caa a22 4500 47574361X CHVBK 20180406123506.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/s003659910001 doi (NATIONALLICENCE)springer-10.1007/s003659910001 An Adaptive Compression Algorithm in Besov Spaces [Elektronische Daten] [L. Birgé, P. Massart] 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. Springer-Verlag New York Inc., 2000 Key words. Signal compression, Besov spaces, Piecewise polynomials, Splines, Wavelets, Metric entropy. AMS Classification. Primary: 41A25, 41A46 nationallicence Secondary: 41A10, 41A15, 41A30 nationallicence Birgé L. Laboratoire de Probabilités, Boite 188 Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France aut Massart P. URA 743 's'sModélisation stochastique et Statistique'' Bât. 425 Université Paris Sud Campus d'Orsay, F-91405 Orsay Cedex, France aut https://doi.org/10.1007/s003659910001 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003659910001 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Birgé L. Laboratoire de Probabilités, Boite 188 Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France aut NATIONALLICENCE 700 1- Massart P. URA 743 's'sModélisation stochastique et Statistique'' Bât. 425 Université Paris Sud Campus d'Orsay, F-91405 Orsay Cedex, France aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer