Transmission-Like Calibration-Free Tomographic Reconstruction With Compton-Scattered Photons

Image-reconstruction with Compton-scattered photons is a nonlinear problem, because it involves both the linear process of scattering and the exponential pre- and post-scatter attenuation. For thin and light objects and with high-energy photons, the exponential terms can be ignored, rendering the problem linear. We show that when attenuation is significant, linearity can also be accomplished by considering scattering as a scaling factor and with subsequent logarithmic transformation, the image-reconstruction problem is converted into a transmission-like problem along the travel lines of incident and scattered radiation. It is shown that this formulation produces images qualitatively reflecting object features in a manner similar to that of backprojection in conventional computed tomography. This is done without the need for calibration or scaling of measurements. The theoretical aspects of the introduced mathematical formulation are developed for idealized pencil-beams, adapted approximately to fan-beam configurations, and applied to imaging with laboratory-acquired measurements. The introduced transmission-like formulation and calibration-free aspects should promote wider use of scatter imaging.