A phase-sensitive method for filtering on the sphere
This work addresses filtering challenges in spherical data processing, which is incremental as it builds on existing harmonic analysis methods.
The paper tackled the problem of filtering on a sphere by analyzing spherical harmonic magnitude and phase, showing that phase is more important for structure, and proposed a method to construct finite-impulse-response filters with properties like associativity and directional filtering, providing examples for spherical and manifold data.
This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the properties of linear phase shifts in the spherical harmonic domain, which suggest a mechanism for constructing finite-impulse-response (FIR) filters. We show that those filters have desirable properties, such as being associative, mapping spherical functions to spherical functions, allowing directional filtering, and being defined by relatively simple equations. We provide examples of the filters for both spherical and manifold data.