Unsupervised Learning with Stein's Unbiased Risk Estimator - implementation -

Rich just sent me the following:

Hi Igor,
We have a new paper that uses Stein’s Unbiased Risk Estimator (SURE) to train neural networks directly from noisy measurements without any ground truth data. We demonstrate training neural networks with SURE in order to solve the denoising and compressive sensing problems.
Paper: https://arxiv.org/abs/1805.10531
Software: https://github.com/ricedsp/D-AMP_Toolbox
We would be very grateful if you shared it on Nuit Blanche!
richb
Richard G. Baraniuk
Victor E. Cameron Professor of Electrical and Computer Engineering
Founder and Director, OpenStax
Rice University

Sure Rich !

Unsupervised Learning with Stein's Unbiased Risk Estimator by Christopher A. Metzler, Ali Mousavi, Reinhard Heckel, Richard G. Baraniuk

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 {\em without any ground truth data.}
Specifically, our goal is to reconstruct an image x from a {\em 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.

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