The effect of linear interpolation of the filtered projections on image noise in x-ray computed tomography

Measured values for image noise variance in x-ray computed tomography were found to be less than half of the values predicted by published formulas. This phenomenon had previously been attributed qualitatively to the use of linear interpolation of the filtered projections in the back projection process. An analysis of the reconstruction process has allowed the derivation of a formula for image noise variance which incorporates the effect of this interpolation, giving results which are less than 50% of the previously predicted values. This formula has been tested with images of a perspex rod produced by an x-ray microtomography scanner and with a similar image derived from mathematically modeled projection data. The predicted noise variance was within 1% of the measured values for both the simulated and the experimental data.