Directional, Shift-Insensitive, Complex Wavelet Transforms with Controllable Redundancy

dc.citation.bibtexNamephdthesisen_US
dc.citation.journalTitlePh.D. Thesisen_US
dc.citation.locationHouston, TXen_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.creatorFernandes, Felixen_US
dc.date.accessioned2007-10-31T00:43:40Zen_US
dc.date.available2007-10-31T00:43:40Zen_US
dc.date.issued2001-08-20en_US
dc.date.modified2003-08-02en_US
dc.date.submitted2003-08-20en_US
dc.descriptionPhD Thesisen_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 decoupled 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 <i>any</i> 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 <sup>(3^m - 1)</sup>/<sub>(2^m - 1)</sub> in <i>m</i> 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.identifier.citation "Directional, Shift-Insensitive, Complex Wavelet Transforms with Controllable Redundancy," <i>Ph.D. Thesis,</i> 2001.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19878en_US
dc.language.isoengen_US
dc.subjectcomplex wavelet transforms directionality shift invariance phase non-redundanten_US
dc.subject.keywordcomplex wavelet transforms directionality shift invariance phase non-redundanten_US
dc.subject.otherWavelet based Signal/Image Processingen_US
dc.titleDirectional, Shift-Insensitive, Complex Wavelet Transforms with Controllable Redundancyen_US
dc.typeThesisen_US
dc.type.dcmiTexten_US
thesis.degree.levelDoctoralen_US
Files
Original bundle
Now showing 1 - 2 of 2
Loading...
Thumbnail Image
Name:
Fer2001Aug3Direction.PDF
Size:
2.53 MB
Format:
Adobe Portable Document Format
No Thumbnail Available
Name:
Fer2001Aug3Direction.PS
Size:
8 MB
Format:
Postscript Files