Various methods have been proposed to restore images acquired by the Hubble Space Telescope (HST). Many of these techniques rely on prior knowledge of the telescope's point-spread function (PSF). However, as noted by R. White (White 1993),
Most HST deconvolutions are carried out using observed PSFs, because theoretically computed PSFs (using Tiny TIM software, for example) are usually not a very good match to the observations. The noise in observed PSFs presents a problem, however: when using a noisy PSF, the restoration algorithm ought to account for the fact that both the image and the PSF are noisy.This problem - the simultaneous estimation of both the object and the PSF - has been referred to as blind deconvolution. Unfortunately, the naive application of a blind deconvolution procedure to HST data will surely lead to difficulties since the trivial solution in which the PSF is estimated as a point or impulse and the object is estimated as the data will produce a perfect match to the data. Therefore, some type of constraints must be used to avoid both this solution and the equally trivial one in which the object is estimated as a point source and the PSF is estimated as the data.
For a related problem in ground-based astronomy, Schulz (1993) has recently proposed a technique for processing a sequence of images degraded by turbulence-induced phase errors. With this technique, the trivial solutions mentioned in the previous paragraph are avoided by using the prior knowledge that the point-spread functions are determined by phase errors distributed across the telescope's aperture. In this paper, this approach is used to derive an image restoration technique applicable to data acquired by the HST.