<title>Application of deconvolution to images from the EGRET gamma-ray telescope</title>

The EGRET gamma-ray telescope has left a legacy of unidentified astronomical sources. Most likely, many of the galactic plane sources will be rotation-powered pulsars. Firm identification has been difficult, given the instrument's poor spatial resolution. The problem is exacerbated by the energy dependant Point Spread Function (PSF) and low numbers of source counts. The main method of identifying sources to-date has been a maximum likelihood method. We have taken a different approach, namely that of regularized deconvolution with a spatially invariant PSF, which is used in optical astronomy and medical X-ray imaging. This technique revealed that wavelet denoising of residuals produced smooth, relatively artefact-free images with improved spatial location. Our source location using standard centroiding produced an improvement in relative spatial location, ranging from 10:1 to 2:1 proportional to source strength. Wavelet deconvolution simultaneously achieves background smoothing, while improving sharpness of the resolved objects. The photon-sparse nature of these images makes them an ideal test bed for such techniques. Although deconvolution does not ordinarily conserve flux, in this instance the flux determination is unaffected in all but the most crowded regions. Finally, we show that the energy dependent PSF can be used to identify objects with a restricted range of energy spectra