The Role of the Translation Distribution in Multi-reference Alignment

Monday, September 17, 2018 - 1:25pm - 2:25pm
Lind 305
William Leeb (University of Minnesota, Twin Cities)
This talk will describe the problem of multireference alignment (MRA), in which a signal is estimated from multiple randomly translated observations with high levels of noise. I will present recent work demonstrating how the sample complexity of MRA depends on properties of the distribution of translations. In particular, I will show that when the distribution is aperiodic, the signal is estimable by an efficient algorithm making use of only second-order statistics of the observations. I will also describe an information-theoretic lower bound showing that this algorithm is optimal in its dependence on the number of observations. This is joint work with Emmanuel Abbe, Tamir Bendory, Joao Perreira, Nir Sharon, and Amit Singer.

William Leeb is an Assistant Professor in the School of Mathematics at the University of Minnesota, Twin Cities. Prior to joining the faculty at UMN, he was a postdoctoral research associate in Amit Singer's research group at Princeton University, where he was supported by the Simons Collaboration on Algorithms and Geometry. He earned his PhD in Mathematics from Yale University in 2015, working under the supervision of Ronald Coifman. His research interests include computational harmonic analysis, signal and image processing, and high-dimensional statistics.