Regularization by denoising (RED) is a powerful framework for solving imaging inverse problems. Most RED algorithms are iterative batch procedures, which limits their applicability to very large datasets. In this paper, we address this limitation by introducing a novel online RED (On-RED) algorithm, which processes a small subset of the data at a time. We establish the theoretical convergence of On-RED in convex settings and empirically discuss its effectiveness in non-convex ones by illustrating its applicability to phase retrieval. Our results suggest that On-RED is an effective alternative to the traditional RED algorithms when dealing with large datasets.
Rochester Institute of Technology（罗切斯特理工学院）；Chosun University（朝鲜大学）
Unpaired image denoising has achieved promising development over the last few years. Regardless of the performance, methods tend to heavily rely on underlying noise properties or any assumption which is not always practical. Alternatively, if we can ground the problem from a structural perspective rather than noise statistics, we can achieve a more robust solution. with such motivation, we propose a self-supervised denoising scheme that is unpaired and relies on spatial degradation followed by a regularized refinement. Our method shows considerable improvement over previous methods and exhibit…
We consider the problem of estimating a vector from its noisy measurements using a prior specified only through a denoising function. Recent work on plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the state-of-the-art performance of estimators under such priors in a range of imaging tasks. In this work, we develop a new block coordinate RED algorithm that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables. We theoretically analyze the convergence of the algorithm and discuss its relationship to the trad…
Washington University in St. Louis（圣路易斯华盛顿大学）；Department of Electrical and Systems Engineering（电气与系统工程系）；Department of Computer Science and Engineering（计算机科学与工程系）
Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications using pre-trained deep neural nets as denoisers. Despite the recent progress, the stable convergence of RED algorithms remains an open problem. The existing RED theory only guarantees stability for convex data-fidelity terms and nonexpansive denoisers. This work addresses this issue by developing a new monotone RED (MRED) algorithm, whose convergence does not …
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…
Xiamen University（厦门大学）；South China University of Technology（华南理工大学）；Columbia University（哥伦比亚大学）
We devise a new regularization, called self-verification, for image denoising. This regularization is formulated using a deep image prior learned by the network, rather than a traditional predefined prior. Specifically, we treat the output of the network as a ``prior'' that we denoise again after ``re-noising''. The comparison between the again denoised image and its prior can be interpreted as a self-verification of the network's denoising ability. We demonstrate that self-verification encourages the network to capture low-level image statistics needed to restore the image. Based on this self…
Regularization by denoising (RED) is a broadly applicable framework for solving inverse problems by using priors specified as denoisers. While RED has been shown to provide state-of-the-art performance in a number of applications, existing RED algorithms require exact knowledge of the measurement operator characterizing the imaging system, limiting their applicability in problems where the measurement operator has parametric uncertainties. We propose a new method, called Calibrated RED (Cal-RED), that enables joint calibration of the measurement operator along with reconstruction of the unknow…
This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two types of complex TV in both isotropic and anisotropic forms. To solve the constrained denoising problem, we adopt a dual approach and derive an accelerated gradient projection algorithm. We further generalize the proposed denoising algorithm as a key building block of the proximal gradient scheme to solve a vast class of complex constrained optimization problems…
The vast majority of image recovery tasks are ill-posed problems. As such, methods that are based on optimization use cost functions that consist of both fidelity and prior (regularization) terms. A recent line of works imposes the prior by the Regularization by Denoising (RED) approach, which exploits the good performance of existing image denoising engines. Yet, the relation of RED to explicit prior terms is still not well understood, as previous work requires too strong assumptions on the denoisers. In this paper, we make two contributions. First, we show that the RED gradient can be seen a…
Task-based Regularization in Penalized Least-Squares for Binary Signal Detection Tasks in Medical Image Denoising
University of Michigan-Shanghai Jiao Tong University Joint Institute（密歇根大学-上海交通大学联合研究院）；Global Institute of Future Technology, Shanghai Jiao Tong University（上海交通大学未来科技全球研究院）；Wyant College of Optical Sciences, University of Arizona（亚利桑那大学怀恩特光学科学学院）；Department of Medical Imaging, University of Arizona（亚利桑那大学医学影像系）
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）
Qingdao University（青岛大学）；Harbin Institute of Technology（哈尔滨工业大学）；University of Electronic Science and Technology of China（电子科技大学）；University of Kentucky（肯塔基大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novel $\ell_{2,\log}$ norm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For the $\ell_{2,\log}$-regularized shrinkage problem, we develop an efficient, closed-form solution, which…
Self-supervised Deep Unrolled Reconstruction Using Regularization by Denoising
State University of New York at Buffalo（纽约州立大学布法罗分校）；Cleveland Clinic（克利夫兰诊所）；Paul C. Lauterbur Research Center for Biomedical Imaging, SIAT, CAS（中国科学院深圳先进技术研究院保罗·C·劳特伯生物医学成像研究中心）
