Moment-based Cosh-Hilbert Inversion and Applications in Single Photon Emission Computed Tomography

Based on Tricomi formula for Hilbert transform and Taylor expansion of cosh-function, a numerical inversion algorithm for cosh-Hilbert transform (CHT) is proposed and applied to single photon emission computed tomography imaging. CHT of a function is represented as its Hilbert transform and a correction term including all of its moments by using Taylor expansion of cosh-function. A linear system about all moments of the function is obtained via Tricomi formula. Finite numbers of moments can be solved by truncating the infinite linear system, and the function can be reconstructed approximately. Numerical simulations are performed to verify the algorithm by comparing with analytical inversion formula.