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dc.contributor.advisorCzaja, Wojciechen_US
dc.contributor.authorWeinberg, Daniel Ericen_US
dc.date.accessioned2015-09-18T06:01:53Z
dc.date.available2015-09-18T06:01:53Z
dc.date.issued2015en_US
dc.identifierhttps://doi.org/10.13016/M2W93Z
dc.identifier.urihttp://hdl.handle.net/1903/17103
dc.description.abstractThis thesis explores the theory and applications of directional representations in the field of anisotropic harmonic analysis. Although wavelets are optimal for decomposing functions in one dimension, they are unable to achieve the same success in two or more dimensions due to the presence of curves and surfaces of discontinuity. In order to optimally capture the behavior of a function at high-dimensional discontinuities, we must be able to incorporate directional information into our analyzing functions, in addition to location and scale. Examples of such representations are contourlets, curvelets, ridgelets, bandelets, wedgelets, and shearlets. Using directional representations, in particular shearlets, we tackle several challenging problems in the processing of remotely sensed data. First, we detect roads and ditches in LIDAR data of rural scenes. Second, we develop an algorithm for superresolution of optical and hyperspectral data. We conclude by presenting a stochastic particle model in which the probability of movement in a particular direction is neighbor-weighted.en_US
dc.language.isoenen_US
dc.titleMultiscale and Directional Representations of High-Dimensional Information Content in Remotely Sensed Dataen_US
dc.typeDissertationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentMathematicsen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledApplied Harmonic Analysisen_US
dc.subject.pquncontrolledDirectional Representationsen_US
dc.subject.pquncontrolledPhototaxisen_US
dc.subject.pquncontrolledRemote Sensingen_US
dc.subject.pquncontrolledRoad Detectionen_US
dc.subject.pquncontrolledSuperresolutionen_US


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