Reconstruction of Image from Simple Back Projection

Reference: http://www.dspguide.com/ch25/5.htm
A basic problem in imaging with x-rays (or other penetrating radiation) is that a two-dimensional image is obtained of a three-dimensional object. This means that structures can overlap in the final image, even though they are completely separate in the object. This is particularly troublesome in medical diagnosis where there are many anatomic structures that can interfere with what the physician is trying to see. During the 1930's, this problem was attacked by moving the x-ray source and detector in a coordinated motion during image formation. From the geometry of this motion, a single plane within the patient remains in focus, while structures outside this plane become blurred. This is analogous to a camera being focused on an object at 5 feet, while objects at a distance of 1 and 50 feet are blurry. These related techniques based on motion blurring are now collectively called classical tomography. The word tomography means "a picture of a plane."