Regularization methods in image restoration: An application to HST images

The mathematic problem of restoring an image degraded by blurring and noise is ill-posed, so that the solution is affected by numeric instability. As a consequence, the solution provided by the so-called inverse filter is completely contaminated by noise and, in general, is deprived of any physical meaning. If one looks for approximate solutions, the ill-posedness of the problem implies that the set of these solutions is too broad. For this reason, one must look for approximate solutions satisfying some kind of a priori constraints, the so-called a priori information. This fact explains the variety of methods, usually called regularization methods, which have been designed for solving this kind of problems. In this article we briefly review some of the most widely used methods, both deterministic and probabilistic, and show their effectiveness in the restoration of some HST images. (C) 1995 John Wiley & Sons, Inc.