Ghosts in tomography – the null space of the radon transform

Let ω 0 , …, ω p −1 ϵ S 1 be p distinct directions and let R denote the Radon transform. The functions f with support in the unit disc and with Rf ( s , ω j ) = 0 for s ϵ [−1, 1] and j = 0, …, p − 1 are given. „Ghosts” are constructed, i.e. functions in the null space that pretend not existent tumors. Methods to avaoid such ghosts are indicated.