Directional, shift-insensitive, complex wavelet transforms with controllable redundancy
| dc.contributor.advisor | Burrus, C. Sidney | |
| dc.creator | Fernandes, Felix Carlos A. | |
| dc.date.accessioned | 2009-06-04T08:48:05Z | |
| dc.date.available | 2009-06-04T08:48:05Z | |
| dc.date.issued | 2002 | |
| dc.description.abstract | Although 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. | |
| dc.format.extent | 144 p. | en_US |
| dc.format.mimetype | application/pdf | |
| dc.identifier.callno | THESIS E.E. 2002 FERNANDES | |
| dc.identifier.citation | Fernandes, 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>. | |
| dc.identifier.uri | https://hdl.handle.net/1911/18077 | |
| dc.language.iso | eng | |
| dc.rights | Copyright 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.subject | Electronics | |
| dc.subject | Electrical engineering | |
| dc.title | Directional, shift-insensitive, complex wavelet transforms with controllable redundancy | |
| dc.type | Thesis | |
| dc.type.material | Text | |
| thesis.degree.department | Electrical Engineering | |
| thesis.degree.discipline | Engineering | |
| thesis.degree.grantor | Rice University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy |
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