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

Recently we published two explicit formulae for finite inverse Hilbert transforms [You, J and Zeng, GL, 2006]. 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 (ROI) tomography using truncated projections and the first formula of the finite inverse Hilbert transform are shown.