The Farey map exploited in wavelet analysis -- Construction of an associated Farey mother wavelet
Sabrine Arfaoui, Riadh Chteoui, Anouar Ben Mabrouk

TL;DR
This paper introduces a new mother wavelet derived from the Farey map, with properties suitable for analyzing hyperbolic problems like PDEs, expanding wavelet analysis tools.
Contribution
It constructs a novel Farey map-based mother wavelet and establishes its key properties for potential application in hyperbolic PDE analysis.
Findings
The wavelet satisfies admissibility and moment conditions.
It has a valid 2-scale relation and reconstruction rule.
Potential for analyzing hyperbolic PDEs.
Abstract
In the present work the well known Farey map is exploited to consruct a new mother wavelet. Properties such as admissibility, moments, 2-scale relation and reconstruction rule have been established. The constructed mother may be a good candidate to analyze hyperbolic problems such as hyperbolic PDEs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsImage and Signal Denoising Methods · Mathematical Analysis and Transform Methods · Advanced Image Fusion Techniques
