Quantitatively accurate data recovery from attenuation-corrected sinogram using filtering of sinusoidal trajectory signals

The statistical distribution of PET measurements precorrected for the effects of attenuation and accidental coincidences is no longer described by the Poisson model and is characterized by increased variance and positive skewness. These attributes affect the quantitative accuracy of the reconstructed image. In this study, we create a numerical cylinder phantom and simulate the attenuation-correction effect by adding highly overdispersed non-stationary noise accommodated by the negative binomial distribution. Further on, we use the novel stackgram domain environment to decompose the sinogram into a collection of constituting sinusoidal trajectory signals. The goal is to investigate the quantitative behaviour of various estimators on finding the underlying activity of attenuation-corrected 1D signals in stackgram domain. We devise a challenging wavelet-based approach to this problem which rests on signal decomposition with rescaled analysis filter bank. Comparative simulation results show that our method is capable of eliminating spurious noise variations without causing any systematical bias, unlike more simple smoothing estimators.