Image processing via undecimated wavelet systems

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dc.contributor.advisorWells, Raymond O., Jr.en_US
dc.creatorZhang, Huipinen_US
dc.date.accessioned2009-06-04T08:41:35Zen_US
dc.date.available2009-06-04T08:41:35Zen_US
dc.date.issued2000en_US
dc.description.abstractWe have studied undecimated wavelet transforms and their applications in image denoising. Because of the redundancy of the undecimated wavelet transform, the inversion scheme which implements the Moore-Penrose inverse of the forward transform makes undecimated wavelet systems have excellent performance in signal denoising. We propose an image denoising algorithm that prunes the complete undecimated discrete wavelet packet binary tree to select the best basis. Since we believe discarding the small coefficients permits to choose the best basis from the set of coefficients that will really contribute to the reconstructed image, we propose to select the best basis based on the thresholded wavelet coefficients rather than the original ones. We also propose an exponential decay model for autocorrelations of undecimated wavelet coefficients of real-world images. This is a model that captures the dependency of wavelet coefficients within a scale. With this model we present a parametric solution for FIR Wiener filtering in the undecimated wavelet domain. The persistence property of wavelet coefficients indicates strong dependency across scales. To capture the persistence of UDWT we propose an extension of the wavelet-domain hidden Markov tree model (HMT). By introducing the concept of composite coefficient, we simplify the general coefficient graph to be a tree-structure graph which is very suitable for training to obtain the HMT model parameters. This Bayesian framework allows us to formulate the image denoising problem as computing the posterior estimate.en_US
dc.format.extent100 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. 2000 ZHANGen_US
dc.identifier.citationZhang, Huipin. "Image processing via undecimated wavelet systems." (2000) Diss., Rice University. <a href="https://hdl.handle.net/1911/19574">https://hdl.handle.net/1911/19574</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19574en_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.subjectMathematicsen_US
dc.subjectStatisticsen_US
dc.subjectElectronicsen_US
dc.subjectElectrical engineeringen_US
dc.titleImage processing via undecimated wavelet systemsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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