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Titolo: MOMS: Maximalorder interpolation of minimal support
Autore: Blu, T; Thevenaz, P; Unser, M;
 Indirizzi:
 Swiss Fed Inst Technol, Biomed Imaging Grp, EPFL, CH1015 Lausanne, Switzerland Swiss Fed Inst Technol Lausanne Switzerland CH1015 ausanne, Switzerland
 Titolo Testata:
 IEEE TRANSACTIONS ON IMAGE PROCESSING
fascicolo: 7,
volume: 10,
anno: 2001,
pagine: 1069  1080
 SICI:
 10577149(200107)10:7<1069:MMIOMS>2.0.ZU;2H
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 QUANTITATIVE FOURIERANALYSIS; APPROXIMATION TECHNIQUES; IMAGERECONSTRUCTION; CUBIC CONVOLUTION; SCAN CONVERSION; MRIMAGES; ALGORITHMS; EXPANSIONS; ROTATION; SPLINES;
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 Engineering, Computing & Technology
 Citazioni:
 38
 Recensione:
 Indirizzi per estratti:
 Indirizzo: Blu, T Swiss Fed Inst Technol, Biomed Imaging Grp, EPFL, CH1015 Lausanne,Switzerland Swiss Fed Inst Technol Lausanne Switzerland CH1015 , Switzerland



 Citazione:
 T. Blu et al., "MOMS: Maximalorder interpolation of minimal support", IEEE IM PR, 10(7), 2001, pp. 10691080
Abstract
We consider the problem of interpolating a signal using a linear combination of shifted versions of a compactlysupported basis function psi (x). We first give the expression of the psi 's that have minimal support for a given accuracy (also known as "approximation order"). This class of functions,which we call maximalorderminimalsupport functions (MOMS) is made of linear combinations of the Bspline of same order and of its derivatives. We provide the explicit form of the MOMS that maximize the approximation accuracy when the stepsize is small enough. We compute the sampling gain obtained by using these optimal basis functions over the splines of same order. We show that it is already substantial for small orders and that it further increases with the approximation order L, When L is large, this sampling gain becomes linear; more specifically, its exact asymptotic expression is 2/(pie)L. Since the optimal functions are continuous, but not differentiable, for even orders, and even only piecewise continuous for odd orders, our result implies that regularity has little to do with approximating performance. These theoretical findings are corroborated by experimental evidence that involves compounded rotations of images.
ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 18/01/20 alle ore 01:51:59