[Ml-stat-talks] PACM Colloquium 4/23/12

Amit Singer amits at math.Princeton.EDU
Mon Apr 23 10:45:28 EDT 2012

DATE: Monday,  April 23, 2012 

PLACE: 214 Fine Hall 


SPEAKER: Laurent Demanet, MIT

TITLE: Super-resolution via sparse recovery: progress and challenges

>From the knowledge of a function in a frequency band, super-resolution
consists in detecting or estimating sharp features which are less than the
inverse of a bandwidth apart from one another. Sparse recovery is one way to
extend this Shannon-Nyquist scaling, but "by how much" and "in which
setting" it is not yet clearly understood. This work attempts to start the
classification of singularity layout vs. noise level for proper
identification by ell-1 minimization. When a condition of constructive
interference is met, ell1-minimization performs optimally: it only breaks
down in the unrecoverable regime where no other method would work either. As
a corollary, we obtain a novel noise-dependent scaling which replaces the
inverse bandwidth rule for super-resolution. Algorithmic alternatives to
ell-1 minimization are presented to attempt to deal with the harder
situation of "destructive interference". 

Coffee & Tea will be served at 3:55 p.m. in 217A Fine Hall

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