Generalized Discrete Radon Transforms and Their Use in the Ridgelet Transform

Authors:
Flavia Colonna;Glenn Easley
Affiliations:
George Mason University, Fairfax;System Planning Corporation, Arlington
Venue:
Journal of Mathematical Imaging and Vision
Year:
2005

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Abstract

We introduce and study a new class of Radon transforms in a discrete setting for the purpose of applying them to the ridgelet and curvelet transforms. We give a detailed analysis of the p-adic case and provide a closed-form formula for an inverse of the p-adic Radon transform. We give conditions for a scaled version of the generalized discrete Radon transform to yield a tight frame, and discuss a direct Radon matrix method for the implementation of a local ridgelet transform. We then study the effectiveness of some types of the generalized Radon transforms in reducing a type of noise known as speckle that is present in synthetic aperture radar (SAR) imagery.