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   -> Volume 13, Issue 1


Preprint: "On the Use of A Priori Information for Sparse Signal Representations and Approximations", by O. Divorra Escoda et al.
 
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Oscar Divorra Escoda (oscar.divorra@epfl.ch)
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PostPosted: Mon Jan 24, 2005 10:44 am    
Subject: Preprint: "On the Use of A Priori Information for Sparse Signal Representations and Approximations", by O. Divorra Escoda et al.
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TWO new technical reports about the use of "a priori" information for sparse signal representations and approximations.

FIRST PREPRINT:

AUTHORS AND TITLE:
O. Divorra Escoda, L. Granai and P. Vandergheynst (2004), "On the Use of A Priori Information for Sparse Signal Representations"

ABSTRACT:

This report studies the effect of introducing a priori knowledge when recovering sparse representations with overcomplete
dictionaries. We focus mainly on Greedy algorithms and Basis Pursuit as for our algorithmic basement, while a priori is
incorporated by suitably weighting the elements of the dictionary. Very recently, sufficient conditions have been established to
guarantee the retrieval of the sparsest representation depending only on the kind of dictionary in use. We generalize these to
take into account the effect of using a priori information. Theoretical results show how the use of ``reliable'' priors can
improve the performances of the Matching Pursuit, Orthogonal Matching Pursuit and Basis Pursuit algorithms. Our results
reduce to the classical case when no a priori information is available. Some examples illustrate our theoretical findings.

PDF:
http://lts1pc19.epfl.ch/repository/Divorra_Escoda2004_927.pdf

SECOND PREPRINT:

AUTHORS AND TITLE:
O. Divorra Escoda, L. Granai and P. Vandergheynst (2004), "On the Use of A Priori Information for Sparse Signal Approximations"

ABSTRACT:

This report is the extension to the case of sparse approximations of our previous study on the effects of introducing a priori knowledge to solve the recovery of sparse representations when overcomplete dictionaries are used. Greedy algorithms and Basis Pursuit Denoising are considered in this work. Theoretical results show how the use of "reliable" a priori information (which in this work appears under the form of weights) can improve the performances of these methods. In particular, we generalize the sufficient conditions established by Tropp and Gribonval & Vandergheynst, that guarantee the retrieval of the sparsest solution, to the case where a priori information is used. We prove how the use of prior models at the signal decomposition stage influences these sufficient conditions. The results found in this work reduce to the classical case of Tropp and Gribonval & Vandergheynst when no a priori information about the signal is available. Finally, examples validate and illustrate the theoretical results.Finally, examples validate and illustrate theoretical results.

PDF:
http://lts1pc19.epfl.ch/repository/Divorra_Escoda2004_1166.pdf
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