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Multiscale Optimal Filtering on the Sphere

Aslam, Adeem; Khalid, Zubair; McEwen, Jason D; (2021) Multiscale Optimal Filtering on the Sphere. IEEE Signal Processing Letters , 28 pp. 394-398. 10.1109/LSP.2021.3056236. Green open access

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Abstract

We present a framework for the optimal filtering of spherical signals contaminated by realizations of an additive, zero-mean, uncorrelated and anisotropic noise process on the sphere. Filtering is performed in the wavelet domain given by the scale-discretized wavelet transform on the sphere. The proposed filter is optimal in the sense that it minimizes the mean square error between the filtered wavelet representation and wavelet representation of the noise-free signal. We also present a simplified formulation of the filter for the case when azimuthally symmetric wavelet functions are used. We demonstrate the use of the proposed optimal filter for denoising of an Earth topography map in the presence of additive, zero-mean, uncorrelated and white Gaussian noise, and show that the proposed filter performs better than the hard thresholding method and weighted spherical harmonic (weighted-SPHARM) signal estimation framework.

Type: Article
Title: Multiscale Optimal Filtering on the Sphere
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/LSP.2021.3056236
Publisher version: https://doi.org/10.1109/LSP.2021.3056236
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions
Keywords: Wavelet domain, Estimation, Harmonic analysis, Discrete wavelet transforms, Power harmonic filters, Filtering, Additives
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Space and Climate Physics
URI: https://discovery.ucl.ac.uk/id/eprint/10198359
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