John Wright

Bio:

John Wright is an associate professor in Electrical Engineering at Columbia University. He is also affiliated with the Department of Applied Physics and Applied Mathematics and Columbia’s Data Science Institute. He received his PhD in Electrical Engineering from the University of Illinois at Urbana Champaign in 2009. Before joining Columbia he was with Microsoft Research Asia from 2009-2011. His research interests include sparse and low-dimensional models for high-dimensional data, optimization (convex and otherwise), and applications in imaging and vision. His work has received a number of awards and honors, including the 2012 COLT Best Paper Award and the 2015 PAMI TC Young Researcher Award.

Title of talk:

Fast Manifold Denoising by Tunneling Riemannian Optimization

Abstract of talk:

Learned denoisers play a central role in state-of-the-art approaches signal generation (diffusion models) and reconstruction (learned compressed sensing): the denoiser is applied repeatedly as part of an iterative process which gradually extracts the desired clean signal from noisy measurements (or pure noise!). This makes denoising a critical computational bottleneck. In this work, we develop provable, test-time efficient denoisers for data sampled from Riemannian submanifolds of a high-dimensional data space. Our approach casts denoising as an optimization problem, and learns a mixed-order Riemannian optimizer over the a-priori unknown data manifold. Here, first-order Riemannian gradient steps facilitate efficient convergence, and zero-order steps enable the method to escape local minimizers. We show how to learn optimizers from streaming data, illustrate the efficiency and performance of this approach, and contrast it with existing provable manifold denoisers, whose test-time complexity is exponential in the intrinsic dimension of the data manifold. Joint with Shiyu Wang, Mariam Avagyan, Yihan Shen, Arnaud Lamy, Zsuzsa Maria, Szabolcs Marka