It was recently demonstrated in [Chaudhury et al.,Non-Local Euclidean Medians,2012] that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the robust Euclidean median. Numerical experiments on synthetic and natural images showed that the latter consistently performed better than NLM beyond a certain noise level, and significantly so for images with sharp edges. The Euclidean mean and median can be put into a common regression (on the patch space) framework, in which the l_2 norm of the residuals is considered in the former, while the l_1 norm is considered in the latter. The natural question then is what happens if we consider l_p (0<p<1) regression? We investigate this possibility in this paper.
GIK Institute of Engineering Sciences and Technology（GIK工程科学与技术学院）
Among the patch-based image denoising processing methods, smooth ordering of local patches (patch ordering) has been shown to give state-of-art results. For image denoising the patch ordering method forms two large TSPs (Traveling Salesman Problem) comprised of nodes in N-dimensional space. Ten approximate solutions of the two large TSPs are then used in a filtering process to form the reconstructed image. Use of large TSPs makes patch ordering a computationally intensive method. A modified patch ordering method for image denoising is proposed. In the proposed method, several smaller-sized TSP…
Inner Mongolia University（内蒙古大学）；University of Hong Kong（香港大学）
Non-local self-similarity based low rank algorithms are the state-of-the-art methods for image denoising. In this paper, a new method is proposed by solving two issues: how to improve similar patches matching accuracy and build an appropriate low rank matrix approximation model for Gaussian noise. For the first issue, similar patches can be found locally or globally. Local patch matching is to find similar patches in a large neighborhood which can alleviate noise effect, but the number of patches may be insufficient. Global patch matching is to determine enough similar patches but the error ra…
In this paper, we propose a novel image denoising algorithm exploiting features from both spatial as well as transformed domain. We implement intensity-invariance based improved grouping for collaborative support-agnostic sparse reconstruction. For collaboration firstly, we stack similar-structured patches via intensity-invariant correlation measure. The grouped patches collaborate to yield desirable sparse estimates for noise filtering. This is because similar patches share the same support in the transformed domain, such similar supports can be used as probabilities of active taps to refine …
Northeastern University at Qinhuangdao（东北大学秦皇岛分校）；Univ Bretagne-Sud（南布列塔尼大学）
Patch-based low-rank minimization for image processing attracts much attention in recent years. The minimization of the matrix rank coupled with the Frobenius norm data fidelity can be solved by the hard thresholding filter with principle component analysis (PCA) or singular value decomposition (SVD). Based on this idea, we propose a patch-based low-rank minimization method for image denoising. The main denoising process is stated in three equivalent way: PCA, SVD and low-rank minimization. Compared to recent patch-based sparse representation methods, experiments demonstrate that the proposed …
Institute for Computer Science and Control, Hungarian Academy of Sciences（匈牙利科学院计算机科学与控制研究所）
In this paper, we propose a novel image denoising algorithm using collaborative support-agnostic sparse reconstruction. An observed image is first divided into patches. Similarly structured patches are grouped together to be utilized for collaborative processing. In the proposed collaborative schemes, similar patches are assumed to share the same support taps. For sparse reconstruction, the likelihood of a tap being active in a patch is computed and refined through a collaboration process with other similar patches in the same group. This provides very good patch support estimation, hence enha…
Liaoning Normal University（辽宁师范大学）；Jilin University（吉林大学）
In this paper, an image denoising algorithm is proposed for salt and pepper noise. First, a generative model is built on a patch as a basic unit and then the algorithm locates the image noise within that patch in order to better describe the patch and obtain better subsequent clustering. Second, the algorithm classifies patches using a generative clustering method, thus providing additional similarity information for noise repair and suppressing the interference of noise, abandoning those categories that consist of a smaller number of patches. Finally, the algorithm builds a non-local switchin…
Instituto de Telecomunicações（葡萄牙电信研究所）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等理工学院）
In this paper, we address the problem of denoising images degraded by Poisson noise. We propose a new patch-based approach based on best linear prediction to estimate the underlying clean image. A simplified prediction formula is derived for Poisson observations, which requires the covariance matrix of the underlying clean patch. We use the assumption that similar patches in a neighborhood share the same covariance matrix, and we use off-the-shelf Poisson denoising methods in order to obtain an initial estimate of the covariance matrices. Our method can be seen as a post-processing step for Po…
