Regularity of generalized Daubechies wavelets reproducing exponential polynomials
arXiv:1210.793825 citationsh-index: 43
Originality Synthesis-oriented
AI Analysis
Provides theoretical smoothness guarantees for a class of wavelets used in signal processing and numerical analysis, but the result is incremental as it extends known regularity bounds to a non-stationary setting.
The paper proves that non-stationary orthogonal wavelets reproducing exponential polynomials have the same regularity as classical Daubechies wavelets, with explicit smoothness estimates.
We investigate non-stationary orthogonal wavelets based on a non-stationary interpolatory subdivision scheme reproducing a given set of exponentials. The construction is analogous to the construction of Daubechies wavelets using the subdivision scheme of Deslauriers-Dubuc. The main result is the smoothness of these Daubechies type wavelets.