Integral Transforms and Signal Processing on the 2-Sphere

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dc.contributor.authorRudoy, Daniel
dc.date2023-05-17T00:49:50.000
dc.date.accessioned2023-05-22T12:53:07Z
dc.date.available2023-05-22T12:53:07Z
dc.date.issued2002-07-08
dc.date.submitted2007-06-22T10:40:22-07:00
dc.description.abstractThis paper is concerned with the group-theoretical background of integral transforms and the role they play in signal processing on the sphere. An overview of topological groups, measure and representation theories, and an overview of the Windowed Fourier Transform and the Continuous Wavelet Transform are presented. A group-theoretical framework within which these transforms arise is presented. The connection between integral transforms and square-integrable group representations is explored. The theory is also generalized beyond groups to homogeneous spaces. The abstract theory is then applied to signal processing on the sphere with a discussion of both global and local methods. A detailed derivation of the continuous spherical harmonic transform is presented. Global methods such as the spherical Fourier transform and convolution are presented in an appendix as well as some background material from group theory and topology.
dc.description.commentsUniversity of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-02-20.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/7077
dc.legacy.articleid1177
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1177&context=cis_reports&unstamped=1
dc.source.issue175
dc.source.journalTechnical Reports (CIS)
dc.source.statuspublished
dc.titleIntegral Transforms and Signal Processing on the 2-Sphere
dc.typeReport
digcom.identifiercis_reports/175
digcom.identifier.contextkey317123
digcom.identifier.submissionpathcis_reports/175
digcom.typereport
dspace.entity.typePublication
upenn.schoolDepartmentCenterTechnical Reports (CIS)
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