Image Restoration Using Gradient Iteration and Constraints for Band Extrapolation

Images obtained with optical microscopes are often blurred and corrupted by noise. Specially in wide-field microscopy, there is a strong out-of-focus blur in focal plane direction, caused mainly by a frequency loss in the acquisition process. In order to restore these images it is important to use non-linear methods and relevant prior knowledge as constraints. In this paper, we propose a projection onto convex sets framework using a sequence of prototype images inspired by the Richardson–Lucy iterative algorithm. Within this framework it is possible to use constraints while restoring the image, during the iterations. We prove that the iterative method can be implemented as a gradient iteration, followed by a sequence of projections onto constraint sets. Moreover, we performed experiments using the techniques in order to improve restoration. The results showed a better restoration of frequencies, an improved focal plane restoration and a better contrast when compared with the regular iterative restoration algorithm.