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SUMMARY:Approximate Strang-Fix: Sparse Sampling with any acquisition devic
 e
DTSTART:20130610T111500
DTEND:20130610T121500
DTSTAMP:20260406T194718Z
UID:aa0f37b2fef3f55bcf75e6f3d639eddc23aeba360f47d13185b03daf
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Pier Luigi Dragotti\, Imperial College London\nThe probl
 em of reconstructing partially observed or sampled signals is an important
  one that finds application in many areas of signal processing. Traditiona
 l acquisition and reconstruction approaches are heavily influences by cla
 ssical Shannon sampling theory which gives an exact sampling and interpola
 tion formula for bandlimited signals. In the last few years\, several new 
 methods have been developed for the sampling and exact reconstruction of s
 pecific classes of sparse non-bandlimited signals known as signals with fi
 nite rate of innovation (FRI). This is achieved by using adequate acquisi
 tion devices (sampling kernels) and reconstruction schemes. Valid sampling
  kernels allow to connect the samples to some essential information of the
  original signal\, typically\, its Fourier or Laplace transform at specifi
 c frequencies. An example of valid kernel is given by the family of expon
 ential reproducing functions. These satisfy the generalised Strang-Fix con
 ditions\, which ensure that proper linear combinations of the kernel with 
 its shifted versions reproduce exponentials exactly.\nIn the first part of
  the talk\, we discuss sampling and perfect reconstruction of parametric s
 parse signals such as piecewise sinusoidal signals or classes of 2-D signa
 ls using exponential reproducing kernels. We then show how to choose the e
 xponential reproducing kernel that leads to the most stable reconstruction
  when estimating FRI signals from noisy samples. This analysis leads to t
 he design of the e-MOMS family of kernels (Maximum order minimum support e
 xponential reproducing kernels)\nwhich we show includes all the compact su
 pport kernels used in FRI theory so far. Next we depart from the situation
  in which we can choose the sampling kernel and develop a new strategy tha
 t is universal in that it works with any kernel. We do so by noting that m
 eeting the exact exponential reproduction condition is too stringent a con
 straint. We thus allow for a controlled error in the reproduction formula 
 in order to use the exponential reproduction idea with arbitrary kernels a
 nd develop a universal reconstruction method which is also robust to noise
 .\nTo emphasize the relevance of these new theories\, we conclude the talk
  by presenting applications in image super-resolution and in neuroscience.
  In particular\, we will present a new fast algorithm for spike detection 
 from two-photon calcium imaging and will show how to perform spike sorting
  at sub-Nyquist rates.\nThis is joint work with T. Blu (CUHK)\, H. Pan (CU
 HK) J. A. Uriguen (ICL)\, J. Onativia Bravo (ICL) and S. Schultz (ICL).\nT
 his work is supported by the European Research Council (ERC) starting inve
 stigator award  Nr. 277800 (RecoSamp).
LOCATION:BC 420 https://plan.epfl.ch/?room==BC%20420
STATUS:CONFIRMED
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