Wavelets for $L^2(B(0,1))$ using Zernike polynomials
Functional Analysis
2025-07-24 v2
Abstract
A set of orthogonal polynomials on the unit disk known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of This naturally leads to a multiresolution analysis of Previously, other authors have dealt with the one dimensional case, and used orthogonal polynomials of a single variable to construct time localized bases for polynomial subspaces of an -space with arbitrary weight. Due to the nature of Zernike polynomials, the wavelet construction given here is well-suited for the analysis of two-dimensional signals defined on circular domains. This is shown by some experimental results done on corneal data.
Cite
@article{arxiv.2405.08129,
title = {Wavelets for $L^2(B(0,1))$ using Zernike polynomials},
author = {Somantika Datta and Kanti B. Datta},
journal= {arXiv preprint arXiv:2405.08129},
year = {2025}
}