Directional, shift-insensitive, complex wavelet transforms with controllable redundancy

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dc.contributor.advisorBurrus, C. Sidneyen_US
dc.creatorFernandes, Felix Carlos A.en_US
dc.date.accessioned2009-06-04T08:48:05Zen_US
dc.date.available2009-06-04T08:48:05Zen_US
dc.date.issued2002en_US
dc.description.abstractAlthough the Discrete Wavelet Transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages. First, the DWT is shift sensitive because input-signal shifts generate unpredictable changes in DWT coefficients. Second, the DWT suffers from poor directionality because DWT coefficients reveal only three spatial orientations. Third, DWT analysis lacks the phase information that accurately describes non-stationary signal behavior. To overcome these disadvantages, we introduce the notion of projection-based complex wavelet transforms. These two-stage, projection-based complex wavelet transforms consist of a projection onto a complex function space followed by a DWT of the complex projection. Unlike other popular transforms that also mitigate DWT shortcomings, the decou pled implementation of our transforms has two important advantages. First, the controllable redundancy of the projection stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, non-redundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and non-redundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. We exploit this flexibility to create the Complex Double-density DWT (CDDWT): a shift-insensitive, directional, complex wavelet transform with a low redundancy of 3m-12m-1 in m dimensions. To the best of our knowledge, no other transform achieves all these properties at a lower redundancy. Besides the mitigation of DWT shortcomings, our transforms have unique properties that will potentially benefit a variety of signal processing applications. As an example, we demonstrate that our projection-based complex wavelet transforms achieve state-of-the-art results in a seismic signal-processing application.en_US
dc.format.extent144 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS E.E. 2002 FERNANDESen_US
dc.identifier.citationFernandes, Felix Carlos A.. "Directional, shift-insensitive, complex wavelet transforms with controllable redundancy." (2002) Diss., Rice University. <a href="https://hdl.handle.net/1911/18077">https://hdl.handle.net/1911/18077</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/18077en_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.titleDirectional, shift-insensitive, complex wavelet transforms with controllable redundancyen_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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