Inversion of a V-line transform arising in emission tomography

Image reconstruction in several tomographic modalities relies on the inversion of the V-line Radon transform. This transform integrates a function of interest along V-shaped trajectories. Depending on the tomographic method, the measured data consists of a subset of these integrals. Thus, in order to recover the function of interest, a restricted V-line Radon transform has to be inverted. In this paper we present a close form inversion formula for the two-dimensional V-line transform with vertices restricted to a detector array. No additional restrictions on the V-lines are posed, which allows for integrating redundant data. This results in good handling of noisy measurements. A numerical implementation of the formula and the results from numerical simulations are discussed.