Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of log likelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern deep learning era, leading to a distribution independent self-supervised image denoising formula without clean reference images. Specifically, by combining with the recent Noise2Score self-supervised image denoising approach and the saddle point approximation of Tweedie distribution, we can provide a general closed-form denoising formula that can be used fo…
In recent years, the supervised learning strategy for real noisy image denoising has been emerging and has achieved promising results. In contrast, realistic noise removal for raw noisy videos is rarely studied due to the lack of noisy-clean pairs for dynamic scenes. Clean video frames for dynamic scenes cannot be captured with a long-exposure shutter or averaging multi-shots as was done for static images. In this paper, we solve this problem by creating motions for controllable objects, such as toys, and capturing each static moment for multiple times to generate clean video frames. In this w…
Image restoration has been an extensively researched topic in numerous fields. With the advent of deep learning, a lot of the current algorithms were replaced by algorithms that are more flexible and robust. Deep networks have demonstrated impressive performance in a variety of tasks like blind denoising, image enhancement, deblurring, super-resolution, inpainting, among others. Most of these learning-based algorithms use a large amount of clean data during the training process. However, in certain applications in medical image processing, one may not have access to a large amount of clean dat…
With recent deep learning based approaches showing promising results in removing noise from images, the best denoising performance has been reported in a supervised learning setup that requires a large set of paired noisy images and ground truth for training. The strong data requirement can be mitigated by unsupervised learning techniques, however, accurate modelling of images or noise variance is still crucial for high-quality solutions. The learning problem is ill-posed for unknown noise distributions. This paper investigates the tasks of image denoising and noise variance estimation in a si…
Xiamen University（厦门大学）；University of Science and Technology of China（中国科学技术大学）；Columbia University（哥伦比亚大学）
We propose a new framework called Noise2Blur (N2B) for training robust image denoising models without pre-collected paired noisy/clean images. The training of the model requires only some (or even one) noisy images, some random unpaired clean images, and noise-free but blurred labels obtained by predefined filtering of the noisy images. The N2B model consists of two parts: a denoising network and a noise extraction network. First, the noise extraction network learns to output a noise map using the noise information from the denoising network under the guidence of the blurred labels. Then, the …
Sungkyunkwan University（成均馆大学）；Yonsei University（延世大学）；Seoul National University（首尔国立大学）
We tackle a challenging blind image denoising problem, in which only single distinct noisy images are available for training a denoiser, and no information about noise is known, except for it being zero-mean, additive, and independent of the clean image. In such a setting, which often occurs in practice, it is not possible to train a denoiser with the standard discriminative training or with the recently developed Noise2Noise (N2N) training; the former requires the underlying clean image for the given noisy image, and the latter requires two independently realized noisy image pair for a clean …
Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie
University of Oxford（牛津大学）；Institut Universitaire de France（法国大学研究院）；Heriot-Watt University（赫瑞瓦特大学）；Maxwell Institute for Mathematical Sciences（麦克斯韦数学科学研究所）
本文针对贝叶斯成像中 Plug & Play (PnP) 先验方法缺乏收敛证明的问题，提出了两种可证明收敛的算法 PnP-ULA 和 PnP-SGD，并建立了详细的收敛保证，适用于图像去模糊、修复和去噪等任务。
Image denoising is an essential tool in computational photography. Standard denoising techniques, which use deep neural networks at their core, require pairs of clean and noisy images for its training. If we do not possess the clean samples, we can use blind-spot neural network architectures, which estimate the pixel value based on the neighbouring pixels only. These networks thus allow training on noisy images directly, as they by-design avoid trivial solutions. Nowadays, the blind-spot is mostly achieved using shifted convolutions or serialization. We propose a novel fully convolutional netw…
Recent studies on learning-based image denoising have achieved promising performance on various noise reduction tasks. Most of these deep denoisers are trained either under the supervision of clean references, or unsupervised on synthetic noise. The assumption with the synthetic noise leads to poor generalization when facing real photographs. To address this issue, we propose a novel deep image-denoising method by regarding the noise reduction task as a special case of the noise transference task. Learning noise transference enables the network to acquire the denoising ability by observing the…
