Nonparametric estimation of intensity maps using Haar wavelets and Poissonnoise characteristics

We present a method for the nonparametric (model-free) estimation of an int ensity map underlying two-dimensional count data with Poisson noise charact eristics. Specifically, we extend the so-called TIPSH (translation invarian t Poisson smoothing using Haar wavelets) methodology, which was formulated for denoising Poisson time series data in the context of gamma-ray bursts. In addition to the obvious extension of TIPSH to the two-dimensional contex t of image data, the primary contribution of this paper is in showing the e xtreme generality under which exact thresholding may be done when using the Haar transform. This generality allows for the efficient evaluation of arb itrarily complex models for observed data within a multiscale framework. Th is latter characteristic has played a critical role in a recent analysis of EGRET data which provided strong evidence for anomalous large-scale emissi on in high-energy gamma-rays (the so-called gamma-ray halo). Here we concen trate on describing the derails of the new thresholding scheme as well as e xploring the results of a number of simulation studies.