Level-dependent interpolatory Hermite subdivision schemes and wavelets
This work advances the theoretical understanding of level-dependent multiresolution analyses for Hermite data, which is relevant for applications in signal and image processing.
The paper studies level-dependent Hermite subdivision schemes that preserve polynomial and exponential data, and derives a result on the decay of associated multiwavelet coefficients for uniformly continuous and differentiable functions using a generalized Taylor formula.
We study many properties of level-dependent Hermite subdivision, focusing on schemes preserving polynomial and exponential data. We specifically consider interpolatory schemes, which give rise to level-dependent multiresolution analyses through a prediction-correction approach. A result on the decay of the associated multiwavelet coefficients, corresponding to a uniformly continuous and differentiable function, is derived. It makes use of the approximation of any such function with a generalized Taylor formula expressed in terms of polynomials and exponentials.