Nankai University（南开大学）；Xi’an Jiaotong University（西安交通大学）；Inception Institute of Artificial Intelligence (IIAI)（人工智能 inception 研究院）；Mohamed bin Zayed University of Artificial Intelligence (MBZUAI)（穆罕默德·本·扎耶德人工智能大学）；Chongqing University（重庆大学）
Supervised deep networks have achieved promisingperformance on image denoising, by learning image priors andnoise statistics on plenty pairs of noisy and clean images. Unsupervised denoising networks are trained with only noisy images. However, for an unseen corrupted image, both supervised andunsupervised networks ignore either its particular image prior, the noise statistics, or both. That is, the networks learned from external images inherently suffer from a domain gap problem: the image priors and noise statistics are very different between the training and test images. This problem become…
School of Mathematics, Sichuan University（四川大学数学学院）
Deep learning based methods have achieved the state-of-the-art performance in image denoising. In this paper, a deep learning based denoising method is proposed and a module called fusion block is introduced in the convolutional neural network. For this so-called Noise Fusion Convolutional Neural Network (NFCNN), there are two branches in its multi-stage architecture. One branch aims to predict the latent clean image, while the other one predicts the residual image. A fusion block is contained between every two stages by taking the predicted clean image and the predicted residual image as a pa…
MPI Informatik（马克斯·普朗克信息学研究所）；University College London（伦敦大学学院）
We seek to reconstruct sharp and noise-free high-dynamic range (HDR) video from a dual-exposure sensor that records different low-dynamic range (LDR) information in different pixel columns: Odd columns provide low-exposure, sharp, but noisy information; even columns complement this with less noisy, high-exposure, but motion-blurred data. Previous LDR work learns to deblur and denoise (DISTORTED->CLEAN) supervised by pairs of CLEAN and DISTORTED images. Regrettably, capturing DISTORTED sensor readings is time-consuming; as well, there is a lack of CLEAN HDR videos. We suggest a method to overco…
Research School of Computer Science, the Australian National University（澳大利亚国立大学计算机科学研究院）；Data61-CSIRO（澳大利亚联邦科学与工业研究组织数据61中心）；OPPO US Research（OPPO美国研究院）
The prevalent convolutional neural network (CNN) based image denoising methods extract features of images to restore the clean ground truth, achieving high denoising accuracy. However, these methods may ignore the underlying distribution of clean images, inducing distortions or artifacts in denoising results. This paper proposes a new perspective to treat image denoising as a distribution learning and disentangling task. Since the noisy image distribution can be viewed as a joint distribution of clean images and noise, the denoised images can be obtained via manipulating the latent representat…
Australian National University（澳大利亚国立大学）；Data61-CSIRO；OPPO US Research（OPPO美国研究院）；GSAI POSTECH（浦项科技大学GSAI）
Invertible networks have various benefits for image denoising since they are lightweight, information-lossless, and memory-saving during back-propagation. However, applying invertible models to remove noise is challenging because the input is noisy, and the reversed output is clean, following two different distributions. We propose an invertible denoising network, InvDN, to address this challenge. InvDN transforms the noisy input into a low-resolution clean image and a latent representation containing noise. To discard noise and restore the clean image, InvDN replaces the noisy latent represen…
Worcester Polytechnic Institute（伍斯特理工学院）；Colorado State University（科罗拉多州立大学）
In this paper, we demonstrate how deep autoencoders can be generalized to the case of inpainting and denoising, even when no clean training data is available. In particular, we show how neural networks can be trained to perform all of these tasks simultaneously. While, deep autoencoders implemented by way of neural networks have demonstrated potential for denoising and anomaly detection, standard autoencoders have the drawback that they require access to clean data for training. However, recent work in Robust Deep Autoencoders (RDAEs) shows how autoencoders can be trained to eliminate outliers…
Learning-based image denoising methods have been bounded to situations where well-aligned noisy and clean images are given, or samples are synthesized from predetermined noise models, e.g., Gaussian. While recent generative noise modeling methods aim to simulate the unknown distribution of real-world noise, several limitations still exist. In a practical scenario, a noise generator should learn to simulate the general and complex noise distribution without using paired noisy and clean images. However, since existing methods are constructed on the unrealistic assumption of real-world noise, the…
Northwestern Polytechnical University（西北工业大学）；National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology（空天地海一体化大数据应用技术国家工程实验室）；Harbin Institute of Technology（哈尔滨工业大学）；Peng Cheng Laboratory（鹏城实验室）；Central South University（中南大学）；National Tsing Hua University（国立清华大学）
