Speaker: Prof. Michael Wakin, IEEE Fellow

Affiliation: Colorado School of Mines

Report Title: Bridging Subspace and Manifold Models in Signal and Radar Processing

Abstract: 

In radar and signal processing, changing parameters such as pulse arrival time, carrier frequency, or target position can cause received signals to trace out a nonlinear, low-dimensional manifold in a much higher-dimensional signal space. Such a “manifold hypothesis” helps inspire and explain the success of many machine learning techniques. Meanwhile, many classical signal processing techniques rely on low-dimensional linear subspace models, from lowpass filtering for noise removal to sparse modeling for signal reconstruction. Bridging these two perspectives opens the door to more powerful tools for signal and radar processing. In this talk, we explore the benefits of using subspace models that extend over localized regions of a manifold. In a variety of problem settings involving signals concentrated in time, frequency, or space (such as identifying spatially localized targets), these subspaces can be remarkably effective for capturing signal energy while remaining nearly orthogonal to out-of-band interference. This property enables a range of practical applications, including modeling and reconstruction of multiband signals, antenna metrology, and through-the-wall radar imaging. We survey several such applications and also discuss fast FFT-like algorithms designed to enable fast computations with the resulting subspaces.

Biography: 

Michael B. Wakin is a Professor of Electrical Engineering at the Colorado School of Mines. Dr. Wakin received a B.S. in electrical engineering and a B.A. in mathematics in 2000 (summa cum laude), an M.S. in electrical engineering in 2002, and a Ph.D. in electrical engineering in 2007, all from Rice University. He was an NSF Mathematical Sciences Postdoctoral Research Fellow at Caltech from 2006-2007, an Assistant Professor at the University of Michigan from 2007-2008, and a Ben L. Fryrear Associate Professor at Mines from 2015-2017. His research interests include signal and data processing using sparse, low-rank, and manifold-based models. In 2007, Dr. Wakin shared the Hershel M. Rich Invention Award from Rice University for the design of a single-pixel camera based on compressive sensing. In 2008, Dr. Wakin received the DARPA Young Faculty Award for his research in compressive multi-signal processing for environments such as sensor and camera networks. In 2012, Dr. Wakin received the NSF CAREER Award for research into dimensionality reduction techniques for structured data sets. In 2014, Dr. Wakin received the Excellence in Research Award for his research as a junior faculty member at Mines. In 2021, Dr. Wakin was elevated to IEEE Fellow. Dr. Wakin is a recipient of the Best Paper Award and the Signal Processing Magazine Best Paper Award from the IEEE Signal Processing Society. He has served as an Associate Editor for both IEEE Signal Processing Letters and IEEE Transactions on Signal Processing and as a Senior Area Editor for IEEE Transactions on Signal Processing.