An Adaptive Compression Algorithm in Besov Spaces |
| |
Authors: | L Birgé P Massart |
| |
Institution: | (1) Laboratoire de Probabilités, Boite 188 Université Paris VI 4 Place Jussieu F-75252 Paris Cedex 05 France lb@ccr.jussieu.fr, FR;(2) URA 743 ``Modélisation stochastique et Statistique' Bat. 425 Université Paris Sud Campus d'Orsay F-91405 Orsay Cedex France pascal.massart@math.u-psud.fr, FR |
| |
Abstract: | Given a function f on 0,1] and a wavelet-type expansion of f , we introduce a new algorithm providing an approximation
$\tilde f of f with a prescribed number D of nonzero coefficients in its expansion. This algorithm depends only on the number of coefficients to be kept and not on
any smoothness assumption on f . Nevertheless it provides the optimal rate D
-α
of approximation with respect to the L
q
-norm when f belongs to some Besov space B
α
p,∈fty
whenever α>(1/p-1/q)
+
. These results extend to more general expansions including splines and piecewise polynomials and to multivariate functions.
Moreover, this construction allows us to compute easily the metric entropy of Besov balls.
June 21, 1996. Dates revised: April 9, 1998; October 14, 1998. Date accepted: October 20, 1998. |
| |
Keywords: | , Signal compression, Besov spaces, Piecewise polynomials, Splines, Wavelets, Metric entropy, AMS Classification,,,,,,Primary: 41A25, 41A46, Secondary: 41A10, 41A15, 41A30, |
本文献已被 SpringerLink 等数据库收录! |
|