Atom selection in continuous dictionaries : reconciling polar and SVD approximations

Frédéric Champagnat 1 Cedric Herzet 2
2 SIMSMART - SIMulation pARTiculaire de Modèles Stochastiques
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : This paper deals with efficient atom selection procedure in a continuous dictionary, as required for instance in a Frank-Wolfe approach within a BLASSO problem for the one-dimensional deconvolution problem. We show that efficient maximization of a correlation between any given vector and an atom sweeping a continuous dictionary can be performed through a particular piece-wise linear approximation of dictionaries: the polar approximation. We finally identify the polar approximation as being optimal in a mean square error sense for dictionaries with raised-cosine Toeplitz kernels.
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Soumis le : mercredi 6 mars 2019 - 18:54:26
Dernière modification le : mercredi 3 juillet 2019 - 16:12:53
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Frédéric Champagnat, Cedric Herzet. Atom selection in continuous dictionaries : reconciling polar and SVD approximations. ICASSP 2019 - IEEE International Conference on Acoustics, Speech, and Signal Processing, May 2019, Brighton, United Kingdom. pp.5516-5520, ⟨10.1109/ICASSP.2019.8683402⟩. ⟨hal-02059703⟩

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