The mathematics of Computed Tomography (CT) and Positron Emission Tomography (PET) medical imaging is based on inverting the Radon transform. The Radon transform is a linear, smoothing operator, so its inverse, while linear, is unbounded, and the presence of noise (especially for PET imaging) makes applying this inverse problematic. David Donoho introduced Wavelet Shrinkage applied to Wavelet-Vaguelette decompositions to solve this problem. This talk describes how Donoho's method can be cast in a variational framework, how to choose the scaling of shrinkage parameters, and gives experimental results that compare our method with the so-far standard method, Filtered Back Projection.
Copyright. All Rights Reserved.