An asymptotic minimax analysis of nonlocal means on edges

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dc.contributor.advisorBaraniuk, Richard G.en_US
dc.creatorNarayan, Manjarien_US
dc.date.accessioned2013-03-08T00:37:05Zen_US
dc.date.available2013-03-08T00:37:05Zen_US
dc.date.issued2012en_US
dc.description.abstractThis thesis analyzes the non-local means denoising algorithm using the criterion of minimax optimality from statistical decision theory. We show that nonlocal means is minimax suboptimal on images with smooth discontinuities [1] with a rate of convergence of [Special characters omitted.] ( n -1 ) comparable to that of wavelet thresholding. The suboptimality is a consequence of the isotropic nature of the algorithm, and its inability to adapt to the smoothness of the discontinuity. However, all is not lost for nonlocal methods. We also propose an anisotropic nonlocal means algorithm [2] that can attain the optimal rate of [Special characters omitted.] ( n -4/3 ) as well as deliver superior denoising performance using image gradients on synthetic and empirical images, respectively. Nonlocal means is an instance of exemplar based image processing methods. This result broadly implies that exemplar methods that respect anisotropy can yield superior performance in estimating edges in both theory and practice.en_US
dc.format.extent76 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS E.E. 2012 NARAYANen_US
dc.identifier.citationNarayan, Manjari. "An asymptotic minimax analysis of nonlocal means on edges." (2012) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/70368">https://hdl.handle.net/1911/70368</a>.en_US
dc.identifier.digitalNarayanMen_US
dc.identifier.urihttps://hdl.handle.net/1911/70368en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectApplied sciencesen_US
dc.subjectApplied mathematicsen_US
dc.subjectElectrical engineeringen_US
dc.titleAn asymptotic minimax analysis of nonlocal means on edgesen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentElectrical Engineeringen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Musicen_US
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