Convolutional Neural Networks are highly successful tools for image recovery and restoration. A major contributing factor to this success is that convolutional networks impose strong prior assumptions about natural images—so strong that they enable image recovery without any training data. A surprising observation that highlights those prior assumptions is that one can remove noise from a corrupted natural image by simply fitting (via gradient descent) a randomly initialized, over-parameterized convolutional generator to the noisy image.
In this talk, we discuss a simple un-trained convolutional network, called the deep decoder, that provably enables image denoising and regularization of inverse problems such as compressive sensing with excellent performance. We formally characterize the dynamics of fitting this convolutional network to a noisy signal and to an under-sampled signal, and show that in both cases early-stopped gradient descent provably recovers the clean signal. Finally, we discuss our own numerical results and numerical results from another group demonstrating that un-trained convolutional networks enable magnetic resonance imaging from highly under-sampled measurements.
Reinhard Heckel is a Rudolf Moessbauer assistant professor in the Department of Electrical and Computer Engineering (ECE) at the Technical University of Munich, and an adjunct assistant professor at Rice University, where he was an assistant professor in the ECE department from 2017-2019. Before that, he spent one and a half years as a postdoctoral researcher in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley, and a year in the Cognitive Computing & Computational Sciences Department at IBM Research Zurich. He completed his PhD in electrical engineering in 2014 at ETH Zurich and was a visiting PhD student at the Statistics Department at Stanford University. Reinhard is working in the intersection of machine learning and signal/information processing with a current focus on deep networks for solving inverse problems, learning from few and noisy samples, and DNA data storage.