Two Finite Inverse Hilbert Transform Formulae for Region-of-Interest Tomography

Recently we published two explicit formulae for finite inverse Hilbert transforms [You and Zeng, Inv Probl 22 (2006), L7-L101]. This paper presents a straightforward proof of the formulae, the data requirements, and some computer simulations to verify the formulae. Examples of region-of-interest tomography using truncated projections and the first formula of the finite inverse Hilbert transform are shown