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SUMMARY:Some New Results on Approximation with Redundant Dictionaries - Mo
 rten Nielsen (Aalborg University)
DTSTART:20130523T140000Z
DTEND:20130523T150000Z
UID:TALK44512@talks.cam.ac.uk
CONTACT:Dr Hansen
DESCRIPTION:Data approximation using sparse linear expansions from overcom
 plete dictionaries has become a central theme in signal and image processi
 ng with applications ranging from data acquisition (compressed sensing) to
  denoising and compression.\n\nFor a given dictionary\, we can also study 
 best m-term approximation rates for any specific function. Interestingly\,
  the notions of sparse expansions and certain asymptotic approximation rat
 es are closely linked in the case of  nice non-redundant dictionaries (e.g
 .\, an orthonormal basis in a Hilbert space.)  \n\nIn this talk\, I will e
 xplore the link between sparse expansions from an overcomplete dictionary 
 and asymptotic approximation rates. Redundancy complicates the analysis\, 
 and we show that the close link between the two notions fails in general. 
 However\, using a probabilistic approach\, we show that the close link is 
 retained for 'many' redundant dictionaries. 
LOCATION:MR 14\, CMS
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