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SUMMARY:On optimal sampling in off-the-grid sparse regularisation. - Dr Cl
 arice Poon\, DAMTP &amp\; Peterhouse
DTSTART:20181129T150000Z
DTEND:20181129T160000Z
UID:TALK113926@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:Sparse regularization is a central technique for both machine 
 learning and imaging sciences. Existing performance guarantees assume a se
 paration of the spikes based on an ad-hoc (usually Euclidean) minimum dist
 ance condition\, which ignore the geometry of the problem. In this talk\, 
 we study the BLASSO (i.e. the off-the-grid version of L1 LASSO regularizat
 ion) and show that the Fisher-Rao distance is the natural way to ensure an
 d quantify support recovery. Under a separation imposed by this distance\,
  I will present results which show that stable recovery of a sparse measur
 e can be achieved when the sampling complexity is (up to log factors) line
 ar with sparsity. On deconvolution problems\, which are translation invari
 ant\, this generalizes to the multi-dimensional setting\nexisting results 
 of the literature. For more complex translation-varying problems\, such as
  Laplace transform inversion\, this gives\nthe first geometry-aware guaran
 tees for sparse recovery. This is joint work with Nicolas Keriven and Gabr
 iel Peyre.
LOCATION:LR12\, Baker Building\, CUED
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