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

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.

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References in corpus (6)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Spherical Needlets for CMB Data Analysis
• Spectral estimation on a sphere in geophysics and cosmology
• A detection of the integrated Sachs-Wolfe imprint of cosmic superstructures using a matched-filter approach
• Determining the depth of Jupiter's Great Red Spot with Juno: a Slepian approach
• Fast directional spatially localized spherical harmonic transform