Wavelets for approximate Fourier transform and data compression

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dc.contributor.advisorBurrus, C. Sidneyen_US
dc.creatorGuo, Haitaoen_US
dc.date.accessioned2009-06-04T08:35:59Zen_US
dc.date.available2009-06-04T08:35:59Zen_US
dc.date.issued1997en_US
dc.description.abstractThis dissertation has two parts. In the first part, we develop a wavelet-based fast approximate Fourier transform algorithm. The second part is devoted to the developments of several wavelet-based data compression techniques for image and seismic data. We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The classical Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. The main advantage of our algorithm is that the good time and frequency localization of wavelets can be exploited to approximate the Fourier transform for many classes of signals, resulting in much less computation. Thus the new algorithm provides an efficient complexity versus accuracy tradeoff. When approximations are allowed, under certain sparsity conditions, the algorithm can achieve linear complexity, i.e. O(N). The proposed algorithm also has built-in noise reduction capability. For waveform and image compression, we propose a novel scheme using the recently developed Burrows-Wheeler transform (BWT). We show that the discrete wavelet transform (DWT) should be used before the Burrows-Wheeler transform to improve the compression performance for many natural signals and images. We demonstrate that the simple concatenation of the DWT and BWT coding performs comparably as the embedded zerotree wavelet (EZW) compression for images. Various techniques that significantly improve the performance of our compression scheme are also discussed. The phase information is crucial for seismic data processing. However, traditional compression schemes do not pay special attention to preserving the phase of the seismic data, resulting in the loss of critical information. We propose a lossy compression method that preserves the phase as much as possible. The method is based on the self-adjusting wavelet transform that adapts to the locations of the significant signal components. The elegant method of embedded zerotree wavelet compression is modified and incorporated into our compression scheme. Our method can be applied to both one dimensional seismic signals and two dimensional seismic images.en_US
dc.format.extent88 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS E.E. 1997 GUOen_US
dc.identifier.citationGuo, Haitao. "Wavelets for approximate Fourier transform and data compression." (1997) Diss., Rice University. <a href="https://hdl.handle.net/1911/19164">https://hdl.handle.net/1911/19164</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19164en_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.subjectGeophysicsen_US
dc.subjectElectronicsen_US
dc.subjectElectrical engineeringen_US
dc.titleWavelets for approximate Fourier transform and data compressionen_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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