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Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 344270 Total View: 3164396
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
ArticleOpen Access http://dx.doi.org/10.26855/jamc.2025.03.008

Computing the Inversion of the Finite Hilbert Transform with Spline Wavelets

Bo Yu*, Leqi Dai

College of Science, China Three Gorges University, Yichang 443002, Hubei, China.

*Corresponding author:Bo Yu

Published: April 21,2025

Abstract

The inversion of the finite Hilbert transform has a wide range of applications in different fields such as medical imaging and signal processing. However, there remains a notable scarcity of effective algorithms for implementing this inversion. Until recently, an interesting fast algorithm for computing the inversion of the finite Hilbert transform by B-splines was developed by B. Yu et al. in 2024. Since B-spline wavelets have many good properties as those of the B-spline itself, for example, the smoothness, the decay, and the vanishing moments, a natural question is: Is it possible to develop a fast algorithm to calculate the inversion of the finite Hilbert transform based on the fast spline wavelet transform? This paper gives a positive answer to this question. Some examples are given in numerical experiments listing  L2-norm error and L-norm error, and these examples show that the method proposed in this paper has faster computation speed and higher computational accuracy compared to previous results, especially in the  L-norm error.

Keywords

Inversion of the finite Hilbert transform; Spline wavelets; Fast algorithms

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How to cite this paper

Computing the Inversion of the Finite Hilbert Transform with Spline Wavelets

How to cite this paper: Bo Yu, Leqi Dai. (2025) Computing the Inversion of the Finite Hilbert Transform with Spline Wavelets. Journal of Applied Mathematics and Computation9(1), 57-65.

DOI: http://dx.doi.org/10.26855/jamc.2025.03.008