Wavelet-based signal modeling and processing algorithms with applications

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dc.contributor.advisorNowak, Robert D.en_US
dc.creatorWan, Yien_US
dc.date.accessioned2009-06-04T08:17:52Zen_US
dc.date.available2009-06-04T08:17:52Zen_US
dc.date.issued2003en_US
dc.description.abstractGood signal representation and the corresponding signal processing algorithms lie at the heart of the signal processing research effort. Since the 1980's wavelet analysis has become more and more a mature tool in many applications such as image compression due to some key advantages over the traditional Fourier analysis. In this thesis we first develop a wavelet-based statistical framework and an efficient algorithm for solving the linear inverse problems with application to image restoration. The result is an efficient method that produces state-of-the-art results for such problems and has potential further applications in other areas. To overcome the issues such as the blocking artifacts in using orthogonal wavelets, we next investigate the design issue of more flexible basis representations based on frames. In particular, we develop a quasi image rotation method that is based on pixel reassignment and hence retains the original image statistics. When combined with translation operators, this method provides very efficient and desirable frames for image processing. Given a frame, due to the large number of redundant basis functions in it, how to efficiently implement a frame-based algorithm is the key issue. We show this through the example of optimal signal denoising in the presence of added zero-mean white noise. We show that the optimal solution exists yet the computation toward the solution is very heavy. We develop a framework that allows for fast approximations to the optimal solution and has clear physical interpretation. This method is in essence different from the other various approximate approaches such the basis pursuit and has applications in other areas such as image segmentation. We also develop a complexity regularized iterative algorithm for getting sparse solutions to the frame-based signal denoising problem.en_US
dc.format.extent79 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS E.E. 2003 WANen_US
dc.identifier.citationWan, Yi. "Wavelet-based signal modeling and processing algorithms with applications." (2003) Diss., Rice University. <a href="https://hdl.handle.net/1911/18577">https://hdl.handle.net/1911/18577</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/18577en_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.subjectElectronicsen_US
dc.subjectElectrical engineeringen_US
dc.titleWavelet-based signal modeling and processing algorithms with applicationsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentElectrical Engineeringen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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