Restoration of three dimensional microscopic images using the row action projection method

Three dimensional (3-D) microscopy is widely used in medical applications and biosciences where a high quality magnified image of a specimen is desired. The 3-D object or specimen which is placed under the microscope is sectioned at regular intervals to acquire a sequence of two dimensional (2-D) images. These images are blurred by in-focus and out-of-focus information due to the finite circular aperture of the microscope. We use a 3-D reflecting microscope that has a high numerical aperture (to keep the blurring effect reduced) and at the same time, provides unity magnification and a large field of view. The microscope consists of two large diameter concave mirrors that face each other and share a common optical axis. We mathematically formulate the blurring effect on the 2D images and use the row action projection (RAP) method to remove the blur. With this set of 2-D clean images, one can use any visualization software to create a 3-D view of the object. Experimental results show that this method yields a very good performance and is computationally feasible.