The Range of Projection Pair Operators

Tomographic techniques have become a vital tool in medicine, allowing doctors to observe patients' features. Modeling the measurement process are so-called projection operators that integrate functions with weights along certain curves. These  are usually subdivided into individual projections, the integration operators associated with specific curves (usually representing certain measurement steps).  Characterization of the range of projection operators (particularly ones involving only finitely many projections) has found various practical applications in the context of tomography. A first step in determining a  projection operator's range is to consider projection pair operators (consisting of only two projections). Naturally, properties of the range of those projection pair operators impose properties on larger projection operators' range. Hence, we discuss the characterization of general projection pair operators' ranges, and our findings' consequences for specific operators.