SKELLAMSHRINK: POISSON INTENSITY ESTIMATION FOR VECTOR-VALUED DATA

Owing to the stochastic nature of discrete processes such as photon counts in imaging, a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of interest. Certain wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts, taking in the simplest case the so-called Skellam distribution. We show that a Skellam mean estimator provides a Poisson intensity estimation method based on shrinkage of filterbank coefficients, and a means of estimating the risk of any Skellam mean estimator is derived in closed form under a frequentist model.