On the Computation of the Inversion of the Finite Hilbert Transform

The inversion of the finite Hilbert transform (FHT) is important in 2D image reconstruction, especially in computer tomography (CT).However, there are few effective algorithms for the inversion of FHT, to the best knowledge of the authors.In 2007, G. Zeng and his collaborators developed a formula that essentially converts the computation of the inversion of the FHT into a form of the FHT of product functions.According to this formula, we present a method for calculating the FHT of B-splines and its equivalent representation.Based on the FHT of B-splines, an effective algorithm is established in this paper.In the calculation, Q is set to be 1.2 and q is set to be 1, with which several interesting examples are implemented.The L 2 -norm errors and L∞-norm errors between the original functions and the results generated according to the proposed algorithm are listed.Numerical experiments show that the proposed method has a good performance in accuracy.