Applied Sampling and Reconstruction of Signals on the Sphere
type: CreativeWork
description: Signals collected with spherical geometry appear in a large number and diverse range of real-world applications in various disciplines, such as geophysics, medical imaging, computer graphics, wireless communications and acoustics. This thesis focuses on the development of signal processing techniques for sampling and reconstruction of signals on the sphere. The objective of developing new spherical signal measurement and reconstruction techniques is driven by meeting the practical requirements of applications where signals are inherently defined on the sphere. The first part of this thesis develops novel sampling schemes on the sphere for the applications of measuring and reconstructing the head-related transfer function (HRTF) in acoustics and the diffusion signal in diffusion magnetic resonance imaging (dMRI). In contrast to existing sampling schemes in the literature, the developed schemes attain the optimal number of samples, equal to the degrees of freedom in spherical harmonic space, while enabling computation of the spherical harmonic transform (SHT) to near machine precision accuracy. In addition, the proposed sampling schemes have computationally efficient algorithms for the computation of the SHT and are designed to satisfy all the practical requirements of their applications. The proposed scheme for HRTF measurement and reconstruction has non-dense sampling near the poles and is iso-latitude, allowing for the measurements to be more easily obtained. Furthermore, the proposed scheme can be configured as fully hierarchical which enables the HRTF to be analyzed at all frequencies in the audible range using the same arrangement of speakers (or microphones). Numerical experiments and simulations are conducted to demonstrate the reconstruction accuracy of the proposed sampling scheme. Two sampling schemes are proposed for the measurement and reconstruction of the diffusion signal in dMRI which exploit the antipodal symmetry of the diffusion signal in the spatia…
abstract: Signals collected with spherical geometry appear in a large number and diverse range of real-world applications in various disciplines, such as geophysics, medical imaging, computer graphics, wireless communications and acoustics. This thesis focuses on the development of signal processing techniques for sampling and reconstruction of signals on the sphere. The objective of developing new spherical signal measurement and reconstruction techniques is driven by meeting the practical requirements of applications where signals are inherently defined on the sphere. The first part of this thesis develops novel sampling schemes on the sphere for the applications of measuring and reconstructing the head-related transfer function (HRTF) in acoustics and the diffusion signal in diffusion magnetic resonance imaging (dMRI). In contrast to existing sampling schemes in the literature, the developed schemes attain the optimal number of samples, equal to the degrees of freedom in spherical harmonic space, while enabling computation of the spherical harmonic transform (SHT) to near machine precision accuracy. In addition, the proposed sampling schemes have computationally efficient algorithms for the computation of the SHT and are designed to satisfy all the practical requirements of their applications. The proposed scheme for HRTF measurement and reconstruction has non-dense sampling near the poles and is iso-latitude, allowing for the measurements to be more easily obtained. Furthermore, the proposed scheme can be configured as fully hierarchical which enables the HRTF to be analyzed at all frequencies in the audible range using the same arrangement of speakers (or microphones). Numerical experiments and simulations are conducted to demonstrate the reconstruction accuracy of the proposed sampling scheme. Two sampling schemes are proposed for the measurement and reconstruction of the diffusion signal in dMRI which exploit the antipodal symmetry of the diffusion signal in the spatia…
author: Bates, Alice P.
language: en
keywords: Spherical signal processing, signal processing, unit sphere, 2 sphere
date published: 2016
date modified: 2026-07-24T01:07:45Z
provider: Australian Catholic University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Australian Catholic University

PropertyValue
property ID: Handle
value: http://hdl.handle.net/1885/116981