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SUMMARY:Locally Sparse Reconstruction Using l^1\,\\infty^-Norms - Pia Hein
 s (University of Münster)
DTSTART:20130516T090000Z
DTEND:20130516T100000Z
UID:TALK45235@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:Sparse reconstructions based on minimizing l^1^-norms have gai
 ned huge attention in signal and image processing\, inverse problems\, and
  compressed sensing recently. However\, the overall sparsity enforced by m
 inimal l^1^-norm is not the only kind of prior information available in pr
 actice. Strong recent direction of research are related to unknowns being 
 matrices\, with prior information being e. g. low rank incorporated via nu
 clear norm minimization or block sparsity (or collaborative sparsity) inco
 rporated by minimization of l^p\,1^-norms with p in (1\,\\infty).\n\nIn th
 is talk we consider another type of sparsity-functionals\, namely l^1\,\\i
 nfty^-norms. Our motivation is a _local sparsity_ that frequently appears 
 in inversion with some spatial dimensions and at least one  additional dim
 ension such as time or spectral information in imaging.\n\nFirst we will m
 otivate the use of the l^1\,\\infty^-norm as regularization functional for
  dictionary based reconstruction of matrix completion problems. \nThen we 
 will reformulate the problem to make it easier accessible and analyze it w
 ith regard to exact recovery.\nIn order to obtain computational results we
  will propose another reformulation of the problem. Finally some basic res
 ults will be presented using splitting techniques.
LOCATION:MR 15\, Centre for Mathematical Sciences
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