A simplified analysis for predicting the relative performance of tomographic filters

The technique of computerized tomography is being studies extensively by engineers, physicists and mathematicians to improve the quality of reconstructed images. Certain error estimates are available for the errors occuring in various tomographic algorithms under the assumption that the ogject cross-section possesses band-limited projection data. It is known, however, that the cross-section function has a finite support, and hence cannot be band-limited. A Sobolev space analysis has already been reported involving certain errror estimates for predicting the inherent error in the convolution backprojection algorithm. The present study is an attempt towards developing a simplified two-dimensional Cartesian formula for predicting the comparative performance to the Fourier filters used in the convolution algorithm. This simplified approach involves the Laplacian of the object function and the second-order (Fourier space) derivates of the filter functions.