The Multiplicative Zak Transform, Dimension Reduction, and Wavelet Analysis of LIDAR Data

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dc.contributor.advisorBenedetto, John Jen_US
dc.contributor.advisorCzaja, Wojciechen_US
dc.contributor.authorFlake, Justin Christopheren_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2010-10-07T05:59:10Z
dc.date.available2010-10-07T05:59:10Z
dc.date.issued2010en_US
dc.description.abstractThis thesis broadly introduces several techniques within the context of timescale analysis. The representation, compression and reconstruction of DEM and LIDAR data types is studied with directional wavelet methods and the wedgelet decomposition. The optimality of the contourlet transform, and then the wedgelet transform is evaluated with a valuable new structural similarity index. Dimension reduction for material classification is conducted with a frame-based kernel pipeline and a spectral-spatial method using wavelet packets. It is shown that these techniques can improve on baseline material classification methods while significantly reducing the amount of data. Finally, the multiplicative Zak transform is modified to allow the study and partial characterization of wavelet frames.en_US
dc.identifier.urihttp://hdl.handle.net/1903/10889
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledApplied Mathematicsen_US
dc.subject.pquncontrolledDimension Reductionen_US
dc.subject.pquncontrolledFramesen_US
dc.subject.pquncontrolledLIDARen_US
dc.subject.pquncontrolledMultiplicative Zaken_US
dc.subject.pquncontrolledWaveletsen_US
dc.titleThe Multiplicative Zak Transform, Dimension Reduction, and Wavelet Analysis of LIDAR Dataen_US
dc.typeDissertationen_US

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