A Fourier rebinning algorithm for cone beam CT

Abstract

It is known that x-ray projections collected from a circular orbit of an x-ray source are insufficient for accurate reconstruction of a 3D object. For each local region of the object (except in the plane containing the source trajectory) there is a conical volume in the object's spatial frequency space that is unmeasured due to the circular geometry. The Feldkamp, Davis and Kress (FDK) algorithm based on filtered backprojection (FBP) involves a 3D backprojection step so that these unmeasured spatial frequencies are set to zero, resulting in cone beam artifacts for certain objects. We present a new type of cone beam CT reconstruction algorithm based on the Fourier rebinning (FORE) framework of Defrise et al. The cone beam x-ray projection data are rebinned into a set of in-plane sinograms using the FORE rebinning approximation, followed by 2D FBP to reconstruct each axial slice. The algorithm is able to extrapolate data into the missing region of the object's frequency space in a computationally efficient way, allowing for a reduction of cone beam artifacts for certain objects. Unlike FDK, the algorithm is exact for an impulse object located anywhere along the axis of rotation. Reconstruction errors are dependent on the radial distance, cone angle, and the second-derivative of the projection data in the longitudinal direction. Finally, an extension to the algorithm is presented that permits reconstruction in regions of the object that are not seen by the detector in every view.