Tomographic Back-Projection Algorithm for 'Incomplete' Compton X-Rays Detectors.

A 'Compton' detector finds the direction of an X-ray by letting it interact with a gaseous, liquid or thin solid material (Tracker) and employing no collimators. This paper takes into account the case of an 'incomplete' solid Tracker where the recoiling electron travels only a few dozen microns and cannot be followed. However, impact positions and incoming and outgoing energies are measured. In this situation, exploiting the Compton Scattering formula, one is only able to identify a cone whose surface the X-ray belongs to. On the other hand, Compton tomography luckily requires only a few views (for example rotating the apparatus in just four positions around the subject), as the 'electronic collimation' that takes place in each position already extracts X-rays coming from many directions. A back-projection algorithm that combines the reconstructed 'cones' in space, weighed according to the Klein-Nishina formula, has been applied to the special case of small animal SPECT (Single Photon Emission Computed Tomography). Here the source is close to the detector, every imaged point in space is calculated from many rays that are emitted at different angles, and the algorithm totally differs from that of the Compton imaging in Astronomy. Tomography reconstruction has been validated by employing simulated data, generated using GEANT4 that includes the Doppler Broadening in the energies of scattered photons, which is due to moving non-free electrons. Space resolution has been assessed. [ABSTRACT FROM AUTHOR]