An improved deprojection and PSF-deconvolution technique for   galaxy-cluster X-ray surface-brightness profiles
  We have developed a regularisation procedure for the direct deprojection and PSF-deconvolution of X-ray surface brightness profiles of clusters of galaxies. This procedure allows us to obtain accurate density profiles in a straightforward manner from X-ray observations (in particular data from XMM-Newton, where the PSF correction is important), while retaining information about substructure in the gas distribution, in contrast to analytic modelling of the profiles. In addition to describing our procedure, we present here a detailed investigation of the accuracy of the method and its error calculations over a wide range of input profile characteristics and data quality using Monte Carlo simulations. We also make comparisons with gas density profiles obtained from Chandra observations, where the PSF correction is small, and with profiles obtained using analytic modelling, which demonstrate that our procedure is a useful improvement over standard techniques. This type of method will be especially valuable in the ongoing analysis of unbiased and complete samples of X-ray clusters, both local and distant, helping to improve the quality of their results. 
J.H. Croston, M. Arnaud, E. Pointecouteau, G.W. Pratt