UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Author: search.filters.author.Weinberg, Daniel EricSubject: search.filters.subject.Directional Representations

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    Multiscale and Directional Representations of High-Dimensional Information Content in Remotely Sensed Data
    (2015) Weinberg, Daniel Eric; Czaja, Wojciech; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This 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.