Unsupervised Learning with Stein's Unbiased Risk Estimator

Abstract

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.

References in corpus (11)

• Adam: A Method for Stochastic Optimization
• Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising
• Message Passing Algorithms for Compressed Sensing
• Classification with Noisy Labels by Importance Reweighting
• Deep Image Prior
• Training Convolutional Networks with Noisy Labels
• Generalized SURE for Exponential Families: Applications to Regularization
• Learned D-AMP: Principled Neural Network based Compressive Image Recovery
• Near optimal compressed sensing without priors: Parametric SURE Approximate Message Passing
• Parameterless Optimal Approximate Message Passing
• Risk Estimation Without Using Stein's Lemma -- Application to Image Denoising

Cited by in corpus (14)

• DeepRED: Deep Image Prior Powered by RED
• High-Quality Self-Supervised Deep Image Denoising
• CDLNet: Noise-Adaptive Convolutional Dictionary Learning Network for Blind Denoising and Demosaicing
• Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting
• ENSURE: A General Approach for Unsupervised Training of Deep Image Reconstruction Algorithms
• Adaptive Denoising via GainTuning
• Deep Learning Techniques for Inverse Problems in Imaging
• Degrees of Freedom Analysis of Unrolled Neural Networks
• Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements
• Credit scoring using neural networks and SURE posterior probability calibration
• Rethinking Deep Image Prior for Denoising
• Model Adaptation for Image Reconstruction using Generalized Stein's Unbiased Risk Estimator
• SUREMap: Predicting Uncertainty in CNN-based Image Reconstruction Using Stein's Unbiased Risk Estimate
• Deep Image Prior using Stein's Unbiased Risk Estimator: SURE-DIP