TY - JOUR
AU1 - Gérot, Cédric
AB - When a subdivision scheme is factorised into lifting steps, it admits an in–place and invertible implementation, and it can be the predictor of many multiresolution biorthogonal wavelet transforms. In the regular setting where the underlying lattice hierarchy is defined by ℤ
s
and a dilation matrix M, such a factorisation should deal with every vertex of each subset in ℤ
s
/Mℤ
s
in the same way. We define a subdivision scheme which admits such a factorisation as being uniformly elementary factorable. We prove a necessary and sufficient condition on the directions of the Box spline and the arity of the subdivision for the scheme to admit such a factorisation, and recall some known keys to construct it in practice.
TI - Elementary factorisation of Box spline subdivision
JF - Advances in Computational Mathematics
DO - 10.1007/s10444-018-9612-x
DA - 2018-06-05
UR - https://www.deepdyve.com/lp/springer-journals/elementary-factorisation-of-box-spline-subdivision-4hID0xEO0h
SP - 153
EP - 171
VL - 45
IS - 1
DP - DeepDyve