Plug-and-Play Priors (PnP) and Regularization by Denoising (RED) are widely-used frameworks for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image priors. While traditional PnP/RED formulations have focused on priors specified using image denoisers, there is a growing interest in learning PnP/RED priors that are end-to-end optimal. The recent Deep Equilibrium Models (DEQ) framework has enabled memory-efficient end-to-end learning of PnP/RED priors by implicitly differentiating through the fixed-point equations without…
Pan-denoising: Guided Hyperspectral Image Denoising via Weighted Represent Coefficient Total Variation
School of Mathematics and Statistics, Northwestern Polytechnical University（西北工业大学数学与统计学院）；Research and Development Institute of Northwestern Polytechnical University in Shenzhen（西北工业大学深圳研究院）
Preventing Overfitting in Deep Image Prior for Hyperspectral Image Denoising
Robotics Institute, Athena Research and Innovation Center（雅典娜研究与创新中心机器人研究所）；School of Electrical and Computer Engineering, National Technical University of Athens（雅典国家技术大学电气与计算机工程学院）
Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display global convergence when given clean data. Neural networks have been used to improve algorithm robustness, but efforts to date are sensitive to initial conditions and give inconsistent performance. Here, we combine iterative methods from phase retrieval with image statistics from deep denoisers, via regularization-by-denoising. The resulting methods inherit …
During the past few years, inverse problem formulations of ultrasound beamforming have attracted a growing interest. They usually pose beamforming as a minimization problem of a fidelity term resulting from the measurement model plus a regularization term that enforces a certain class on the resulting image. Herein, we take advantages of alternating direction method of multipliers to propose a flexible framework in which each term is optimized separately. Furthermore, the proposed beamforming formulation is extended to replace the regularization term by a denoising algorithm, based on the rece…
Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising
School of Mathematics, University of Birmingham（伯明翰大学数学学院）；Department of Mathematical Sciences, University of Bath（巴斯大学数学科学系）；DAMTP, University of Cambridge（剑桥大学应用数学与理论物理系）
本文提出凸三复合优化的随机原始-对偶三算子分裂算法 TOS-SPDHG，证明 O(1/K) 遍历收敛率，并结合 RED 与等变扩展用于成像逆问题。
The spatio-spectral total variation (SSTV) model has been widely used as an effective regularization of hyperspectral images (HSI) for various applications such as mixed noise removal. However, since SSTV computes local spatial differences uniformly, it is difficult to remove noise while preserving complex spatial structures with fine edges and textures, especially in situations of high noise intensity. To solve this problem, we propose a new TV-type regularization called Graph-SSTV (GSSTV), which generates a graph explicitly reflecting the spatial structure of the target HSI from noisy HSIs a…
University of Florida（佛罗里达大学）；Sun Yat-Sen University（中山大学）
One popular strategy for image denoising is to design a generalized regularization term that is capable of exploring the implicit prior underlying data observation. Convolutional neural networks (CNN) have shown the powerful capability to learn image prior information through a stack of layers defined by a combination of kernels (filters) on the input. However, existing CNN-based methods mainly focus on synthetic gray-scale images. These methods still exhibit low performance when tackling multi-channel color image denoising. In this paper, we optimize CNN regularization capability by developin…
Recently, the low-rank property of different components extracted from the image has been considered in man hyperspectral image denoising methods. However, these methods usually unfold the 3D tensor to 2D matrix or 1D vector to exploit the prior information, such as nonlocal spatial self-similarity (NSS) and global spectral correlation (GSC), which break the intrinsic structure correlation of hyperspectral image (HSI) and thus lead to poor restoration quality. In addition, most of them suffer from heavy computational burden issues due to the involvement of singular value decomposition operatio…
A Novel Truncated Norm Regularization Method for Multi-channel Color Image Denoising
College of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）；Big Data and Intelligence Engineering School, Chongqing College of International Business and Economics（重庆对外经贸学院大数据与智能工程学院）
Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard x-rays. Here, we propose a phase retrieval approach for inline x-ray holography based on Tikhonov regularization applied to the full nonlinear forward model of image formation. The approach can be seen as a nonlinear generalization of the well-established contrast-transfer-function (CTF) reconstruction method. While similar methods have been proposed before, t…
In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV prior is prone to oversmoothness, staircasing effect, and contrast losses. Nonlocal TV (NLTV) mitigates the contrast losses by adaptively weighting the smoothness based on the similarity measure of image patches. Although it suppresses the noise effectively in the flat regions, it might leave residual noise surrounding the edges especially when the image is no…
$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many remote sensing problems, such as image fusion, target detection, image super-resolution, and others and have led to promising results. However, solving such sparse reconstruction problems is computationally expensive and has limitations in its practical use. In this paper, we proposed a novel efficient algorithm for solving the complex-valued $L_1$ regulariz…
X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector and the phase of the diffraction patterns is estimated using phase retrieval techniques. Most phase retrieval algorithms make the solution well-posed by relying on the constraints imposed by the overlapping region between neighboring diffraction pattern samples. As the overlap between neighboring diffraction patterns reduces, the problem becomes ill-posed and the object cannot be recovered. To avoid the ill-posedness, we investigate the eff…
