Model asymmetrical detector response function with a skew normal distribution function in PET

Abstract

In PET image reconstruction, a point-spread-function (PSF) in the form of normal distribution is commonly used to model the detector response function. The PSF becomes asymmetrical off the center of the field-of-view. This effect has been modeled with dual-half normal distribution functions with different standard deviations on the left and right side. This method is subject to unequal noise in the estimated parameters between the two half normal distribution, due to the difference in the number of data points for asymmetrical PSF. In this work, we present a skew normal distribution that includes a standard deviation and a skewness parameter to model the asymmetrical detector response function using both sides of the data profile. The skew normal distribution model noticeably improves the goodness of fit to the raw data over the dual-half normal distribution model by an average of 44% in sum of squared differences, thus giving more reliable estimation of the PSF.