On an integral transform and its inverse in nuclear imaging

In a nuclear imaging modality, the goal is to reconstruct the object under study from photon intensity distributions on a detector. However, photon scattering, mainly as a consequence of the Compton effect, considerably affects the image quality of the object. This is why most image reconstruction methods operate only with primary or non-scattered photons. Nevertheless the restored image remains noisy and weak in intensity. In this paper a new relation between the object and photon intensity distributions, generated by photons scattered at various deflection angles is established. It takes the form of an integral transform, compounded from Fourier and Hankel transforms. Most importantly this new transformation is invertible . As a result a novel principle for image reconstruction using scattered photons is derived and may lead to the conception of a new type of imaging device.