Non-local patch based methods were until recently state-of-the-art for image denoising but are now outperformed by CNNs. Yet they are still the state-of-the-art for video denoising, as video redundancy is a key factor to attain high denoising performance. The problem is that CNN architectures are hardly compatible with the search for self-similarities. In this work we propose a new and efficient way to feed video self-similarities to a CNN. The non-locality is incorporated into the network via a first non-trainable layer which finds for each patch in the input image its most similar patches in…
VBM3D is an extension to video of the well known image denoising algorithm BM3D, which takes advantage of the sparse representation of stacks of similar patches in a transform domain. The extension is rather straightforward: the similar 2D patches are taken from a spatio-temporal neighborhood which includes neighboring frames. In spite of its simplicity, the algorithm offers a good trade-off between denoising performance and computational complexity. In this work we revisit this method, providing an open-source C++ implementation reproducing the results. A detailed description is given and the…
Supervised neural networks are known to achieve excellent results in various image restoration tasks. However, such training requires datasets composed of pairs of corrupted images and their corresponding ground truth targets. Unfortunately, such data is not available in many applications. For the task of image denoising in which the noise statistics is unknown, several self-supervised training methods have been proposed for overcoming this difficulty. Some of these require knowledge of the noise model, while others assume that the contaminating noise is uncorrelated, both assumptions are too …
Filtering images of more than one channel is challenging in terms of both efficiency and effectiveness. By grouping similar patches to utilize the self-similarity and sparse linear approximation of natural images, recent nonlocal and transform-domain methods have been widely used in color and multispectral image (MSI) denoising. Many related methods focus on the modeling of group level correlation to enhance sparsity, which often resorts to a recursive strategy with a large number of similar patches. The importance of the patch level representation is understated. In this paper, we mainly inve…
Patch-based denoising algorithms like BM3D have achieved outstanding performance. An important idea for the success of these methods is to exploit the recurrence of similar patches in an input image to estimate the underlying image structures. However, in these algorithms, the similar patches used for denoising are obtained via Nearest Neighbour Search (NNS) and are sometimes not optimal. First, due to the existence of noise, NNS can select similar patches with similar noise patterns to the reference patch. Second, the unreliable noisy pixels in digital images can bring a bias to the patch sea…
In this paper, we propose a new image denoising method, tailored to specific classes of images, assuming that a dataset of clean images of the same class is available. Similarly to the non-local means (NLM) algorithm, the proposed method computes a weighted average of non-local patches, which we interpret under the importance sampling framework. This viewpoint introduces flexibility regarding the adopted priors, the noise statistics, and the computation of Bayesian estimates. The importance sampling viewpoint is exploited to approximate the minimum mean squared error (MMSE) patch estimates, us…
Gaussian noise removal is an interesting area in digital image processing not only to improve the visual quality, but for its impact on other post-processing algorithms like image registration or segmentation. Many presented state-of-the-art denoising methods are based on the self-similarity or patch-based image processing. Specifically, Non-Local Means (NLM) as a patch-based filter has gained increasing attention in recent years. Essentially, this filter tends to obtain the noise-less signal value by computing the Gaussian-weighted Euclidean distance between the patch under-processing and oth…
Taishan University（泰山学院）；Nankai University（南开大学）；The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Guangxi Normal University（广西师范大学）；Inception Institute of Artificial Intelligence（起源人工智能研究院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
Non-local self similarity (NSS) is a powerful prior of natural images for image denoising. Most of existing denoising methods employ similar patches, which is a patch-level NSS prior. In this paper, we take one step forward by introducing a pixel-level NSS prior, i.e., searching similar pixels across a non-local region. This is motivated by the fact that finding closely similar pixels is more feasible than similar patches in natural images, which can be used to enhance image denoising performance. With the introduced pixel-level NSS prior, we propose an accurate noise level estimation method, …
Image denoising methods must effectively model, implicitly or explicitly, the vast diversity of patterns and textures that occur in natural images. This is challenging, even for modern methods that leverage deep neural networks trained to regress to clean images from noisy inputs. One recourse is to rely on "internal" image statistics, by searching for similar patterns within the input image itself. In this work, we propose a new method for natural image denoising that trains a deep neural network to determine whether patches in a noisy image input share common underlying patterns. Given a pai…
