRSC-CS). In the proposed JGRSC-CS, patch group is treated as the basic unit of sparse coding and two dictionaries (namely internal and external dictionaries) are applied to exploit the sparse representation of each g…
