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CATEGORIES:Cambridge Image Analysis Seminars
SUMMARY:Locally Sparse Reconstruction Using l^1\,\\infty^-
Norms - Pia Heins (University of Münster)
DTSTART;TZID=Europe/London:20130516T100000
DTEND;TZID=Europe/London:20130516T110000
UID:TALK45235AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/45235
DESCRIPTION:Sparse reconstructions based on minimizing l^1^-no
rms have gained huge attention in signal and image
processing\, inverse problems\, and compressed se
nsing recently. However\, the overall sparsity enf
orced by minimal l^1^-norm is not the only kind of
prior information available in practice. Strong r
ecent direction of research are related to unknown
s being matrices\, with prior information being e.
g. low rank incorporated via nuclear norm minimiz
ation or block sparsity (or collaborative sparsity
) incorporated by minimization of l^p\,1^-norms wi
th p in (1\,\\infty).\n\nIn this talk we consider
another type of sparsity-functionals\, namely l^1\
,\\infty^-norms. Our motivation is a _local sparsi
ty_ that frequently appears in inversion with some
spatial dimensions and at least one additional d
imension such as time or spectral information in i
maging.\n\nFirst we will motivate the use of the l
^1\,\\infty^-norm as regularization functional for
dictionary based reconstruction of matrix complet
ion problems. \nThen we will reformulate the probl
em to make it easier accessible and analyze it wit
h regard to exact recovery.\nIn order to obtain co
mputational results we will propose another reform
ulation of the problem. Finally some basic results
will be presented using splitting techniques.
LOCATION:MR 15\, Centre for Mathematical Sciences
CONTACT:Carola-Bibiane Schoenlieb
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