Distinguished Seminar in Computational Science and Engineering
February 8, 2024, 12 PM
Eigenmatrix for Unstructured Sparse Recovery
Lexing Ying
Professor of Mathematics
Department of Mathematics
Institute for Computational and Mathematical Engineering
Stanford University
Abstract:
This talk discusses the unstructured sparse recovery problems of a general form. The task is to recover the spike locations and weights of an unknown sparse signal from a collection of its unstructured observations. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are the noise in the sample values and the unstructured nature of the sample locations. We propose the eigenmatrix construction, a data-driven approach to this problem. The eigenmatrix turns this non-linear inverse problem into an eigen-decomposition problem with desired eigenvalue and eigenvector pairs. This approach extends the classical Prony’s method and offers a new way for these sparse, unstructured recovery problems.
Bio:
Lexing Ying has been a Professor of Mathematics at Stanford University since 2012. Prior to that, he was a professor at the University of Texas at Austin from 2006 to 2012. His research focuses on numerical analysis and scientific computing. He received his Ph.D. from New York University and was a postdoctoral scholar at California Institute of Technology.
Eigenmatrix for Unstructured Sparse Recovery
Lexing Ying
Professor of Mathematics
Stanford University