This paper presents a patch-wise low-rank based image denoising method with constrained variational model involving local and nonlocal regularization. On one hand, recent patch-wise methods can be represented as a low-rank matrix approximation problem whose convex relaxation usually depends on nuclear norm minimization (NNM). Here, we extend the NNM to the nonconvex schatten p-norm minimization with additional weights assigned to different singular values, which is referred to as the Weighted Schatten p-Norm Minimization (WSNM). An efficient algorithm is also proposed to solve the WSNM problem…
Hangzhou Dianzi University（杭州电子科技大学）；Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；Tsinghua University（清华大学）；University of Science and Technology of China（中国科学技术大学）
The depth images denoising are increasingly becoming the hot research topic nowadays because they reflect the three-dimensional (3D) scene and can be applied in various fields of computer vision. But the depth images obtained from depth camera usually contain stains such as noise, which greatly impairs the performance of depth related applications. In this paper, considering that group-based image restoration methods are more effective in gathering the similarity among patches, a group based nuclear norm and learning graph (GNNLG) model was proposed. For each patch, we find and group the most …
Nanjing University（南京大学）；Southeast University（东南大学）；University of Oulu（奥卢大学）
Group-based sparse representation has shown great potential in image denoising. However, most existing methods only consider the nonlocal self-similarity (NSS) prior of noisy input image. That is, the similar patches are collected only from degraded input, which makes the quality of image denoising largely depend on the input itself. However, such methods often suffer from a common drawback that the denoising performance may degrade quickly with increasing noise levels. In this paper we propose a new prior model, called group sparsity residual constraint (GSRC). Unlike the conventional group-b…
University of California at San Diego（加州大学圣地亚哥分校）；Purdue University（普渡大学）
We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a database that contains only relevant patches. We formulate the denoising problem as an optimal filter design problem and make two contributions. First, we determine the basis function of the denoising filter by solving a group sparsity minimization problem. The optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the …
University of Colorado at Boulder（科罗拉多大学博尔德分校）；Yale University（耶鲁大学）
The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy image. The algorithm relies on the following two observations: (1) the low-index eigenvectors of the diffusion, or graph Laplacian, operators are very robust to random perturbations of the weights and random changes in the connections of the patch-graph; and (2) patches extracted from smooth regions of the image are organized along smooth low-dimensional struc…
The Hong Kong University of Science and Technology（香港科技大学）；SenseTime Group Limited（商汤集团有限公司）；National Institute of Informatics（国立情报学研究所）；Graduate University for Advanced Studies（综合研究大学院大学）
Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the…
National Engineering Laboratory for Video Technology, Peking University（北京大学视频技术国家工程实验室）
In this letter, we propose a novel image denoising method based on correlation preserving sparse coding. Because the instable and unreliable correlations among basis set can limit the performance of the dictionary-driven denoising methods, two effective regularized strategies are employed in the coding process. Specifically, a graph-based regularizer is built for preserving the global similarity correlations, which can adaptively capture both the geometrical structures and discriminative features of textured patches. In particular, edge weights in the graph are obtained by seeking a nonnegativ…
School of Statistics and Data Science, Nankai University（南开大学统计与数据科学学院）；The First Affiliated Hospital of Xi’an Jiaotong University（西安交通大学第一附属医院）；Shanxi Engineering Research Center of Computational Imaging and Medical Intelligence（山西省计算成像与医学智能工程研究中心）
Sungkyunkwan University（成均馆大学）；Ulsan National Institute of Science and Technology（蔚山科学技术院）；Shanghai Jiao Tong University（上海交通大学）；Seoul National University（首尔国立大学）
Regression that predicts continuous quantity is a central part of applications using computational imaging and computer vision technologies. Yet, studying and understanding self-supervised learning for regression tasks - except for a particular regression task, image denoising - have lagged behind. This paper proposes a general self-supervised regression learning (SSRL) framework that enables learning regression neural networks with only input data (but without ground-truth target data), by using a designable pseudo-predictor that encapsulates domain knowledge of a specific application. The pa…
Hanyang University（汉阳大学）；NAVER LABS（NAVER实验室）；Chungnam National University（忠南国立大学）；SK T-Brain
In this study, we propose a simple and effective fine-tuning algorithm called "restore-from-restored", which can greatly enhance the performance of fully pre-trained image denoising networks. Many supervised denoising approaches can produce satisfactory results using large external training datasets. However, these methods have limitations in using internal information available in a given test image. By contrast, recent self-supervised approaches can remove noise in the input image by utilizing information from the specific test input. However, such methods show relatively lower performance o…
Technion – Israel Institute of Technology（以色列理工学院）
