Methods for analyzing certain signals and images in astronomy using Haar wavelets

There are a number of signal and image analysis problems in high-energy astrophysics for which wavelet-based denoising methods seem particularly appropriate. These problems typically are characterized by photon counting often at low levels. As a result, care is needed in choosing thresholds that adequately account for the Poisson nature of the noise; simple adaptation of typical Gaussian-based methods usually oversmooths peaks and other sharp structures. The author present a method for denoising Poisson signals and images which contain a sparse structure amid a relatively diffuse background, using Haar wavelets. The method is a variant of the standard wavelet shrinkage algorithm, with appropriately calibrated thresholds, and is implemented in a translation-invariant fashion. The performance of this method is demonstrated using astrophysical data collected on board NASA's Compton Gamma-Ray Observatory.