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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