Coherent imaging has a wide range of applications in, for example, microscopy, astronomy, and radar imaging. Particularly interesting is the field of microscopy, where the optical quality of the lens is the main limiting factor. In this article, novel algorithms for the restoration of blurred images in a system with known optical aberrations are presented. Physically motivated by the scalar diffraction theory, the new algorithms are based on Haugazeau POCS and FISTA, and are faster and more robust than methods presented earlier. With the new approach the level of restoration quality on real images is very high, thereby blurring and ringing caused by defocus can be effectively removed. In classical microscopy, lenses with very low aberration must be used, which puts a practical limit on their size and numerical aperture. A coherent microscope using the novel restoration method overcomes this limitation. In contrast to incoherent microscopy, severe optical aberrations including defocus can be removed, hence the requirements on the quality of the optics are lower. This can be exploited for an essential price reduction of the optical system. It can be also used to achieve higher resolution than in classical microscopy, using lenses with high numerical aperture and high aberration. All this makes the coherent microscopy superior to the traditional incoherent in suited applications.