The field of image denoising is currently dominated by discriminative deep learning methods that are trained on pairs of noisy input and clean target images. Recently it has been shown that such methods can also be trained without clean targets. Instead, independent pairs of noisy images can be used, in an approach known as Noise2Noise (N2N). Here, we introduce Noise2Void (N2V), a training scheme that takes this idea one step further. It does not require noisy image pairs, nor clean target images. Consequently, N2V allows us to train directly on the body of data to be denoised and can therefor…
Harbin Institute of Technology（哈尔滨工业大学）；University of Tianjin（天津大学）；Peng Cheng Lab（鹏城实验室）
We investigate the task of learning blind image denoising networks from an unpaired set of clean and noisy images. Such problem setting generally is practical and valuable considering that it is feasible to collect unpaired noisy and clean images in most real-world applications. And we further assume that the noise can be signal dependent but is spatially uncorrelated. In order to facilitate unpaired learning of denoising network, this paper presents a two-stage scheme by incorporating self-supervised learning and knowledge distillation. For self-supervised learning, we suggest a dilated blind…
In recent years, deep neural network-based restoration methods have achieved state-of-the-art results in various image deblurring tasks. However, one major drawback of deep learning-based deblurring networks is that large amounts of blurry-clean image pairs are required for training to achieve good performance. Moreover, deep networks often fail to perform well when the blurry images and the blur kernels during testing are very different from the ones used during training. This happens mainly because of the overfitting of the network parameters on the training data. In this work, we present a …
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…
Xiamen University（厦门大学）；The University of Hong Kong（香港大学）；Deepwise（深睿医疗）；Columbia University（哥伦比亚大学）
The effectiveness of existing denoising algorithms typically relies on accurate pre-defined noise statistics or plenty of paired data, which limits their practicality. In this work, we focus on denoising in the more common case where noise statistics and paired data are unavailable. Considering that denoising CNNs require supervision, we develop a new \textbf{adaptive noise imitation (ADANI)} algorithm that can synthesize noisy data from naturally noisy images. To produce realistic noise, a noise generator takes unpaired noisy/clean images as input, where the noisy image is a guide for noise g…
Supervised learning-based methods yield robust denoising results, yet they are inherently limited by the need for large-scale clean/noisy paired datasets. The use of unsupervised denoisers, on the other hand, necessitates a more detailed understanding of the underlying image statistics. In particular, it is well known that apparent differences between clean and noisy images are most prominent on high-frequency bands, justifying the use of low-pass filters as part of conventional image preprocessing steps. However, most learning-based denoising methods utilize only one-sided information from th…
Image denoising is still a challenging issue in many computer vision sub-domains. Recent studies show that significant improvements are made possible in a supervised setting. However, few challenges, such as spatial fidelity and cartoon-like smoothing remain unresolved or decisively overlooked. Our study proposes a simple yet efficient architecture for the denoising problem that addresses the aforementioned issues. The proposed architecture revisits the concept of modular concatenation instead of long and deeper cascaded connections, to recover a cleaner approximation of the given image. We fi…
When it comes to image compression in digital cameras, denoising is traditionally performed prior to compression. However, there are applications where image noise may be necessary to demonstrate the trustworthiness of the image, such as court evidence and image forensics. This means that noise itself needs to be coded, in addition to the clean image itself. In this paper, we present a learning-based image compression framework where image denoising and compression are performed jointly. The latent space of the image codec is organized in a scalable manner such that the clean image can be deco…
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…
Recent denoising algorithms based on the "blind-spot" strategy show impressive blind image denoising performances, without utilizing any external dataset. While the methods excel in recovering highly contaminated images, we observe that such algorithms are often less effective under a low-noise or real noise regime. To address this gap, we propose an alternative denoising strategy that leverages the architectural inductive bias of implicit neural representations (INRs), based on our two findings: (1) INR tends to fit the low-frequency clean image signal faster than the high-frequency noise, an…
