Phase transition

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.
Wednesday, October 9, 2013 - 2:00pm - 2:50pm
Omer Bobrowski (Duke University)
In manifold learning, one wishes to infer geometric and topological features of an unknown manifold, embedded in a d-dimensional Euclidean space, from a finite (random) point cloud. One topological invariant of a considerable interest is the homology of the underlying space.
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