Spatio-spectral Formulation and Design of Spatially-Varying Filters for Signal Estimation on the 2-Sphere

TL;DR

This paper introduces an optimal spatio-spectral filter for signal estimation on the 2-sphere, effectively handling anisotropic noise and signal properties by leveraging localized spherical harmonic transforms.

Contribution

It develops a novel joint spatio-spectral filtering framework for signals on the 2-sphere, improving estimation accuracy in anisotropic noise conditions.

Findings

The filter is optimal under mean-square error criterion.

Demonstrated effectiveness with an example involving anisotropic noise.

Enhances signal estimation by considering anisotropic properties.

Abstract

In this paper, we present an optimal filter for the enhancement or estimation of signals on the 2-sphere corrupted by noise, when both the signal and noise are realizations of anisotropic processes on the 2-sphere. The estimation of such a signal in the spatial or spectral domain separately can be shown to be inadequate. Therefore, we develop an optimal filter in the joint spatio-spectral domain by using a framework recently presented in the literature --- the spatially localized spherical harmonic transform --- enabling such processing. Filtering of a signal in the spatio-spectral domain facilitates taking into account anisotropic properties of both the signal and noise processes. The proposed spatio-spectral filtering is optimal under the mean-square error criterion. The capability of the proposed filtering framework is demonstrated with by an example to estimate a signal corrupted by an anisotropic noise process.