chapter  10
32 Pages

Wavelets and Local Tomography

WithCarlos A. Berenstein, David F. Walnut

In this paper, formulas relating the Radon transform and Radon transform inversion to various wavelet and multiscale transformations, including the continuous wavelet transform, the semi-continuous wavelet transform of Mallat, steerable multiscale filters of Freeman and Adelson, and separable orthogonal and nonorthogonal wavelet bases, are given. The use of wavelets as a valuable tool in the local inversion of the Radon transform in even dimensions is justified, and explicit estimates on the decay of ramp-filtered wavelets is given.