A new method for improving the resolution of astronomical images is presented. It is based on the principle that sampled data cannot be fully deconvolved without violating the sampling theorem. Thus, the sampled image should not be deconvolved by the total Point Spread Function, but by a narrower function chosen so that the resolution of the deconvolved image is compatible with the adopted sampling. Our deconvolution method gives results which are, in at least some cases, superior to those of other commonly used techniques: in particular, it does not produce ringing around point sources superimposed on a smooth background. Moreover, it allows to perform accurate astrometry and photometry of crowded fields. These improvements are a consequence of both the correct treatment of sampling and the recognition that the most probable astronomical image is not a flat one. The method is also well adapted to the optimal combination of different images of the same object, as can be obtained, e.g., from infrared observations or via adaptive optics techniques.

22 pages, LaTex file + 10 color jpg and postscript figures. To be published in ApJ, Vol 484 (1997 Feb.)