Leveraging Deep Stein's Unbiased Risk Estimator for Unsupervised X-ray Denoising

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 experimental results demonstrate the effectiveness of SURE based approach for denoising X-ray images.Comment: Machine Learning for Health (ML4H) Workshop at NeurIPS 2018 arXiv:1811.0721

Unsupervised Learning with Stein's Unbiased Risk Estimator

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 consider two scenarios: one where no additional data is available and one where we have measurements of other images that are drawn from the same noisy distribution as $x$, but have no access to the clean images. Such is the case, for instance, in the context of medical imaging, microscopy, and astronomy, where noise-less ground truth data is rarely available. We show that in this situation, SURE can be used to estimate the mean-squared-error loss associated with an estimate of $x$. Using this estimate of the loss, we train networks to perform denoising and compressed sensing recovery. In addition, we also use the SURE framework to partially explain and improve upon an intriguing results presented by Ulyanov et al. in "Deep Image Prior": that a network initialized with random weights and fit to a single noisy image can effectively denoise that image. Public implementations of the networks and methods described in this paper can be found at https://github.com/ricedsp/D-AMP_Toolbox

WhiteNNer-Blind Image Denoising via Noise Whiteness Priors

The accuracy of medical imaging-based diagnostics is directly impacted by the quality of the collected images. A passive approach to improve image quality is one that lags behind improvements in imaging hardware, awaiting better sensor technology of acquisition devices. An alternative, active strategy is to utilize prior knowledge of the imaging system to directly post-process and improve the acquired images. Traditionally, priors about the image properties are taken into account to restrict the solution space. However, few techniques exploit the prior about the noise properties. In this paper, we propose a neural network-based model for disentangling the signal and noise components of an input noisy image, without the need for any ground truth training data. We design a unified loss function that encodes priors about signal as well as noise estimate in the form of regularization terms. Specifically, by using total variation and piecewise constancy priors along with noise whiteness priors such as auto-correlation and stationary losses, our network learns to decouple an input noisy image into the underlying signal and noise components. We compare our proposed method to Noise2Noise and Noise2Self, as well as non-local mean and BM3D, on three public confocal laser endomicroscopy datasets. Experimental results demonstrate the superiority of our network compared to state-of-the-art in terms of PSNR and SSIM.Comment: 9 page

Ground Truth Free Denoising by Optimal Transport

We present a learned unsupervised denoising method for arbitrary types of data, which we explore on images and one-dimensional signals. The training is solely based on samples of noisy data and examples of noise, which -- critically -- do not need to come in pairs. We only need the assumption that the noise is independent and additive (although we describe how this can be extended). The method rests on a Wasserstein Generative Adversarial Network setting, which utilizes two critics and one generator

Boosting CNN beyond Label in Inverse Problems

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 in their formulation of an unbiased estimator of the prediction error, but each of them are associated with its own limitations. Based on these observations, we provide a novel boosting estimator for the prediction error. In particular, by employing combinatorial convolutional frame representation of encoder-decoder CNN and synergistically combining it with the batch normalization, we provide a close form formulation for the unbiased estimator of the prediction error that can be minimized for neural network training beyond the label. Experimental results show that the resulting algorithm, what we call Noise2Boosting, provides consistent improvement in various inverse problems under both supervised and unsupervised learning setting

Self-Supervised Poisson-Gaussian Denoising

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 hyperparameters from the loss function, which is important in a self-supervised regime where no ground truth data is available to guide hyperparameter tuning. We show how our denoiser can be adapted to the test data to improve performance. Our evaluations on microscope image denoising benchmarks validate our approach.Comment: to appear in IEEE WACV 202

Degrees of Freedom Analysis of Unrolled Neural Networks

Unrolled neural networks emerged recently as an effective model for learning inverse maps appearing in image restoration tasks. However, their generalization risk (i.e., test mean-squared-error) and its link to network design and train sample size remains mysterious. Leveraging the Stein's Unbiased Risk Estimator (SURE), this paper analyzes the generalization risk with its bias and variance components for recurrent unrolled networks. We particularly investigate the degrees-of-freedom (DOF) component of SURE, trace of the end-to-end network Jacobian, to quantify the prediction variance. We prove that DOF is well-approximated by the weighted \textit{path sparsity} of the network under incoherence conditions on the trained weights. Empirically, we examine the SURE components as a function of train sample size for both recurrent and non-recurrent (with many more parameters) unrolled networks. Our key observations indicate that: 1) DOF increases with train sample size and converges to the generalization risk for both recurrent and non-recurrent schemes; 2) recurrent network converges significantly faster (with less train samples) compared with non-recurrent scheme, hence recurrence serves as a regularization for low sample size regimes

Unsupervised MRI Reconstruction with Generative Adversarial Networks

Deep learning-based image reconstruction methods have achieved promising results across multiple MRI applications. However, most approaches require large-scale fully-sampled ground truth data for supervised training. Acquiring fully-sampled data is often either difficult or impossible, particularly for dynamic contrast enhancement (DCE), 3D cardiac cine, and 4D flow. We present a deep learning framework for MRI reconstruction without any fully-sampled data using generative adversarial networks. We test the proposed method in two scenarios: retrospectively undersampled fast spin echo knee exams and prospectively undersampled abdominal DCE. The method recovers more anatomical structure compared to conventional methods

Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images

In the last few years, image denoising has benefited a lot from the fast development of neural networks. However, the requirement of large amounts of noisy-clean image pairs for supervision limits the wide use of these models. Although there have been a few attempts in training an image denoising model with only single noisy images, existing self-supervised denoising approaches suffer from inefficient network training, loss of useful information, or dependence on noise modeling. In this paper, we present a very simple yet effective method named Neighbor2Neighbor to train an effective image denoising model with only noisy images. Firstly, a random neighbor sub-sampler is proposed for the generation of training image pairs. In detail, input and target used to train a network are images sub-sampled from the same noisy image, satisfying the requirement that paired pixels of paired images are neighbors and have very similar appearance with each other. Secondly, a denoising network is trained on sub-sampled training pairs generated in the first stage, with a proposed regularizer as additional loss for better performance. The proposed Neighbor2Neighbor framework is able to enjoy the progress of state-of-the-art supervised denoising networks in network architecture design. Moreover, it avoids heavy dependence on the assumption of the noise distribution. We explain our approach from a theoretical perspective and further validate it through extensive experiments, including synthetic experiments with different noise distributions in sRGB space and real-world experiments on a denoising benchmark dataset in raw-RGB space.Comment: CVPR202

Unpaired Learning of Deep Image Denoising

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-spot network (D-BSN) to learn denoising solely from real noisy images. Due to the spatial independence of noise, we adopt a network by stacking 1x1 convolution layers to estimate the noise level map for each image. Both the D-BSN and image-specific noise model (CNN\_est) can be jointly trained via maximizing the constrained log-likelihood. Given the output of D-BSN and estimated noise level map, improved denoising performance can be further obtained based on the Bayes' rule. As for knowledge distillation, we first apply the learned noise models to clean images to synthesize a paired set of training images, and use the real noisy images and the corresponding denoising results in the first stage to form another paired set. Then, the ultimate denoising model can be distilled by training an existing denoising network using these two paired sets. Experiments show that our unpaired learning method performs favorably on both synthetic noisy images and real-world noisy photographs in terms of quantitative and qualitative evaluation.Comment: 20 pages, 6 figures, ECC