Double-centering method for increasing efficiency of cone-beam X-ray CT reconstruction

A method of increasing the efficiency of hardware-based circular and helical cone beam x-Ray CT reconstruction is presented. During reconstruction, an image slice at any arbitrary axial position is created by backprojecting reconstructed image pixels to corresponding positions on the detector array. This is computationally inefficient for cylindrical arrays because the backprojection equations for the channel and segment positions involve time-consuming arctangent calculations. Since the detector array matrix is smaller than the reconstruction matrix, backprojection speed can be increased if the system geometry is changed so that the arctangent calculations are performed on the detector array matrix rather than the reconstruction matrix. The most efficient configuration is where a row of reconstructed image pixels projects to a single row of detector channels with constant segment number and constant spacing along the channels. This configuration can be achieved by double centering; which consists of reprojecting the original cylindrical array projection data onto a flat virtual detector located in the xz plane. A double-centering algorithm with corresponding cone-beam reconstruction algorithm has been developed and implemented on a PC for the circular case. Cone-beam circular projection data from a ball phantom has been generated by simulation, double-centered, and reconstructed. The image quality of the double-centered reconstructions has been assessed, and the details and tradeoffs of practical implementation from an image quality standpoint are discussed.