Analytic noise-propagation in indirect fan-beam FBP reconstruction

Precise knowledge of the local image noise is an essential ingredient to efficient application of post-processing methods such as wavelet or diffusion filtering to computed tomography (CT) images. The non-stationary, object dependent nature of noise in CT images is a direct result from the noise present in the projection data. Since quantum and electronics noise are the dominating noise sources, comparably simple models can be used for direct noise estimates in the individual projections. In this article, we describe the analytic propagation of these noise estimates through fan-beam filtered backprojection (FBP) reconstruction. Contrary to earlier publications in this field, we include the correlations within the parallel projections resulting from the rebinning, the convolution, and the backprojection processes. The method has been validated against Monte-Carlo results and good accuracy with an average relative error below 3.6% was achieved for arbitrary objects and over the full range of commonly used convolution kernels and field-of-view settings.