Achieving uniform noise in direct fan-beam CT reconstruction through bowtie filter design

This work concerns the standard deviation of computed tomography (CT) images reconstructed with the classical direct fan-beam FBP algorithm using noisy data taken over a full scan. We show how a suitable modification of the bowtie filter shape can yield reconstructions with relatively uniform noise profiles. These findings are supported with standard deviation profiles estimated with Monte Carlo Poisson noise simulations which incorporate the effects of the bowtie filter. In particular, we demonstrate that the standard deviation profile can be made nearly uniform by adding just one parameter to the description of the bowtie filter, and then optimizing this parameter. This result is shown to be robust to changes in the apodization of the ramp filter kernel as well as to changes in the noise level.