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SUMMARY:Sampling in the 21st century: at the heart of hybrid analogue/digi
 tal processing - Pier Luigi Dragotti (Imperial College London)
DTSTART:20151111T150000Z
DTEND:20151111T160000Z
UID:TALK62441@talks.cam.ac.uk
CONTACT:Dr Hansen
DESCRIPTION:Modelling signals as sparse in a proper domain has proved frui
 tful in many signal and image processing\napplications.\nRecently\, the no
 tion of sparsity has lead to new sampling theories that have demonstrated 
 that the\nprior knowledge that signals can be sparsely described in a basi
 s or in a parametric space can be used\nto sample and perfectly reconstruc
 t such signals at a significantly reduced rate.\nThe insight that sub-Nyqu
 ist sampling can\, under some circumstances\, allow perfect\nreconstructio
 n is revolutionizing signal processing\, communications and inverse proble
 ms.\n\nIn this talk we first recall that sampling involves the reconstruct
 ion of continuous-time\nor continuous-space signals from discrete measurem
 ents (samples) and show how to relate the\ndiscrete measurements to some p
 roperties of the original continuous signal (e.g.\, its Fourier transform\
 nat specific frequencies). This is achieved by using the theory of approxi
 mation of exponentials and the so called generalized Strang-Fix conditions
 .\nGiven this partial knowledge of the original\nsignal\, we then reconstr
 uct it by using sparsity priors and in particular we provide exact reconst
 ruction formulas for specific classes of 1-D and 2-D signals.\nThe reconst
 ruction algorithms are all based around variations of the evergreen Prony'
 s method.\n\nWe then consider applications of these ideas\nto super-resolu
 tion imaging\, neuroscience and inverse problems.\nIn particular\, we pres
 ent a method for enhancing image resolution by one order of magnitude\,\na
  new fast algorithm for calcium-transients detection from two-photon calci
 um imaging and\na method for estimating diffusion fields driven by localiz
 ed sources using spatio-temporal sensor measurements.\n\nThis is joint wor
 k with T. Blu (CUHK)\, J. A. Uriguen (ICL)\, J. Onativia Bravo (ICL)\,  J.
  Murray-Bruce (ICL)\, A. Scholefield (ICL) and S. Schultz (ICL).\nThis wor
 k is supported by the European Research Council (ERC) starting investigato
 r award Nr. 277800 (RecoSamp).
LOCATION:MR 14\, CMS
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