SUPERRESOLUTION IN PATTERN-RECOGNITION AND IMAGE-RESTORATION PROBLEMS

The problem of limiting resolving power for blurred images is considered in the framework of image restoration and pattern recognition approaches. Both inner (photon) and external (background) types of noise are taken into account, as well as smoothing by any imaging system. The exact form of the most powerful test for distinguishing alternative initial objects is found. As a consequence the pattern recognition approach gives the desired dependence of the minimum detectable separation rho(min) between components of a double source on object flux, point spread function (PSF), background level and reliability of recognition. The exact expression for rho(min) can be accurately approximated by a simple power law. The limiting resolving power attained by an efficient image restoration method is somewhat less than with the pattern recognition approach. It has been shown by numerical simulations that both limits are quite close one to another. The expected and real limiting resolving power of the Hubble Space Telescope (HST) are calculated as an illustration of the derived relations. Due to the sharp core of the HST PSF the resolution of the telescope drops only by a few times for relatively bright objects (m(B)<25), but is much worse for fainter objects.