Task classes favoring Fourier-Bessel or dyadic frequency organization

Determine the classes of tasks for which the approximately linear radial frequency organization of Fourier-Bessel wavelets or the dyadic frequency organization of conventional wavelets is preferable.

Background

The paper develops Fourier-Bessel wavelets whose radial frequencies are determined by Neumann eigenvalues of the disk and are approximately linearly spaced, in contrast to the dyadic scale organization used by conventional wavelets and Solid Harmonics. Preliminary experiments indicate flatter frequency coverage for Fourier-Bessel filter banks in the tested configurations, but the notes do not establish that linear spacing is generally superior. The authors explicitly leave unresolved which classes of applications benefit from either frequency organization, particularly given that dyadic scaling may be advantageous for tasks such as image classification while approximately uniform frequency coverage may be useful for reconstruction-oriented tasks.