We consider the spectral estimation problem of finding point-like frequencies of a signal from its noisy samples in the time domain. I will present some subspace methods, in particular, MUSIC, ESPRIT and the matrix pencil method. These methods are well known for their super-resolution phenomenon – the capability of resolving closely spaced frequencies. We will give a theoretical guarantee of the resolution limit of these subspace methods through a sharp bound on the conditioning of Vandermondes matrices with nodes on the unit circle.

This presentation is part of Minisymposium “MS42 - Low dimensional structures in imaging science (3 parts)”
organized by: Wenjing Liao (Georgia Institute of Technology) , Haizhao Yang (Duke University) , Zhizhen Zhao (University of Illinois Urbana-Champaign) .

Authors:

Wenjing Liao (Georgia Institute of Technology)

Keywords:

conditioning of vandermonde matrices, esprit, inverse problems, music, super-resolution