In fan-beam tomography an x-ray source moves on a circle around the object that is to be imaged. The emitted x-rays are attenuated when passing through the object and an image of the interior of the object is computed from measurements of these attenuated x-rays. The most often used reconstruction method is the standard filtered backprojection algorithm. While having been very successful in many applications, it has nevertheless a number of drawbacks, including poor performance when the radius of the source circle is relatively small. A straightforward derivation of a related algorithm is presented that largely remedies this and other drawbacks.
Furthermore, it is shown that the corresponding pi-line based algorithm performs even better for small source radius.