On the recovery of a function on a circular domain

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dc.contributor.authorPawlak, M
dc.contributor.authorLiao, SX
dc.date.accessioned2007-09-07T18:59:06Z
dc.date.available2007-09-07T18:59:06Z
dc.date.issued2002-10-31T18:59:06Z
dc.description.abstractWe consider the problem of estimating a function f (x, y) on the unit disk {(x, y): x(2) -l- y(2) less than or equal to 1}, given a discrete and noisy data recorded on a regular square grid. An estimate of f (x, y) based on a class of orthogonal and complete functions over the unit disk is proposed. This class of functions has a distinctive property of being invariant to rotation of axes about the origin of coordinates yielding therefore a rotationally invariant estimate. For radial functions, the orthogonal set has a particularly simple form being related to the classical Legendre polynomials. We give the statistical accuracy analysis of the proposed estimate of f (x, y) in the sense of the L-2 metric. It is found that there is an inherent limitation in the precision of the estimate due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to the celebrated problem in the analytic number theory called the lattice points of a circle. In fact, the obtained bounds for the mean integrated squared error are determined by the best known result so far on the problem of lattice points within the circular domain.en
dc.format.extent735115 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.citation0018-9448; IEEE TRANS INFORM THEORY, OCT 2002, vol. 48, no. 10, p.2736 to 2753.en
dc.identifier.doihttp://dx.doi.org/10.1109/TIT.2002.802627
dc.identifier.urihttp://hdl.handle.net/1993/2790
dc.language.isoengen_US
dc.rights©2002 IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Manitoba's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.en
dc.rightsrestricted accessen_US
dc.statusPeer revieweden
dc.subjectaccuracyen
dc.subjectcircle orthogonal polynomialsen
dc.subjectcircle problemen
dc.subjectcircular domainen
dc.subjectlattice pointsen
dc.subjectnonparametric estimateen
dc.subjectradial functionsen
dc.subjectrotational invarianceen
dc.subjecttwo-dimensional (2-D) functionsen
dc.subjectZernike functionsen
dc.subjectIMAGE-ANALYSISen
dc.subjectZERNIKE MOMENTSen
dc.subjectRECONSTRUCTIONen
dc.subjectRECOGNITIONen
dc.subjectREPRESENTATIONen
dc.subjectPOLYNOMIALSen
dc.titleOn the recovery of a function on a circular domainen
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