Zai Yang, Professor, Xi'an Jiaotong University )

Yafeng Liu, Associate Professor

Geometry and recovery of spectral-sparse signals

16:00-17:00 December 22(Thursday), Tencent Meeting ID: 478-1365-3406

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.