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CATEGORIES:Applied and Computational Analysis
SUMMARY:Sampling in the 21st century: at the heart of hybr
id analogue/digital processing - Pier Luigi Dragot
ti (Imperial College London)
DTSTART;TZID=Europe/London:20151111T150000
DTEND;TZID=Europe/London:20151111T160000
UID:TALK62441AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/62441
DESCRIPTION:Modelling signals as sparse in a proper domain has
proved fruitful in many signal and image processi
ng\napplications.\nRecently\, the notion of sparsi
ty has lead to new sampling theories that have dem
onstrated that the\nprior knowledge that signals c
an be sparsely described in a basis or in a parame
tric space can be used\nto sample and perfectly re
construct such signals at a significantly reduced
rate.\nThe insight that sub-Nyquist sampling can\,
under some circumstances\, allow perfect\nreconst
ruction is revolutionizing signal processing\, com
munications and inverse problems.\n\nIn this talk
we first recall that sampling involves the reconst
ruction of continuous-time\nor continuous-space si
gnals from discrete measurements (samples) and sho
w how to relate the\ndiscrete measurements to some
properties 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 generaliz
ed Strang-Fix conditions.\nGiven this partial know
ledge of the original\nsignal\, we then reconstruc
t it by using sparsity priors and in particular we
provide exact reconstruction formulas for specifi
c classes of 1-D and 2-D signals.\nThe reconstruct
ion algorithms are all based around variations of
the evergreen Prony's method.\n\nWe then consider
applications of these ideas\nto super-resolution i
maging\, neuroscience and inverse problems.\nIn pa
rticular\, we present a method for enhancing image
resolution by one order of magnitude\,\na new fas
t algorithm for calcium-transients detection from
two-photon calcium imaging and\na method for estim
ating diffusion fields driven by localized sources
using spatio-temporal sensor measurements.\n\nThi
s is joint work with T. Blu (CUHK)\, J. A. Uriguen
(ICL)\, J. Onativia Bravo (ICL)\, J. Murray-Bruc
e (ICL)\, A. Scholefield (ICL) and S. Schultz (ICL
).\nThis work is supported by the European Researc
h Council (ERC) starting investigator award Nr. 27
7800 (RecoSamp).
LOCATION:MR 14\, CMS
CONTACT:Dr Hansen
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