Recently, Stein's unbiased risk estimator (SURE) has been applied to unsupervised training of deep neural network Gaussian denoisers that outperformed classical non-deep learning based denoisers and yielded comparable performance to those trained with ground truth. While SURE requires only one noise realization per image for training, it does not take advantage of having multiple noise realizations per image when they are available (e.g., two uncorrelated noise realizations per image for Noise2Noise). Here, we propose an extended SURE (eSURE) to train deep denoisers with correlated pairs of noise realizations per image and applied it to the case with two uncorrelated realizations per image to achieve better performance than SURE based method and comparable results to Noise2Noise. Then, we further investigated the case with imperfect ground truth (i.e., mild noise in ground truth) that may be obtained considering painstaking, time-consuming, and even expensive processes of collecting ground truth images with multiple noisy images. For the case of generating noisy training data by adding synthetic noise to imperfect ground truth to yield correlated pairs of images, our proposed eSURE based training method outperformed conventional SURE based method as well as Noise2Noise.
Deep learning image reconstruction algorithms often suffer from model mismatches when the acquisition scheme differs significantly from the forward model used during training. We introduce a Generalized Stein's Unbiased Risk Estimate (GSURE) loss metric to adapt the network to the measured k-space data and minimize model misfit impact. Unlike current methods that rely on the mean square error in kspace, the proposed metric accounts for noise in the measurements. This makes the approach less vulnerable to overfitting, thus offering improved reconstruction quality compared to schemes that rely o…
Information Technology University（信息技术大学）；University of Toronto（多伦多大学）
Among the plethora of techniques devised to curb the prevalence of noise in medical images, deep learning based approaches have shown the most promise. However, one critical limitation of these deep learning based denoisers is the requirement of high-quality noiseless ground truth images that are difficult to obtain in many medical imaging applications such as X-rays. To circumvent this issue, we leverage recently proposed approach of [7] that incorporates Stein's Unbiased Risk Estimator (SURE) to train a deep convolutional neural network without requiring denoised ground truth X-ray data. Our…
Deep learning algorithms that rely on extensive training data are revolutionizing image recovery from ill-posed measurements. Training data is scarce in many imaging applications, including ultra-high-resolution imaging. The deep image prior (DIP) algorithm was introduced for single-shot image recovery, completely eliminating the need for training data. A challenge with this scheme is the need for early stopping to minimize the overfitting of the CNN parameters to the noise in the measurements. We introduce a generalized Stein's unbiased risk estimate (GSURE) loss metric to minimize the overfi…
We propose a new image denoising algorithm, dubbed as Fully Convolutional Adaptive Image DEnoiser (FC-AIDE), that can learn from an offline supervised training set with a fully convolutional neural network as well as adaptively fine-tune the supervised model for each given noisy image. We significantly extend the framework of the recently proposed Neural AIDE, which formulates the denoiser to be context-based pixelwise mappings and utilizes the unbiased estimator of MSE for such denoisers. The two main contributions we make are; 1) implementing a novel fully convolutional architecture that boo…
Convolutional neural networks (CNN) have emerged as a powerful tool for solving computational imaging reconstruction problems. However, CNNs are generally difficult-to-understand black-boxes. Accordingly, it is challenging to know when they will work and, more importantly, when they will fail. This limitation is a major barrier to their use in safety-critical applications like medical imaging: Is that blob in the reconstruction an artifact or a tumor? In this work we use Stein's unbiased risk estimate (SURE) to develop per-pixel confidence intervals, in the form of heatmaps, for compressive se…
Ulsan National Institute of Science and Technology (UNIST)（蔚山国立科学技术院（UNIST））
Recently developed deep-learning-based denoisers often outperform state-of-the-art conventional denoisers such as the BM3D. They are typically trained to minimize the mean squared error (MSE) between the output image of a deep neural network (DNN) and a ground truth image. Thus, it is important for deep-learning-based denoisers to use high quality noiseless ground truth data for high performance. However, it is often challenging or even infeasible to obtain noiseless images in some applications. Here, we propose a method based on Stein's unbiased risk estimator (SURE) for training DNN denoiser…
Learning from unlabeled and noisy data is one of the grand challenges of machine learning. As such, it has seen a flurry of research with new ideas proposed continuously. In this work, we revisit a classical idea: Stein's Unbiased Risk Estimator (SURE). We show that, in the context of image recovery, SURE and its generalizations can be used to train convolutional neural networks (CNNs) for a range of image denoising and recovery problems without any ground truth data. Specifically, our goal is to reconstruct an image $x$ from a noisy linear transformation (measurement) of the image. We conside…
Ulsan National Institute of Science and Technology（蔚山科学技术院）
