Tutorials

Atomic Norms and Super-resolution

Prof. Gongguo Tang, Colorado School of Mines, USA

Abstract:

By generalizing the L1 norm for sparse recovery and the nuclear norm for matrix completion, atomic norm provides a powerful framework for constructing convex regularizers to solve inverse problems. Super-resolution studies the recovery of a discrete/atomic measure from linear functional measurements and concerns the resolvability of the measure’s support. Both problems find numerous applications in array signal processing, radar, data analysis, computational imaging, and machine learning. When the atoms defining an atomic norm are specified by the same linear functional measurements in super-resolution, the problem of super-resolution is equivalent to the atomic decomposition problem, which in turn forms the foundation of atomic regularization. In the past three years, researchers have developed many results on atomic norms and super-resolution. The tutorial will report most recent advances on both topics and their connections.

Biography:

Dr. Gongguo Tang is an Assistant Professor in the Electrical Engineering and Computer Science Department 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 Post-doctoral Research Associate at the Department of Electrical and Computer Engineering, University of Wisconsin-Madison in 2011–2013, and a visiting scholar at University of California, Berkley in 2013. Gongguo’s research interests are in the area of signal processing, convex optimization, machine learning, and their applications in data analysis, optics, imaging, and networks.