Adv Comput Math https://doi.org/10.1007/s10444-018-9612-x Cedric ´ Ger ´ ot Received: 22 March 2017 / Accepted: 20 April 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract 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 multires- olution biorthogonal wavelet transforms. In the regular setting where the underlying lattice hierarchy is defined by Z and a dilation matrix M, such a factorisation should s s deal with every vertex of each subset in Z /MZ in the same way. We define a sub- division 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. Keywords Box spline · Subdivision scheme · Biorthogonal filter bank · Elementary factorisation · Lifting scheme Mathematics Subject Classification (2010) 65D17 · 65D07 · 65T50 · 42C40 · 15A23 · 13P25 Communicated by: Tom Lyche This work has been partially done during a visit at the School of Engineering
Advances in Computational Mathematics – Springer Journals
Published: Jun 5, 2018
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