Super-resolution via iterative phase retrieval for blurred and saturated biological images

One of the most fascinating problems addressed today is retrieving high-resolution data of blurred images obtained from biological objects. In most cases the research relays either on a priory knowledge of the image nature or a large number of images (either of the same object or of different objects obtained by the same imaging setup). If saturation is added to the blurring, most algorithms fail to sharpen the image and in some cases researchers decline to use such images as an input. In this work a single captured blurred and saturated image is given with no a priori knowledge except of the fact that the primary blurring is due to defocused imaging setup. The authors suggest a novel three-stage approach for retrieving higher resolution data from the intensity distribution of the blurred and saturated image. The core of the process is the phase retrieval algorithm suggested by Gerchberg and Saxton in 1972. The new method is explained in details and the algorithm is tested numerically and experimentally on several images to show the improvement in the sharpness of the spatial details.