Hyperspectral image (HSI) denoising aims to restore clean HSI from the noise-contaminated one. Noise contamination can often be caused during data acquisition and conversion. In this paper, we propose a novel spatial-spectral total variation (SSTV) regularized nonconvex local low-rank (LR) tensor approximation method to remove mixed noise in HSIs. From one aspect, the clean HSI data have its underlying local LR tensor property, even though the real HSI data may not be globally low-rank due to out-liers and non-Gaussian noise. According to this fact, we propose a novel tensor $L_γ$-norm to form…
Convolutional neural networks (CNNs) have shown outstanding performance on image denoising with the help of large-scale datasets. Earlier methods naively trained a single CNN with many pairs of clean-noisy images. However, the conditional distribution of the clean image given a noisy one is too complicated and diverse, so that a single CNN cannot well learn such distributions. Therefore, there have also been some methods that exploit additional noise level parameters or train a separate CNN for a specific noise level parameter. These methods separate the original problem into easier sub-proble…
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…
California Polytechnic State University（加州州立理工大学）；University of Georgia（佐治亚大学）；Providence College（普罗维登斯学院）；University of Colorado Colorado Springs（科罗拉多大学科罗拉多斯普林斯分校）
We extend the blindspot model for self-supervised denoising to handle Poisson-Gaussian noise and introduce an improved training scheme that avoids hyperparameters and adapts the denoiser to the test data. Self-supervised models for denoising learn to denoise from only noisy data and do not require corresponding clean images, which are difficult or impossible to acquire in some application areas of interest such as low-light microscopy. We introduce a new training strategy to handle Poisson-Gaussian noise which is the standard noise model for microscope images. Our new strategy eliminates hyper…
Southeast University（东南大学）；Jiangsu Industrial Technology Research Institute（江苏集萃工业技术研究院）
Deep learning based image denoising methods have been extensively investigated. In this paper, attention mechanism enhanced kernel prediction networks (AME-KPNs) are proposed for burst image denoising, in which, nearly cost-free attention modules are adopted to first refine the feature maps and to further make a full use of the inter-frame and intra-frame redundancies within the whole image burst. The proposed AME-KPNs output per-pixel spatially-adaptive kernels, residual maps and corresponding weight maps, in which, the predicted kernels roughly restore clean pixels at their corresponding loc…
With the advent of recent advances in unsupervised learning, efficient training of a deep network for image denoising without pairs of noisy and clean images has become feasible. However, most current unsupervised denoising methods are built on the assumption of zero-mean noise under the signal-independent condition. This assumption causes blind denoising techniques to suffer brightness shifting problems on images that are greatly corrupted by extreme noise such as salt-and-pepper noise. Moreover, most blind denoising methods require a random masking scheme for training to ensure the invarianc…
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…
The Chinese University of Hong Kong（香港中文大学）；SenseTime Research（商汤科技研究院）
The lack of large-scale noisy-clean image pairs restricts supervised denoising methods' deployment in actual applications. While existing unsupervised methods are able to learn image denoising without ground-truth clean images, they either show poor performance or work under impractical settings (e.g., paired noisy images). In this paper, we present a practical unsupervised image denoising method to achieve state-of-the-art denoising performance. Our method only requires single noisy images and a noise model, which is easily accessible in practical raw image denoising. It performs two steps it…
Variations of deep neural networks such as convolutional neural network (CNN) have been successfully applied to image denoising. The goal is to automatically learn a mapping from a noisy image to a clean image given training data consisting of pairs of noisy and clean images. Most existing CNN models for image denoising have many layers. In such cases, the models involve a large amount of parameters and are computationally expensive to train. In this paper, we develop a dilated residual CNN for Gaussian image denoising. Compared with the recently proposed residual denoiser, our method can achi…
We apply basic statistical reasoning to signal reconstruction by machine learning -- learning to map corrupted observations to clean signals -- with a simple and powerful conclusion: it is possible to learn to restore images by only looking at corrupted examples, at performance at and sometimes exceeding training using clean data, without explicit image priors or likelihood models of the corruption. In practice, we show that a single model learns photographic noise removal, denoising synthetic Monte Carlo images, and reconstruction of undersampled MRI scans -- all corrupted by different proces…
