Wavelet shrinkage estimation has been found to be a powerful tool for the n
on-parametric estimation of spatially variable phenomena. Most work in this
area to date has concentrated primarily on the use of wavelet shrinkage te
chniques in contexts where the data are modeled as observations of a signal
plus additive, Gaussian noise. In this paper, I introduce an approach to e
stimating intensity functions for a certain class of "burst-like" Poisson p
rocesses using wavelet shrinkage. The proposed method is based on the shrin
kage of wavelet coefficients of the original count data, as opposed to the
current approach of pre-processing the data using Anscombe's square root tr
ansform and working with the resulting data in a Gaussian framework. "Corre
cted" versions of the usual Gaussian-based shrinkage thresholds are used. T
he corrections explicitly account for effects of the first few cumulants of
the Poisson distribution on the tails of the coefficient distributions. A
large deviations argument is used to justify these corrections. The perform
ance of the new method is examined, and compared to that of the pre-process
ing approach, in the context of an application to an astronomical gamma-ray
burst signal.