Noise in ML-EM reconstruction of SPECT images with attenuation correction

The authors derive a closed form expression for the pixel variance in the iterative ML-EM reconstruction of a uniform circular source embedded in a uniformly attenuating circular object. The derivation includes both the photon noise in the projection data and the noise in the attenuation map used for attenuation correction. The variance is found to increase with the number of iterations, but converges to a finite value. The noise to signal ratio at convergence is the sum of two terms which correspond to the contributions from the photon noise in the projection data and the attenuation map noise. The noise component due to the photon noise varies inversely with the total number of detected counts in the projection data. The relative variance at infinite iterations is similar in magnitude to that obtained for the filtered backprojection algorithm. The component due to attenuation map noise is proportional to the relative variance of the attenuation coefficient in the attenuation map. These observations are consistent with the results of the authors' previous computer simulation and experimental studies.