Joint SO(3)-Spectral Domain Filtering of Spherical Signals in the Presence of Anisotropic Noise

TL;DR

This paper introduces a novel joint SO(3)-spectral domain filtering method using DSLSHT for enhancing spherical signals contaminated by anisotropic noise, achieving optimal noise reduction and signal estimation.

Contribution

The work develops an optimal filter in the joint SO(3)-spectral domain for anisotropic noise removal on spherical signals, with a least-square solution for source signal estimation.

Findings

Effective noise suppression demonstrated on Earth topography data

Outperforms existing joint spatial-spectral filtering methods

Achieves minimum mean square error in signal estimation

Abstract

We present a joint SO(3)-spectral domain filtering framework using directional spatially localized spherical harmonic transform (DSLSHT), for the estimation and enhancement of random anisotropic signals on the sphere contaminated by random anisotropic noise. We design an optimal filter for filtering the DSLSHT representation of the noise-contaminated signal in the joint SO(3)-spectral domain. The filter is optimal in the sense that the filtered representation in the joint domain is the minimum mean square error estimate of the DSLSHT representation of the underlying (noise-free) source signal. We also derive a least-square solution for the estimate of the source signal from the filtered representation in the joint domain. We demonstrate the capability of the proposed filtering framework using the Earth topography map in the presence of anisotropic, zero-mean, uncorrelated Gaussian noise, and compare its performance with the joint spatial-spectral domain filtering framework.