On a C2-nonlinear subdivision scheme avoiding Gibbs oscillations
For researchers in signal/image processing and numerical analysis, this scheme solves the long-standing trade-off between Gibbs artifact removal and smoothness in subdivision schemes.
This paper presents a new nonlinear subdivision scheme that eliminates Gibbs oscillations near discontinuities while achieving limit functions with Hölder regularity index larger than 1.192 (numerically estimated as 2.438). It is the first scheme to simultaneously control Gibbs phenomenon and maintain regularity above 1.
This paper is devoted to the presentation and the analysis of a new nonlinear subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence, stability and order of approximation are analyzed. It is proved that this schemes converges towards limit functions of Hölder regularity index larger than 1.192. Numerical estimates provide an Hölder regularity index of 2.438. Up to our knowledge, this scheme is the first one that achieves simultaneously the control of the Gibbs phenomenon and regularity index larger than 1 for its limit functions.