Theoretical understanding of Compton scattering-based reconstruction-free anatomical imaging method

A reconstruction-free anatomical imaging algorithm that localizes the Compton scattering of annihilation $\gamma$ rays within an object using ultrafast time-of-flight information and provides an anatomical cross-section image without tomographic reconstruction has been previously proposed. However, the spatial performance of generated images remains unclear. This study introduces a theoretical understanding and supporting simulation results of a Compton scattering-based reconstruction-free anatomical imaging method. First, we provide the exact algebraic solution, which was solved approximately in a previous study. Using the algebraic solution, the system performance can be quantitatively estimated via total differentiation. Total differentiation indicated that the difference in the path lengths of annihilation $\gamma$ rays, which can be theoretically interpreted as the Compton scattering angle in an object strongly impacting the spatial resolution of the anatomical image. Monte Carlo simulations demonstrated that the spatial resolution of the generated images is improved by selecting events with large Compton scattering angles, which is consistent with the theory derived based on the algebraic solution. Furthermore, the use of energy information helped enhance the image quality by eliminating multiple scattering events in the imaging object.