Improved two-dimensional rebinning of helical cone-beam computerized tomography data using John's equation

This paper deals with three-dimensional (3D) image reconstruction for helical computerized tomography with multi-row detectors. We describe a method to improve the accuracy of the rebinning algorithms, which separate 3D reconstruction into independent 2D reconstructions for a set of oblique slices. Each oblique slice is reconstructed from an estimate of its 2D Radon transform obtained from the cone-beam projections acquired while the x-ray source moves along a segment of the helix. Because this helix segment is not contained within the oblique slice, the estimated 2D Radon transform is approximate. In theory, exact rebinning could be achieved by solving John's partial differential equation to virtually move the x-ray source within the oblique slice. In contrast with previous work by Patch (2002 IEEE Trans. Med. Imaging 21 801-13), we do not attempt to solve John's equation exactly. Instead, we use John's equation to compute a first order correction to the rebinning algorithm. Tests with simulated data demonstrate a significant improvement of image quality, obtained with a negligible increase of the computation time and of the sensitivity to noise.