  This contribution deals with image restoration in optical systems with
coherent illumination, which is an important topic in astronomy, coherent
microscopy and radar imaging. Such optical systems suffer from wavefront
distortions, which are caused by imperfect imaging components and conditions.
Known image restoration algorithms work well for incoherent imaging, they fail
in case of coherent images. In this paper a novel wavefront correction
algorithm is presented, which allows image restoration under coherent
conditions. In most coherent imaging systems, especially in astronomy, the
wavefront deformation is known. Using this information, the proposed algorithm
allows a high quality restoration even in case of severe wavefront distortions.
We present two versions of this algorithm, which are an evolution of the
Gerchberg-Saxton and the Hybrid-Input-Output algorithm. The algorithm is
verified on simulated and real microscopic images.
