Fast 3D Image Reconstruction by Separable Moments based on Hahn and Krawtchouk Polynomials

In this paper, we will present a new method of fast and stable computation of 3D image reconstruction using a new collection of 3D separable discrete orthogonal moments called: the 3D Hahn-Hahn-Krawtchouk moments (HHKMs). The latter are generated as the product of Hahn and Krawtchouk discrete orthogonal polynomials. In this method, we will use the 3D image cuboids representation (ICR) to accelerate the computation time of HHKM and improve the quality of 3D images reconstruction for small orders. Simulation results confirm the effectiveness of the proposed method in terms of the calculation time of HHKMs as well as the speed and quality of 3D image reconstruction, with respect to the global method, and the ability of the 3D image reconstruction using the HHKMs is compared by the classical moments of Hahn and Krawtchouk.