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Radon transforms on circular arcs and Compton scatter tomography

Compton scatter tomography (CST) is an imaging process which is based on the exploitation of Compton scattering. Current imaging processes such as the X-ray scanner or Computed Tomography (CT), the Single Photon Emission Computed Tomography (SPECT) or the Positron Emission Tomography (PET), use the properties of rectilinear propagation of radiation in matter (attenuation and emission). Their common mathematical basis is the classical Radon transform (along straight lines in the plane). We show that three modalities of CST require Radon tranforms on arcs of circle in the plane and derive explicit inversion formulas. This opens the way to their implementation as new possible investigative methods for medical and industrial applications.

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