Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	杨在教授，西安交通大学
Inviter:	刘亚锋
Title:	Geometry and recovery of spectral-sparse signals
Language:	Chinese
Time & Venue:	2022.12.22 16:00-17:00 腾讯会议:478-1365-3406
Abstract:	Spectral-sparse signals are those sparse in the Fourier domain and are very common in wireless communications, radar, sonar, medical imaging and other applications. Their recovery from noisy, limited measurements is a constantly important problem and has motivated the prominent research topic of compressed sensing. It is cast in state-of-the-art methods as low-rank structured (Hankel, Toeplitz) matrix recovery by applying Kronecker and Carathéodory-Fejér theorems. In this talk, we will introduce previous low-rank matrix recovery methods and point out their limitations from a geometric point of view. After that, we propose a new low-rank optimization method, which resolves the previous limitations, by studying the geometry of spectrally sparse signals. We demonstrate its effectiveness with a simple nonconvex algorithm. Finally, extensions and future research directions will be highlighted.