Notes on Fourier-Bessel wavelets
These notes develop the mathematical foundations and construction of a Fourier-Bessel wavelet family inspired by the disk harmonics of Shaqfa et al.[9]. We begin with the relevant properties of Bessel and modified Bessel functions and introduce the wavelet properties required for the construction. We then derive the Fourier-Bessel disk harmonics as solutions to the Helmholtz equation on the unit disk subject to a Neumann boundary condition. Building on this basis, we construct a wavelet family by applying a Gaussian spatial envelope and introducing a zero-mean correction for the zeroth angular order. We derive the corresponding normalisation constants for $L^2$-based applications and disc...
| Authors | Marcel Venturotti, Georgios Exarchakis |
|---|---|
| Primary category | cs.LG |
| Published | 22 September 2026 |
| Last updated at source | 22 September 2026 |
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