Princeton University

School of Engineering & Applied Science

Optimal Spectral Estimation via Atomic Norm Minimization

Gongguo Tang, Colorado School of Mines
B205 Engineering Quadrangle
Wednesday, November 14, 2018 - 12:30pm


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.


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