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UID:8156@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150220T140000
DTEND;TZID=Europe/Paris:20150220T150000
DTSTAMP:20241120T210048Z
URL:https://www.i2m.univ-amu.fr/evenements/c-herzet-inria-beyond-uniform-c
 onditions-for-sparse-reconstruction/
SUMMARY: (...): C. Herzet (Inria): Beyond Uniform Conditions for Sparse Rec
 onstruction
DESCRIPTION:: Beyond Uniform Conditions for Sparse Reconstruction\nBy Cédr
 ic Herzet\\\, Inria\n\nThis talk takes place within the context of sparse 
 representations\\\, in which one tries to decompose a vector/function as a
  combination of a few elementary signals.  This model has recently been sh
 own to be well-suited to the characterization of many signals and has thus
  sparked a surge of interest in the scientific community. Unfortunatley\\\
 , given a particular set of elementary signals\\\, the search of the spars
 est solution is known to be NP-Hard. Hence\\\, many heuristic algorithms h
 ave been proposed in the literature to compute approximate but tractable s
 olutions. Because these algorithms are suboptimal (in the sense that they 
 do not address the exact sparse representation problem)\\\, the derivation
  of conditions ensuring their success is of particular interest. \n\nIn th
 is talk\\\, we will focus our attention on the guarantees of success of tw
 o particular algorithms: "Orthogonal Matching Pursuit" (OMP) and "Orthogon
 al Least Squares" (OLS). While the behavior of OMP has been known for a de
 cade\\\, the condition of success of OLS has only been derived recently. W
 e will review these conditions and show how they can be adapted/relaxed in
  two particular cases of practical interest: i) when some prior informatio
 n is available about the position of the nonzero coefficients\\\; ii) when
  the nonzero coefficients of the sparse signal obey some decay. \n\nThe pr
 esentation will be based on the following set of papers:\n\nC. Herzet \\\,
  A. Drémeau\\\, C. Soussen\\\, «Relaxed Recovery Conditions for OMP/OLS 
 by Exploiting both Coherence and Decay»\\\,  ArXiV 1401.7533 \nC. Herzet\
 \\, C. Soussen\\\, J. Idier\\\, R. Gribonval\\\, «Exact Recovery Conditio
 ns for Sparse Representations With Partial Support Information »\\\, IEEE
  Trans. on Information Theory\\\, vol 59\\\, nr 11\\\, 2013. \nC. Soussen\
 \\, R. Gribonval\\\, J. Idier\\\, C. Herzet\\\, «Joint k-step analysis of
  Orthogonal Matching Pursuit and Orthogonal Least Squares»\\\, IEEE Trans
 . on Information Theory\\\, vol 59\\\, nr 5\\\, May 2013. 
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