Advances in Fast Nonconvex Algorithms for Low-Rank Hankel Matrix Recovery
Abstract
This talk studies the robust matrix completion problem for low-rank Hankel matrices. Low-rank Hankel matrix recovery provides a unified framework for spectral compressed sensing, which aims to reconstruct spectrally sparse signals from a limited number of randomly sampled time-domain observations. This problem arises frequently in signal processing and related areas. We give a partial overview of recent nonconvex approaches with provable guarantees, focusing on their sample complexity and convergence. In addition, to address practical challenges such as partial observations, impulsive noise, and ill-conditioning, we present a Newton-like algorithm designed to handle these issues in a unified manner.