Decomposition and reconstruction algorithms for spline wavelets on a bounded interval (Q1331824)

The authors describe new decomposition and reconstruction algorithms for spline wavelets on a bounded interval. The algorithms are based on the observation that for a bounded interval, it is possible to perform both decomposition and reconstruction by computing with finite banded matrices. Divided in 6 parts (Introduction, Construction of spline wavelets for \(L^ 2[0,1]\), The decomposition algorithm, The reconstruction algorithm, An improved decomposition algorithm and Numerical examples) this paper is richly illustrated (7 figures and 3 tables). A comparative analysis of some comparable methods: Daubechies, linear spline wavelets (boundary case and real axis), cubic spline wavelets (boundary case and real axis) is made.