Correlated point processes in radiological imaging

A variety of problems in radiological imaging can be formulated in terms of point processes, which are random processes where every sample function is a sum of delta functions. Under certain postulates, especially one relating to statistical independence of the points, the first- and second-order statistics of the process are well known. This paper treats correlated point processes where the postulates are not satisfied. The main kinds of correlation considered result from randomness in the radiation source and image amplification. Expressions are given for the mean, the autocorrelation and autocovariance functions and, in the stationary approximation, the power spectral density.