ON A NONLINEAR SUBDIVISION SCHEME AVOIDING GIBBS OSCILLATIONS AND CONVERGING TOWARDS Cs FUNCTIONS WITH s > 1

被引：13
作者：
Amat, S. [1 ]
Dadourian, K. [2 ]
Liandrat, J. [2 ]
机构：
[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain
[2] Ecole Cent Marseille, Lab Anal Topol & Probabil, Marseille, France
来源：
MATHEMATICS OF COMPUTATION | 2011年 / 80卷 / 274期
关键词：
Nonlinear subdivision scheme; limit function; regularity; stability; Gibbs phenomenon; MEDIAN-INTERPOLATION; MULTIRESOLUTION; REPRESENTATION;
D O I：
10.1090/S0025-5718-2010-02434-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents a new nonlinear dyadic subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence, stability and order of approximation are analyzed. It is proved that this scheme converges towards limit functions Holder continuous with exponent larger than 1.299. Numerical estimates provide a Holder exponent of 2.438. This subdivision scheme is the first one that simultaneously achieves the control of the Gibbs phenomenon and has limit functions with Holder exponent larger than 1.
引用
收藏
页码：959 / 971
页数：13
相关论文
共 22 条
  • [1] On the stability of the PPH nonlinear multiresolution
    Amat, S
    Liandrat, J
    [J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2005, 18 (02) : 198 - 206
  • [2] Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms
    Amat, S.
    Dadourian, K.
    Liandrat, J.
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2011, 34 (03) : 253 - 277
  • [3] Tensor product multiresolution analysis with error control for compact image representation
    Amat, S
    Aràndiga, F
    Cohen, A
    Donat, R
    [J]. SIGNAL PROCESSING, 2002, 82 (04) : 587 - 608
  • [4] Amat S., 2006, CURVES SURFACES FITT, P1
  • [5] Analysis of a new nonlinear subdivision scheme. Applications in image processing
    Amat, Sergio
    Donat, Rosa
    Liandrat, Jacques
    Trillo, J. Carlos
    [J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2006, 6 (02) : 193 - 225
  • [6] Nonlinear multiscale decompositions:: The approach of A.!Harten
    Aràndiga, F
    Donat, R
    [J]. NUMERICAL ALGORITHMS, 2000, 23 (2-3) : 175 - 216
  • [7] CATMULL EE, 1978, COMPUT AIDED DESIGN, V19, P350
  • [8] CHAIKIN GM, 1974, COMPUT GRAPHICS IMAG, V3, P346
  • [9] Quasilinear subdivision schemes with applications to ENO interpolation
    Cohen, A
    Dyn, N
    Matei, B
    [J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2003, 15 (02) : 89 - 116
  • [10] Normal multiresolution approximation of curves
    Daubechies, I
    Runborg, O
    Sweldens, W
    [J]. CONSTRUCTIVE APPROXIMATION, 2004, 20 (03) : 399 - 463
123