The filtered backprojection algorithm is probably the most often used reconstruction algorithm in 2D-computerized tomography. For a semi-discrete version in the parallel scanning geometry we
prove optimal L2-convergence rates for density distributions in Sobolev spaces. The key to success is a new representation of the filtered backprojection which enables us to apply techniques from approximation theory. Our analysis
provides further a modification of the Shepp-Logan reconstruction filter with an improved convergence behavior. Numerical experiments in the fully discrete setting reproduce the theoretical predictions.
Copyright. All Rights Reserved.