Simultaneous Fidelity and Regularization Learning for Image Restoration
Tianjin University（天津大学）；Hong Kong Polytechnic University（香港理工大学）；Harbin Institute of Technology（哈尔滨工业大学）；Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；University of California, Merced（加州大学默塞德分校）
Dongwei Ren, Wangmeng Zuo, David Zhang, Lei Zhang, Ming-Hsuan Yang
Most existing non-blind restoration methods are based on the assumption that a precise degradation model is known. As the degradation process can only be partially known or inaccurately modeled, images may not be well restored. Rain streak removal and image deconvolution with inaccurate blur kernels are two representative examples of such tasks. For rain streak removal, although an input image can be decomposed into a scene layer and a rain streak layer, there exists no explicit formulation for modeling rain streaks and the composition with scene layer. For blind deconvolution, as estimation error of blur kernel is usually introduced, the subsequent non-blind deconvolution process does not restore the latent image well. In this paper, we propose a principled algorithm within the maximum a posterior framework to tackle image restoration with a partially known or inaccurate degradation model. Specifically, the residual caused by a partially known or inaccurate degradation model is spatially dependent and complexly distributed. With a training set of degraded and ground-truth image pairs, we parameterize and learn the fidelity term for a degradation model in a task-driven manner. Furthermore, the regularization term can also be learned along with the fidelity term, thereby forming a simultaneous fidelity and regularization learning model. Extensive experimental results demonstrate the effectiveness of the proposed model for image deconvolution with inaccurate blur kernels, deconvolution with multiple degradations and rain streak removal.
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…
A Regularization-Guided Equivariant Approach for Image Restoration
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China（西安交通大学数学与统计学学院）；Macau University of Science and Technology, Taipa, Macao（澳门科学技术大学）；Pengcheng Laboratory, Shenzhen, China（鹏城实验室）
Institute of Optics and Electronics, Chinese Academy of Sciences（中国科学院光电技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Image quality is the basis of image communication and understanding tasks. Due to the blur and noise effects caused by imaging, transmission and other processes, the image quality is degraded. Blind image restoration is widely used to improve image quality, where the main goal is to faithfully estimate the blur kernel and the latent sharp image. In this study, based on experimental observation and research, an adaptively sparse regularized minimization method is originally proposed. The high-order gradients combine with low-order ones to form a hybrid regularization term, and an adaptive opera…
Efficient Degradation-agnostic Image Restoration via Channel-Wise Functional Decomposition and Manifold Regularization
Mohamed bin Zayed University of Artificial Intelligence（莫扎德·本·泽德人工智能大学）；University of Trento（特伦托大学）；ETH Zürich（苏黎世联邦理工学院）；HKUST (GZ)（香港科技大学（广州））；Peking University（北京大学）；University of California, Merced（加州大学默塞德分校）
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…
RELD: Regularization by Latent Diffusion Models for Image Restoration
University of Bologna（博洛尼亚大学）；University of Macerata（马切拉塔大学）；University of Modena and Reggio Emilia（摩德纳大学与雷焦艾米利亚大学）；University of Milan（米兰大学）；Washington University in St. Louis（圣路易斯华盛顿大学）
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…
A wavelet frame coefficient total variational model for image restoration
College of Information Engineering, Shenzhen University（深圳大学信息工程学院）；Department of Electrical and Computer Engineering, University of Delaware（特拉华大学电气与计算机工程系）
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 …
Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image noise. In this work, we combine the robustness merit of model-based approaches and the learning power of data-driven approaches for real image denoising. Specifically, by integrating graph Laplacian regularization as a trainable module into a deep learning framework, we are less susceptible to overfitting than pure CNN-based approaches, achieving higher robust…
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）
This paper presents a scalable approximate Bayesian method for image restoration using total variation (TV) priors. In contrast to most optimization methods based on maximum a posteriori estimation, we use the expectation propagation (EP) framework to approximate minimum mean squared error (MMSE) estimators and marginal (pixel-wise) variances, without resorting to Monte Carlo sampling. For the classical anisotropic TV-based prior, we also propose an iterative scheme to automatically adjust the regularization parameter via expectation-maximization (EM). Using Gaussian approximating densities wi…
Image Restoration with Point Spread Function Regularization and Active Learning
College of Electronic Information and Optical Engineering, Taiyuan（太原电子信息与光学工程学院）；Peng Cheng Lab, Shenzhen（鹏城实验室）；Department of Physics, Durham University（杜伦大学物理系）；National Astronomical Observatories, Beijing（中国科学院国家天文台）；Yunnan Observatories, Kunming（中国科学院云南天文台）
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…
Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration
National Laboratory of Radar Signal Processing, Xidian University（西安电子科技大学雷达信号处理国家重点实验室）；Science and Technology on Multispectral Information Processing Laboratory, School of Automation, Huazhong University of Science and Technology（华中科技大学自动化学院多谱信息处理技术国家级重点实验室）
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）
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））
Unifying Heterogeneous Degradations: Uncertainty-Aware Diffusion Bridge Model for All-in-One Image Restoration
School of Intelligent Systems Engineering, Shenzhen Campus of Sun Yat-sen University, Shenzhen, Guangdong 518107, China（中山大学智能系统工程学院深圳校区）；Department of Frontier Research, Peng Cheng Laboratory, Shenzhen, Guangdong 518055, China（鹏城实验室前沿研究部）；Guangdong Provincial Key Laboratory of Fire Science and Technology, Guangzhou 510006, China（广东省消防科学与技术重点实验室）
Zhengzhou University（郑州大学）；Univ Lyon, Ens de Lyon, Univ Lyon 1, CNRS, Laboratoire de Physique（里昂大学，里昂高等师范学院，里昂第一大学，法国国家科学研究中心，物理实验室）
Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, often solved by minimizing a non-smooth penalized co-log-likelihood function. Although the solution is easily interpretable with theoretic guarantees, its estimation relies on an optimization process that can take time. Considering the research effort in deep learning for image classification and segmentation, this class of methods offers a serious alternative to perform image restoration but stays challenging to solve inverse problems. In this work, we design a deep network, named DeepPDNet…
As a real scenes sensing approach, depth information obtains the widespread applications. However, resulting from the restriction of depth sensing technology, the depth map captured in practice usually suffers terrible noise and missing values at plenty of pixels. In this paper, we propose a fast low-rank matrix completion via dual-graph regularization for depth restoration. Specifically, the depth restoration can be transformed into a low-rank matrix completion problem. In order to complete the low-rank matrix and restore it to the depth map, the proposed dual-graph method containing the loca…
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…
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. …
