Computational Methods and Data Science Journal Club with Zahra Kadhkodaie

by Ms Zahra Kadkhodaie (NYU/CCN)

Tuesday Aug 2, 2022, 3:00 PM → 4:00 PM America/New_York

4th Floor Classroom/4-Simons Foundation (160 5th Avenue)

Please note that a reception follows in the CCN 4th floor pantry.

Zahra Kadkhodaie, Doctoral Candidate in Data Science, NYU, and Guest Researcher, CCN LCV Group

Title: Stochastic Solutions for Linear Inverse Problems using the Prior Implicit in a Denoiser

Abstract: 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.

https://simonsfoundation.zoom.us/j/95284610644?pwd=bWNyMkticFE2SldOWnhzT0puNTJ3dz09

Passcode: 874467