Approximate inverse based implementation for Tuy´s formula

It is well known that Tuy´s inversion formula is not generally implemented in practice. Recently, based on approximate inverse where reconstruction kernels are precomputed independently, a fast inversion algorithm has been derived from the 3D inverse Radon transform with the classical single-circular trajectory. In this paper, based on the relationship between Tuy´s formula and the 3D inverse Radon transform, we derive the reconstruction kernel of Tuy´s formula with a two-orthogonal-circular trajectory. Moreover, with the two-orthogonal-circular scanning, the reconstruction kernel of Tuy´s formula keeps the invariance properties.