On azimuthally symmetric 2-sphere convolution

Authors:
Rodney A. Kennedy;Tharaka A. Lamahewa;Liying Wei
Affiliations:
Research School of Engineering, CECS, The Australian National University, Canberra, ACT, Australia;Research School of Engineering, CECS, The Australian National University, Canberra, ACT, Australia and Canberra Research Laboratories, National ICT Australia, Australia;Research School of Engineering, CECS, The Australian National University, Canberra, ACT, Australia
Venue:
Digital Signal Processing
Year:
2011

Citing 6
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Abstract

We consider the problem of azimuthally symmetric convolution of signals defined on the 2-Sphere. Applications of such convolution include but are not limited to: geodesy, astronomical data (such as the famous Wilkinson Microwave Anisotropy Probe data), and 3D beamforming/sensing. We review various definitions of convolution from the literature and show a nontrivial equivalence between different definitions. Some convolution formulations based on SO(3) are shown not to be well formed for applications and we demonstrate a simpler framework to understand, use and generalize azimuthally symmetric convolution.