Non-stationary noise characteristics for SPECT images

A theoretical formulation for characterization of SPECT (single photon emission computed tomography) image noise for a filtered-backprojection reconstructed image was derived. The formulation takes into account all segments of the reconstruction process including the effects of discrete filtering and backprojection as well as nonstationarity in both the projection data and the reconstructed image. It allows calculations of the local noise properties of a reconstructed image in the spatial and frequency domains. This facilitates studies of nonstationary image noise. The formulation was validated by comparing the local autocovariance matrix and noise power spectrum calculated using the theoretical formulation with these quantities calculated from an ensemble of 12000 reconstructed images. The assumption of stationarity for SPECT reconstructed images is examined. The results show that SPECT image noise is nonstationary over large uniform regions, except near the center of the uniform region and over small regions of interest near image edges.<>