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Stochastic Solutions for Linear Inverse Problems using the Prior Implicit in a Denoiser
Zahra Kadkhodaie · Eero Simoncelli

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @ None #None

Deep neural networks have provided state-of-the-art solutions for problems such as image denoising, which implicitly rely on a prior probability model of natural images. Two recent lines of work – Denoising Score Matching and Plug-and-Play – propose methodologies for drawing samples from this implicit prior and using it to solve inverse problems, respectively. Here, we develop a parsimonious and robust generalization of these ideas. We rely on a classic statistical result that shows the least-squares solution for removing additive Gaussian noise can be written directly in terms of the gradient of the log of the noisy signal density. We use this to derive a stochastic coarse-to-fine gradient ascent procedure for drawing high-probability samples from the implicit prior embedded within a CNN trained to perform blind denoising. A generalization of this algorithm to constrained sampling provides a method for using the implicit prior to solve any deterministic linear inverse problem, with no additional training, thus extending the power of supervised learning for denoising to a much broader set of problems. The algorithm relies on minimal assumptions and exhibits robust convergence over a wide range of parameter choices. To demonstrate the generality of our method, we use it to obtain state-of-the-art levels of unsupervised performance for deblurring, super-resolution, and compressive sensing.

Author Information

Zahra Kadkhodaie (New York University)
Eero Simoncelli (FlatIron Institute / New York University)

Eero P. Simoncelli received the B.S. degree in Physics in 1984 from Harvard University, studied applied mathematics at Cambridge University for a year and a half, and then received the M.S. degree in 1988 and the Ph.D. degree in 1993, both in Electrical Engineering from the Massachusetts Institute of Technology. He was an Assistant Professor in the Computer and Information Science department at the University of Pennsylvania from 1993 until 1996. He moved to New York University in September of 1996, where he is currently a Professor in Neural Science, Mathematics, and Psychology. In August 2000, he became an Associate Investigator of the Howard Hughes Medical Institute, under their new program in Computational Biology. In Fall 2020, he resigned his HHMI appointment to become the scientific director of the Center for Computational Neuroscience at the Flatiron Institute, of the Simons Foundation. His research interests span a wide range of topics in the representation and analysis of visual images, in both machine and biological systems.

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