Recent work in image processing suggests that operating on (overlapping) patches in an image may lead to state-of-the-art results. This has been demonstrated for a variety of problems including denoising, inpainting, deblurring, and super-resolution. The work reported in [1,2] takes an extra step forward by showing that ordering these patches to form an approximate shortest path can be leveraged for better processing. The core idea is to apply a simple filter on the resulting 1D smoothed signal obtained after the patch-permutation. This idea has been also explored in combination with a wavelet…
Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past, convex optimization with sparsity-promoting convex regularization was usually regarded as a standard scheme for estimating sparse signals in noise. However, using convex regularization can not still obtain the correct sparsity solution under some practical problems including image inverse problems. In this paper we propose a non-convex weighted $\ell_p$ minimization based group …
Image denoising is a classical signal processing problem that has received significant interest within the image processing community during the past two decades. Most of the algorithms for image denoising has focused on the paradigm of non-local similarity, where image blocks in the neighborhood that are similar, are collected to build a basis for reconstruction. Through rigorous experimentation, this paper reviews multiple aspects of image denoising algorithm development based on non-local similarity. Firstly, the concept of non-local similarity as a foundational quality that exists in natur…
Institut de Mathématiques de Bordeaux, CNRS, Université de Bordeaux, Bordeaux INP（波尔多数学研究所、法国国家科学研究中心、波尔多大学、波尔多国立理工学院）；University of California, San Diego（加利福尼亚大学圣地亚哥分校）
Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular Expected Patch Log-Likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture model (GMM) prior learned on clean image patches as a way to regularize degraded patches. In this paper, we show that a generalized Gaussian mixture model (GGMM) captures the underlying distribution of patches better than a GMM. Even though GGMM is a powerful prior to combine with EPLL, the non-Gaussianity of its components presents major challenges to be applied to a comp…
Image textures, as a kind of local variations, provide important information for human visual system. Many image textures, especially the small-scale or stochastic textures are rich in high-frequency variations, and are difficult to be preserved. Current state-of-the-art denoising algorithms typically adopt a nonlocal approach consisting of image patch grouping and group-wise denoising filtering. To achieve a better image denoising while preserving the variations in texture, we first adaptively group high correlated image patches with the same kinds of texture elements (texels) via an adaptive…
Group sparse representation has shown promising results in image debulrring and image inpainting in GSR [3] , the main reason that lead to the success is by exploiting Sparsity and Nonlocal self-similarity (NSS) between patches on natural images, and solve a regularized optimization problem. However, directly adapting GSR[3] in image denoising yield very unstable and non-satisfactory results, to overcome these issues, this paper proposes a progressive image denoising algorithm that successfully adapt GSR [3] model and experiments shows the superior performance than some of the state-of-the-art…
We propose a new grayscale image denoiser, dubbed as Neural Affine Image Denoiser (Neural AIDE), which utilizes neural network in a novel way. Unlike other neural network based image denoising methods, which typically apply simple supervised learning to learn a mapping from a noisy patch to a clean patch, we formulate to train a neural network to learn an \emph{affine} mapping that gets applied to a noisy pixel, based on its context. Our formulation enables both supervised training of the network from the labeled training dataset and adaptive fine-tuning of the network parameters using the giv…
The Chinese University of Hong Kong（香港中文大学）；Tianjin University（天津大学）
Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorithm to recover the clean image from noisy one with the unknown noise model. To model the empirical noise of an image, our method introduces the mixture of Gaussian distribution, which is flexible enough to approximate different continuous distributions. The problem of blind image d…
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）
The Euclidean Median (EM) of a set of points $Ω$ in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in $Ω$. While there exits no closed-form expression for the EM, it can nevertheless be computed using iterative methods such as the Wieszfeld algorithm. The EM has classically been used as a robust estimator of centrality for multivariate data. It was recently demonstrated that the EM can be used to perform robust patch-based denoising of images by generalizing the popular Non-Local Means algorithm. In this paper, we propose a novel a…
Heterogeneous window transformer for image denoising
Northwestern Polytechnical University（西北工业大学）；National Tsing Hua University（国立清华大学）；Xidian University（西安电子科技大学）；Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳市人工智能与机器人研究院）
Guangdong University of Technology（广东工业大学）；South China University of Technology（华南理工大学）；Sun Yat-sen University（中山大学）；Nanjing University of Science and Technology（南京理工大学）
Real-world image denoising is a practical image restoration problem that aims to obtain clean images from in-the-wild noisy inputs. Recently, the Vision Transformer (ViT) has exhibited a strong ability to capture long-range dependencies, and many researchers have attempted to apply the ViT to image denoising tasks. However, a real-world image is an isolated frame that makes the ViT build long-range dependencies based on the internal patches, which divides images into patches, disarranges noise patterns and damages gradient continuity. In this article, we propose to resolve this issue by using …
