Improved two-dimensional rebinning of helical cone-beam computerized tomography datausing John’s equation

Abstract

This paper deals with three-dimensional (3D) image reconstruction for helical computerizedtomography with multi-row detectors. We describe a method to improve the accuracy ofthe rebinning algorithms, which separate 3D reconstruction into independent 2Dreconstructions for a set of oblique slices. Each oblique slice is reconstructed from anestimate of its 2D Radon transform obtained from the cone-beam projections acquiredwhile the x-ray source moves along a segment of the helix. Because this helixsegment is not contained within the oblique slice, the estimated 2D Radon transformis approximate. In theory, exact rebinning could be achieved by solving John’spartial differential equation to virtually move the x-ray source within the obliqueslice. In contrast with previous work by Patch (2002 IEEE Trans. Med. Imaging 21801–13), we do not attempt to solve John’s equation exactly. Instead, we use John’sequation to compute a first order correction to the rebinning algorithm. Testswith simulated data demonstrate a significant improvement of image quality,obtained with a negligible increase of the computation time and of the sensitivity tonoise.