Wavelet-domain modeling and estimation of Poisson processes

This paper develops a new wavelet-domain Bayesian framework for modeling and estimating the intensity of a Poisson process directly from count observations. A new multiscale, multiplicative innovations model is developed as a prior for the underlying intensity function. The new prior model leads to a simple and efficient closed-form estimator that requires O(N) computations, where N is the dimension of the intensity function. We compare the new method with previously proposed wavelet-based approaches to this problem.