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Compressive sensing with un-trained neural networks: Gradient descent finds a smooth approximation
Reinhard Heckel · Mahdi Soltanolkotabi

Tue Jul 14 02:00 PM -- 02:45 PM & Wed Jul 15 03:00 AM -- 03:45 AM (PDT) @ None #None

Un-trained convolutional neural networks have emerged as highly successful tools for image recovery and restoration. They are capable of solving standard inverse problems such as denoising and compressive sensing with excellent results by simply fitting a neural network model to measurements from a single image or signal without the need for any additional training data. For some applications, this critically requires additional regularization in the form of early stopping the optimization. For signal recovery from a few measurements, however, un-trained convolutional networks have an intriguing self-regularizing property: Even though the network can perfectly fit any image, the network recovers a natural image from few measurements when trained with gradient descent until convergence. In this paper, we provide numerical evidence for this property and study it theoretically. We show that---without any further regularization---an un-trained convolutional neural network can approximately reconstruct signals and images that are sufficiently structured, from a near minimal number of random measurements.

Author Information

Reinhard Heckel (Rice University)
Mahdi Soltanolkotabi (University of Southern California)

Mahdi Soltanolkotabi is an assistant professor in the Ming Hsieh Department of Electrical and Computer Engineering and Computer Science at the University of Southern California where he holds an Andrew and Erna Viterbi Early Career Chair. Prior to joining USC, he completed his PhD in electrical engineering at Stanford in 2014. He was a postdoctoral researcher in the EECS department at UC Berkeley during the 2014-2015 academic year. His research focuses on developing the mathematical foundations of data analysis at the confluence of optimization, machine learning, signal processing, high dimensional statistics, computational imaging and artificial intelligence. Mahdi is the recipient of the Packard Fellowship in Science and Engineering, a Sloan Research Fellowship, an NSF Career award, an Airforce Office of Research Young Investigator award (AFOSR-YIP), and a Google faculty research award.

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