Optimal Spectral Estimation via Atomic Norm Minimization

Speaker: Gongguo Tang

Date: 5 May 2017

Time: 14:00-15:00

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Atomic norm minimisation is a convex relaxation framework that greatly generalises  norm for compressed sensing and nuclear norm for matrix completion. In particular, it allows one to construct convex regularise for signals that have sparse representations with respect to continuously parameter dictionaries.

In this talk, Gongguo Tang will focus on the application of this framework to line spectral estimation, which can be viewed as a sparse recovery problem whose atoms are indexed by the continuous frequency variable.

The optimal of atomic norm minimisation will be highlighted:

1) It completes a signal from a minimal number of observations;

2) It denoises a signal with near minimal performance;

3) It estimates the frequencies with an accuracy approaching the Cramer-Rao bound;

4) It achieves the best possible resolution; and 5) it removes a maximal number of outliers