Speckle2Self: Self-Supervised Ultrasound Speckle Reduction Without Clean Data
Computer Aided Medical Procedures, Technical University of Munich, Munich, Germany（技术大学慕尼黑计算机辅助医疗程序）；Munich Center for Machine Learning (MCML), Munich, Germany（慕尼黑机器学习中心）
Lightweight Data-Free Denoising for Detail-Preserving Biomedical Image Restoration
School of Computation, Information and Technology, Technical University of Munich（计算信息学院，慕尼黑技术大学）；Helmholtz AI, Helmholtz Munich - German Research Center for Environmental Health（海德堡人工智能，海德堡-德国环境健康研究所以及研究中心）；School of Biomedical Engineering and Imaging Sciences, King’s College London（生物医学工程与成像科学学院，伦敦国王学院）
Recently, significant progress has been made on image denoising with strong supervision from large-scale datasets. However, obtaining well-aligned noisy-clean training image pairs for each specific scenario is complicated and costly in practice. Consequently, applying a conventional supervised denoising network on in-the-wild noisy inputs is not straightforward. Although several studies have challenged this problem without strong supervision, they rely on less practical assumptions and cannot be applied to practical situations directly. To address the aforementioned challenges, we propose a no…
Image super-resolution and denoising are two important tasks in image processing that can lead to improvement in image quality. Image super-resolution is the task of mapping a low resolution image to a high resolution image whereas denoising is the task of learning a clean image from a noisy input. We propose and train a single deep learning network that we term as SuRDCNN (super-resolution and denoising convolutional neural network), to perform these two tasks simultaneously . Our model nearly replicates the architecture of existing state-of-the-art deep learning models for super-resolution a…
Harbin Institute of Technology（哈尔滨工业大学）；The Hong Kong Polytechnic University（香港理工大学）；Graz University of Technology（格拉茨技术大学）；Xi’an Jiaotong University（西安交通大学）
Discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denois…
Center for Advanced Medical Computing and Analysis, Massachusetts General Hospital and Harvard Medical School（麻省总医院与哈佛医学院高级医学计算与分析中心）；Gordon Center for Medical Imaging, Massachusetts General Hospital and Harvard Medical School（麻省总医院与哈佛医学院戈登医学成像中心）
Deep neural networks have been proved efficient for medical image denoising. Current training methods require both noisy and clean images. However, clean images cannot be acquired for many practical medical applications due to naturally noisy signal, such as dynamic imaging, spectral computed tomography, arterial spin labeling magnetic resonance imaging, etc. In this paper we proposed a training method which learned denoising neural networks from noisy training samples only. Training data in the acquisition domain was split to two subsets and the network was trained to map one noisy set to the…
Deep learning approaches in image processing predominantly resort to supervised learning. A majority of methods for image denoising are no exception to this rule and hence demand pairs of noisy and corresponding clean images. Only recently has there been the emergence of methods such as Noise2Void, where a deep neural network learns to denoise solely from noisy images. However, when clean images that do not directly correspond to any of the noisy images are actually available, there is room for improvement as these clean images contain useful information that fully unsupervised methods do not …
SABILab（SABI实验室）；École Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Laboratoire de mathématiques d’Orsay（奥赛数学实验室）；Laboratoire J. A. Dieudonné（J·A·迪厄多内实验室）；Université Côte d’Azur（蔚蓝海岸大学）；Télécom SudParis（南巴黎电信学院）
We propose a novel self-supervised image blind denoising approach in which two neural networks jointly predict the clean signal and infer the noise distribution. Assuming that the noisy observations are independent conditionally to the signal, the networks can be jointly trained without clean training data. Therefore, our approach is particularly relevant for biomedical image denoising where the noise is difficult to model precisely and clean training data are usually unavailable. Our method significantly outperforms current state-of-the-art self-supervised blind denoising algorithms, on six p…
On one hand, the transmitted ultrasound beam gets attenuated as propagates through the tissue. On the other hand, the received Radio-Frequency (RF) data contains an additive Gaussian noise which is brought about by the acquisition card and the sensor noise. These two factors lead to a decreasing Signal to Noise Ratio (SNR) in the RF data with depth, effectively rendering deep regions of B-Mode images highly unreliable. There are three common approaches to mitigate this problem. First, increasing the power of transmitted beam which is limited by safety threshold. Averaging consecutive frames is…
