A Parametric Family of Polynomial Wavelets for Signal and Image Processing
Journal:
arXiv
Published Date:
Mar 16, 2025
Abstract
This paper investigates the potential applications of a parametric family of
polynomial wavelets that has been recently introduced starting from de la
Vall\'ee Poussin (VP) interpolation at Chebyshev nodes. Unlike classical
wavelets, which are constructed on the real line, these VP wavelets are defined
on a bounded interval, offering the advantage of handling boundaries naturally
while maintaining computational efficiency. In fact, the structure of these
wavelets enables the use of fast algorithms for decomposition and
reconstruction. Furthermore, the flexibility offered by a free parameter allows
a better control of localized singularities, such as edges in images. On the
basis of previous theoretical foundations, we show the effectiveness of the VP
wavelets for basic signal denoising and image compression, emphasizing their
potential for more advanced signal and image processing tasks.
