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.

Date Published: 26 September 2013
PDF: 13 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88580L (26 September 2013); doi: 10.1117/12.2023932

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)