Friday, February 17, 2017 - 10:15am - 11:05am
Hai Zhang (Hong Kong University of Science and Technology)
We develop a mathematical theory to explain the mechanism of super-resolution in resonant media which consists of sub-wavelength resonators. Examples includes: Helmholtz resonators, plasmonic particles, and bubbles. For the media consists of small finite number of resonators, we show that super-resolution is due to sub-wavelength propagating modes; for the case of large number of resonators, we derive an effective media theory and show that super-resolution is due to the effective high contrast in the wave speed.
Thursday, January 28, 2016 - 3:15pm - 4:05pm
Weiyu Xu (The University of Iowa)
In this talk, we explore the performance limits of recovering structured signals from low-dimensional linear projections, using tools from high dimensional convex geometry. In particular, we focus on two signal reconstruction applications: a total variation minimization for recovering gradient-sparse signals and a low-rank Hankel matrix completion for super-resolution of spectrally sparse signals. Using the tool of Gaussian width, we obtain counter-intuitive performance bounds on the sample complexity for these two applications.
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