[talks] Wednesday, November 14, 12:30pm, E-Quad B205 - Gongguo Tang, Colorado School of Mines

[Emily Lawrence]

EE SEMINAR SERIES

 

 


Speaker: 

Gongguo Tang, Colorado School of Mines


Title: 

Optimal Spectral Estimation via Atomic Norm Minimization


Day: 

Wednesday, November 14, 2018


Time:

12:30 pm


Room: 

B205 Engineering Quadrangle


Host:

Prof. Yuxin Chen


 


Abstract:

Atomic norm minimization is a convex relaxation framework that greatly
generalizes l1 norm for compressed sensing and nuclear norm for matrix
completion. In particular, it allows one to construct convex regularizers
for signals that have sparse representations with respect to continuously
parameterized dictionaries. In this talk, the speaker 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. In particular, the method's accuracy in
inferring the frequencies and complex magnitudes from noisy observations of
a mixture of complex sinusoids will be analyzed. When the Signal-to-Noise
Ratio is reasonably high and the true frequencies are well-separated, the
atomic norm estimator is shown to localize the correct number of
frequencies, each within a neighborhood of one of the true frequencies,
whose size matches the Cramér–Rao lower bound up to a logarithmic factor.
The analysis is based on a primal–dual witness construction procedure.  The
analysis also reveals that the atomic norm minimization can be viewed as a
convex way to solve a l1-norm regularized, nonlinear and nonconvex
least-squares problem to global optimality.


 




Bio:

Dr. Gongguo Tang is an Assistant Professor in the Department of Electrical
Engineering at Colorado School of Mines since 2014. He received his Ph.D.
degree in Electrical Engineering from Washington University in St. Louis in
2011. He was a Postdoctoral Research Associate at the Department of
Electrical and Computer Engineering, University of Wisconsin-Madison from
2011 to 2013, and a visiting scholar at the University of California,
Berkeley in 2013. Dr. Tang's research interests are in the area of
optimization, signal processing, and machine learning, and their
applications in big data analytics, optics, imaging, and networks.

 


 

This seminar is supported with funds from the Korhammer Lecture Series

 

			

 

 

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