Polar coordinate interior tomography

In this paper, a pair of Hilbert transforms is presented for computed tomography in the polar coordinate. The first one is an approximate Hilbert transform along azimuthal orientation, named azimuthal Hilbert transform; while another is an exact Hilbert transform along radial orientation, named radial Hilbert transform. Based on the Hilbert transform based POCS method proposed by Kudo et al, an approximate interior tomography is developed in the polar coordinate, named polar coordinate interior tomography. Computer simulations have been carried out in parallel-beam geometry to validate its characteristic.