Angular multiselectivity with spherical wavelets

TL;DR

This paper introduces directional spherical wavelets with adaptive angular selectivity, enabling detailed analysis of spherical signals by capturing various directional features, a novel approach for spherical data analysis.

Contribution

It presents the first construction of spherical wavelets with multiselectivity and adaptive angular sensitivity, extending multiscale analysis techniques to spherical signals.

Findings

Developed spherical wavelets with directional and adaptive properties

Proposed a multiselectivity scheme for spherical signals

Enabled detailed feature extraction from spherical data

Abstract

We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of real images, ranging from highly directional to fully isotropic ones, was quite intensively studied for the case of signals over the Euclidean space. However, the present paper is the first attempt to deal with this task in the case of spherical signals. A multiselectivity scheme, similar to that proposed for $\mathbb R^2$-functions, is presented.