Nonlinear approximation with dictionaries. II. Inverse Estimates

Rémi Gribonval, Morten Nielsen

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5 Citationer (Scopus)

Abstract

In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually incoherent bases introduced by Donoho and Huo. The Bernstein inequality obtained for such dictionaries is proved to be sharp, but it has an exponent that does not match that of the corresponding Jackson inequality.
Udgivelsesdato: SEP
OriginalsprogEngelsk
TidsskriftConstructive Approximation
Vol/bind24
Udgave nummer2
Sider (fra-til)157-173
Antal sider17
ISSN0176-4276
DOI
StatusUdgivet - 2006

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