List-mode data reconstruction via the finite Hilbert transform of the derivative of the backprojection

An exact analytical image reconstruction method is presented for two-dimensional (2D) imaging. The method performs backprojection, the derivative and finite Hilbert transforms. This method can be applied to many imaging geometries. The backprojection procedure is imaging- geometry dependent, while the differentiation and the finite Hilbert transform procedures are identical for all imaging geometries. This algorithm is applicable to list-mode data in nuclear medicine, while other filtered backprojection algorithms cannot be applied directly to the list-mode data.