Article thumbnail

Multiscale and Directional Representations of High-Dimensional Information Content in Remotely Sensed Data

By Daniel Eric Weinberg


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

Topics: Mathematics, Applied Harmonic Analysis, Directional Representations, Phototaxis, Remote Sensing, Road Detection, Superresolution
Publisher: 'Wiley'
Year: 2015
DOI identifier: 10.13016/M2W93Z
OAI identifier:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.