Multiscale analysis for intensity and density estimation

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dc.contributor.advisorNowak, Robert D.
dc.creatorWillett, Rebecca M.
dc.date.accessioned2009-06-04T08:26:25Z
dc.date.available2009-06-04T08:26:25Z
dc.date.issued2002
dc.description.abstractThe nonparametric multiscale polynomial and platelet algorithms presented in this thesis are powerful new tools for signal and image denoising and reconstruction. Unlike traditional wavelet-based multiscale methods, these algorithms are both well suited to processing Poisson and multinomial data and capable of preserving image edges. At the heart of these new algorithms lie multiscale signal decompositions based on polynomials in one dimension and multiscale image decompositions based on platelets in two dimensions. This thesis introduces platelets, localized atoms at various locations, scales and orientations that can produce highly accurate, piecewise linear approximations to images consisting of smooth regions separated by smooth boundaries. Polynomial- and platelet-based maximum penalized likelihood methods for signal and image analysis are both tractable and computationally efficient. Simulations establish the practical effectiveness of these algorithms in applications such as medical and astronomical, density estimation, and networking; statistical risk bounds establish the theoretical near-optimality of these algorithms.
dc.format.extent86 p.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS E.E. 2002 WILLETT
dc.identifier.citationWillett, Rebecca M.. "Multiscale analysis for intensity and density estimation." (2002) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/17563">https://hdl.handle.net/1911/17563</a>.
dc.identifier.urihttps://hdl.handle.net/1911/17563
dc.language.isoeng
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.
dc.subjectElectronics
dc.subjectElectrical engineering
dc.titleMultiscale analysis for intensity and density estimation
dc.typeThesis
dc.type.materialText
thesis.degree.departmentElectrical Engineering
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science
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