TY - JOUR
T1 - On a Nonlinear 4-Point Ternary and Interpolatory Multiresolution Scheme Eliminating the Gibbs Phenomenon
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 261
EP - 280
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/719.html
KW - Nonlinear ternary subdivision scheme, regularity, nonlinear multiresolution, stability, Gibbs phenomenon, signal processing.
AB - <p style="text-align: justify;">A nonlinear ternary 4-point interpolatory subdivision scheme is
presented. It is based on a nonlinear perturbation of the ternary subdivision
scheme studied in Hassan M.F., Ivrissimtzis I.P., Dodgson N.A. and Sabin M.A.
(2002): &quot;An interpolating 4-point ternary stationary subdivision scheme&quot;, Comput.
Aided Geom. Design, 19, 1-18. The convergence of the scheme and the
regularity of the limit function are analyzed. It is shown that the Gibbs phenomenon,
classical in linear schemes, is eliminated. The stability of the associated
nonlinear multiresolution scheme is established. Up to our knowledge, this is
the first interpolatory scheme of regularity larger than one, avoiding Gibbs oscillations
and for which the stability of the associated multiresolution analysis
is established. All these properties are very important for real applications.</p>