ERROR ANALYSIS OF TOMOGRAPHIC FILTERS .1. THEORY

The technique of computerized tomography is being studied extensively by engineers, physicists and mathematicians to improve the quality of reconstructed images. Certain error estimates are available for the er rors occurring in various tomographic algorithms under the assumption that the object cross-section possesses band-limited projection data. It is known, however, that the cross-section function has a finite sup port, and hence cannot be band-limited. A Sobolev space analysis has a lready been reported involving certain error estimates for predicting the inherent error in the convolution backprojection algorithm. The pr esent study is an attempt towards developing a simplified two-dimensio nal Cartesian formula for predicting the comparative performance of th e Fourier filters used in the convolution algorithm. This simplified a pproach involves the Laplacian of the object function and the second-o rder (Fourier space) derivatives of the filter functions.