A family of π-scheme exponential Radon transforms and the uniqueness of their inverses

We propose a family of pi-scheme exponential Radon transforms (ERTs) of an object function, which characterize the data functions that arise in pi-scheme single-photon emission computed tomography (SPELT) with uniform attenuation. Single-interval 180 acquisition in SPELT can be interpreted as a special case of the proposed pi-scheme SPELT. We show the existence and uniqueness of the inverse pi-scheme ERT and provide an iterative algorithm for obtaining the object function from the pi-scheme ERT. Numerical results in our simulation studies confirm the mathematical results.