Noise in reconstructed images in tomography parallel, fan and cone beam projections

A principle source of noise in X-ray and emission computer tomography is at the detectors that measure the projection of the object. The noise can be approximated by additive, signal-independent white Gaussian statistics by ignoring the negligible effects of scattering and diffraction of the source beam. The back-projection filter that is used significantly alters power spectral density of the noise, such that the back-projected noise at each reconstructed point is no longer white. However, to effectively restore the reconstructed image using maximum a posteriori techniques via mean field annealing (MFA), a reasonable estimate of the autocorrelation of the back-projected noise is necessary. This work derives the autocorrelation and power spectra of the reconstructed noise for parallel, fan, and cone beam projections and also shows some preliminary results of MFA restorations