Some uniqueness theorems for a conical Radon transform

The conical Radon transform, which assigns to a given function $f$ on $\mathbb R^3$ its integrals over conical surfaces, arises in several imaging techniques, e.g. in astronomy and homeland security, especially when the so-called Compton cameras are involved. In many practical situations we know this transform only on a subset of its domain. In these situations, it is a natural question what we can say about $f$ from partial information. In this paper, we investigate some uniqueness theorems regarding a conical Radon transform.