ABSTRACT
The 3D cone beam computed tomography (CBCT) reconstructions can be done either analytically or iteratively. An analytic approach has an explicit formula for reconstructing the 3D volumetric images from a set of x-ray projection data. In particular, the well-known Feldkamp, Davis, and Kress (FDK) algorithm [1] oers a computationally ecient approximate formula that has an advantage of obtaining fair quality 3D images without requiring excess computations. Given the excessive number of voxels to be reconstructed for a CBCT image (oen a few tens of millions of voxels), this low complexity formula has been the most commonly used CBCT reconstruction method in practice. It will be shown in
CONTENTS 3.1 Introduction 31 3.2 FDK Algorithm for CBCT Reconstruction 32
3.2.12D Filtered Back Projection 32 3.2.23D Filtered Back Projection: FDK Algorithm 36
3.3GPU Implementation 39 3.3.1Cosine Weighting 41 3.3.2Ramp Filtering 41 3.3.3Back Projection 42
3.4Examples and Performance 44 References 45
Section 3.4 that, by using a currently available o-the-shelf graphics processing unit (GPU) computer, near real-time 3D CBCT reconstruction is possible. is computational advantage came from the fact that the reconstruction algorithm is derived from a simple yet neat mathematical x-ray projection model that includes an innitesimal focal spot of the x-ray source, pencil beams from the source without any scattering, no measurement noise at the detector, etc. For this reason, the analytic method is not too exible to incorporate various nonideal factors in the real system or to leverage possible additional information that can be used for further improving the image quality.