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Philips Research North America（飞利浦北美研究院）；Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）
Increasing use of CT in modern medical practice has raised concerns over associated radiation dose. Reduction of radiation dose associated with CT can increase noise and artifacts, which can adversely affect diagnostic confidence. Denoising of low-dose CT images on the other hand can help improve diagnostic confidence, which however is a challenging problem due to its ill-posed nature, since one noisy image patch may correspond to many different output patches. In the past decade, machine learning based approaches have made quite impressive progress in this direction. However, most of those me…
Recently, it was demonstrated in [CS2012,CS2013] that the robustness of the classical Non-Local Means (NLM) algorithm [BCM2005] can be improved by incorporating $\ell^p (0 < p \leq 2)$ regression into the NLM framework. This general optimization framework, called Non-Local Patch Regression (NLPR), contains NLM as a special case. Denoising results on synthetic and natural images show that NLPR consistently performs better than NLM beyond a moderate noise level, and significantly so when $p$ is close to zero. An iteratively reweighted least-squares (IRLS) algorithm was proposed for solving the r…
Color image denoising is frequently encountered in various image processing and computer vision tasks. One traditional strategy is to convert the RGB image to a less correlated color space and denoise each channel of the new space separately. However, such a strategy can not fully exploit the correlated information between channels and is inadequate to obtain satisfactory results. To address this issue, this paper proposes a new multi-channel optimization model for color image denoising under the nuclear norm minus Frobenius norm minimization framework. Specifically, based on the block-matchin…
Closed-Form Nonlocal Shrinkage for Multiplicative Image Denoising and SAR Despeckling
School of Electronic Engineering, Xidian University（西安电子科技大学电子工程学院）；Kunshan Innovation Institute of Xidian University（西安电子科技大学昆山创新研究院）；University of Montenegro（黑山大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Macquarie University（麦考瑞大学）
There are two main streams in up-to-date image denoising algorithms: non-local self similarity (NSS) prior based methods and convolutional neural network (CNN) based methods. The NSS based methods are favorable on images with regular and repetitive patterns while the CNN based methods perform better on irregular structures. In this paper, we propose a block-matching convolutional neural network (BMCNN) method that combines NSS prior and CNN. Initially, similar local patches in the input image are integrated into a 3D block. In order to prevent the noise from messing up the block matching, we f…
Duke University（杜克大学）；Télécom ParisTech, Université Paris-Saclay（巴黎高科电信学院，巴黎-萨克雷大学）；Université Paris Descartes（巴黎笛卡尔大学）；Universidad de la República（共和国大学）
Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an approach is particularly unstable for most inverse problems beyond denoising. In this work, we propose the use of a hyperprior to model image patches, in order to stabilize the estimation procedure. There are two main advantages to the proposed restoration scheme: Firstly it is adapted to diagonal degradation matrices, and in particular to missing data problems…
Technion – Israel Institute of Technology（以色列理工学院）
We propose an image processing scheme based on reordering of its patches. For a given corrupted image, we extract all patches with overlaps, refer to these as coordinates in high-dimensional space, and order them such that they are chained in the "shortest possible path", essentially solving the traveling salesman problem. The obtained ordering applied to the corrupted image, implies a permutation of the image pixels to what should be a regular signal. This enables us to obtain good recovery of the clean image by applying relatively simple 1D smoothing operations (such as filtering or interpol…
Technion Institute of Technology（以色列理工学院）；Google Research（谷歌研究院）
Image denoising is a well studied problem with an extensive activity that has spread over several decades. Despite the many available denoising algorithms, the quest for simple, powerful and fast denoisers is still an active and vibrant topic of research. Leading classical denoising methods are typically designed to exploit the inner structure in images by modeling local overlapping patches, while operating in an unsupervised fashion. In contrast, recent newcomers to this arena are supervised and universal neural-network-based methods that bypass this modeling altogether, targeting the inferen…
The Hong Kong Polytechnic University（香港理工大学）；Xidian University（西安电子科技大学）
Most of the existing denoising algorithms are developed for grayscale images, while it is not a trivial work to extend them for color image denoising because the noise statistics in R, G, B channels can be very different for real noisy images. In this paper, we propose a multi-channel (MC) optimization model for real color image denoising under the weighted nuclear norm minimization (WNNM) framework. We concatenate the RGB patches to make use of the channel redundancy, and introduce a weight matrix to balance the data fidelity of the three channels in consideration of their different noise sta…