Compressive sensing is a method to recover the original image from undersampled measurements. In order to overcome the ill-posedness of this inverse problem, image priors are used such as sparsity in the wavelet domain, minimum total-variation, or self-similarity. Recently, deep learning based compressive image recovery methods have been proposed and have yielded state-of-the-art performances. They used deep learning based data-driven approaches instead of hand-crafted image priors to solve the ill-posed inverse problem with undersampled data. Ironically, training deep neural networks for them…
We address the problem of image denoising in additive white noise without placing restrictive assumptions on its statistical distribution. In the recent literature, specific noise distributions have been considered and correspondingly, optimal denoising techniques have been developed. One of the successful approaches for denoising relies on the notion of unbiased risk estimation, which enables one to obtain a useful substitute for the mean-square error. For the case of additive white Gaussian noise contamination, the risk estimation procedure relies on Stein's lemma. Sophisticated wavelet-base…
Deep learning denoiser assisted roughness measurements extraction from thin resists with low Signal-to-Noise Ratio(SNR) SEM images: analysis with SMILE
imec（比利时微电子研究中心）；University of Bologna（博洛尼亚大学）；Paul Scherrer Institut（保罗·谢尔研究所）
KAIST（韩国科学技术院）；Samsung Advanced Institute of Technology（三星先进技术研究院）
Convolutional neural networks (CNN) have been extensively used for inverse problems. However, their prediction error for unseen test data is difficult to estimate a priori since the neural networks are trained using only selected data and their architecture are largely considered a blackbox. This poses a fundamental challenge to neural networks for unsupervised learning or improvement beyond the label. In this paper, we show that the recent unsupervised learning methods such as Noise2Noise, Stein's unbiased risk estimator (SURE)-based denoiser, and Noise2Void are closely related to each other …
Poisson2Gaussian: Noise Gaussianization to Enhance Image Denoising
College of AI, Tsinghua University（清华大学人工智能学院）；Department of Automation, Tsinghua University（清华大学自动化系）；School of Electronic and Information Engineering, Beihang University（北京航空航天大学电子信息工程学院）
Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data to train the deep networks is often unavailable in several applications, restricting the applicability of the above methods. We introduce a novel metric termed the ENsemble Stein's Unbiased Risk Estimate (ENSURE) framework, which can be used to train deep image reconstruction algorithms without fully sampled and noise-free images. The proposed framework is t…
In this letter, we investigate the shrinkage problem for the non-local means (NLM) image denoising. In particular, we derive the closed-form of the optimal blockwise shrinkage for NLM that minimizes the Stein's unbiased risk estimator (SURE). We also propose a constant complexity algorithm allowing fast blockwise shrinkage. Simulation results show that the proposed blockwise shrinkage method improves NLM performance in attaining higher peak signal noise ratio (PSNR) and structural similarity index (SSIM), and makes NLM more robust against parameter changes. Similar ideas can be applicable to o…
Reliable MRI is crucial for accurate interpretation in therapeutic and diagnostic tasks. However, undersampling during MRI acquisition as well as the overparameterized and non-transparent nature of deep learning (DL) leaves substantial uncertainty about the accuracy of DL reconstruction. With this in mind, this study aims to quantify the uncertainty in image recovery with DL models. To this end, we first leverage variational autoencoders (VAEs) to develop a probabilistic reconstruction scheme that maps out (low-quality) short scans with aliasing artifacts to the diagnostic-quality ones. The VA…
Deep networks provide state-of-the-art performance in multiple imaging inverse problems ranging from medical imaging to computational photography. However, most existing networks are trained with clean signals which are often hard or impossible to obtain. Equivariant imaging (EI) is a recent self-supervised learning framework that exploits the group invariance present in signal distributions to learn a reconstruction function from partial measurement data alone. While EI results are impressive, its performance degrades with increasing noise. In this paper, we propose a Robust Equivariant Imagi…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Kim Jaechul Graduate School of AI（金在哲人工智能研究生院）
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 mod…
AstroSURE: Learning to Remove Noise from Astronomical Images Without Ground Truth Data
National Research Council Herzberg Astronomy an Astrophysics Research Centre, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada（国家研究委员会赫兹伯格天文学与天体物理学研究中心，5071号西萨安奇路，维多利亚，BC V9E 2E7，加拿大）；Department of Computer Science, , University of British Columbia, Vancouver, BC, V6T 1Z4, Canada（计算机科学系，不列颠哥伦比亚大学，温哥华，BC，V6T 1Z4，加拿大）
Self-supervised Conformal Prediction for Uncertainty Quantification in Imaging Problems
Technical University of Denmark（丹麦技术大学）；Heriot-Watt University（赫瑞瓦特大学）；Maxwell Institute for Mathematical Sciences（麦克斯韦数学研究所）；Université de Paris Cité（巴黎西岱大学）
Multispectral image denoising with optimized vector non-local mean filter
CSE Department, College of Engineering, Qatar University, P.O. Box 2713, Doha-Qatar（卡塔尔大学工程学院计算机科学与工程系）；LE2i Lab, UMR CNRS 6306, University of Burgundy, BP 47870, 21078, Dijon-France（布尔格斯大学）；Department of Computer Science, University of Biskra, 07000, Algeria（阿尔及利亚比斯克拉大学计算机科学系）
Robust multi-coil MRI reconstruction via self-supervised denoising
Stanford University（斯坦福大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Intel Corporation（英特尔公司）；MD Anderson Cancer Center（MD安德森癌症中心）；Dell Medical School Department of Diagnostic Medicine（德克萨斯大学戴维斯医学中心诊断医学系）；Oden Institute for Computational Engineering and Sciences（奥登计算工程与科学研究院）
