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SUMMARY:Compressive sampling - Emmanuel Candes (California Institute of Te
 chnology)
DTSTART:20080117T150000Z
DTEND:20080117T160000Z
UID:TALK8892@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:One of the central tenets of signal processing is the Shannon/
 Nyquist sampling theory: the number of samples needed to reconstruct a sig
 nal without error is dictated by its\nbandwidth-the length of the shortest
  interval which contains the\nsupport of the spectrum of the signal under 
 study.  Very\nrecently\, an alternative sampling or sensing theory has eme
 rged\nwhich goes against this conventional wisdom.  This theory allows\nth
 e faithful recovery of signals and images from what appear to\nbe highly i
 ncomplete sets of data\, i.e. from far fewer data bits\nthan traditional m
 ethods use.  Underlying this metholdology is a\nconcrete protocol for sens
 ing and compressing data\nsimultaneously.\n\nThis talk will present the ke
 y mathematical ideas underlying this\nnew sampling or sensing theory\, and
  will survey some of the most\nimportant results. We will argue that this 
 is a robust\nmathematical theory\; not only is it possible to recover sign
 als\naccurately from just an incomplete set of measurements\, but it is\na
 lso possible to do so when the measurements are unreliable and\ncorrupted 
 by noise. We will see that the reconstruction\nalgorithms are very concret
 e\, stable (in the sense that they\ndegrade smoothly as the noise level in
 creases) and practical\; in\nfact\, they only involve solving very simple 
 convex optimization\nprograms.\n\nAn interesting aspect of this theory is 
 that it has bearings on\nsome fields in the applied sciences and engineeri
 ng such as\nstatistics\, information theory\, coding theory\, theoretical\
 ncomputer science\, and others as well.  If time allows\, we will\ntry to 
 explain these connections via a few selected examples.\n\n
LOCATION:MR14\, CMS
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