Generalized discrete Radon transforms and their use in the ridgelet transform

We introduce and study anew 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.