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Atom selection in continuous dictionaries : reconciling polar and SVD approximations

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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Submitted on : Wednesday, March 6, 2019 - 6:54:26 PM
Last modification on : Friday, May 20, 2022 - 9:04:50 AM
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Frédéric Champagnat, Cédric 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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