computer methods and programs in biomedicine 98 ( 2 0 1 0 ) 253–260 journal homepage: www.intl.elsevierhealth.com/journals/cmpb Algorithm for hyperfast cone-beam spiral backprojection Sven Steckmann ∗ , Michael Knaup, Marc Kachelrieß Institute of Medical Physics (IMP), University of Erlangen-Nürnberg, Henkestr. 91, 91052 Erlangen, Germany article info Article history: Received 3 February 2009 Received in revised form 14 July 2009 Accepted 14 August 2009 Keywords: CT Image reconstruction Backprojection Spiral CT High performance computing abstract Cone-beam spiral backprojection is computationally highly demanding. At first sight, the backprojection requirements are similar to those of cone-beam backprojection from circu- lar scans such as it is performed in the widely used Feldkamp algorithm. However, there is an additional complication: the illumination of each voxel, i.e. the range of angles the voxel is seen by the X-ray cone is a complex function of the voxel position. The weight function has no analytically closed form and must be numerically determined. Storage of the weights is prohibitive since the amount of memory required equals the number of vox- els per spiral rotation times the number of projections a voxel receives contributions and therefore is in the order of 10 9 to 10 11 floating point values for typical spiral scans. We pro- pose a new algorithm that combines the spiral symmetry with the ability of today’s 64bit CPUs to store large amounts of precomputed weights. Using the spiral symmetry in this way allows to exploit data-level parallelism and thereby to achieve a very high level of vector- ization. An additional postprocessing step rotates these slices back to normal images. Our new backprojection algorithm achieves up to 24.6Giga voxel updates per second (GUPS) on our systems that are equipped with two standard Intel X5570 quad core CPUs (Intel Xeon 5500 platform, 2.93 GHz, Intel Corporation). This equals the reconstruction of 410 images per second assuming each slice consists of 512 × 512 pixels, receiving contributions from 512 projections. © 2009 Elsevier Ireland Ltd. All rights reserved. 1. Introduction High performance image reconstruction (HPIR) basically means high performance backprojection since backprojec- tion is the most demanding step in the image reconstruction pipeline. Recently, we published our work on high perfor- mance parallel beam backprojection and high performance perspective cone-beam backprojection using cell broadband engine (CBE) based implementations and central processing unit (CPU) based implementations [1]. Spiral backprojection is, however, more complicated since the illumination of the voxels by the cone exhibits a complex voxel location-dependent behavior that must be taken into account during the backprojection step. Basically, this requires ∗ Corresponding author. Tel.: +49 91318525830. E-mail address: sven.steckmann@imp.uni-erlangen.de (S. Steckmann). to compute a weight function w(x, y, z, ˛), where (x, y, z) is the voxel position and ˛ is the angle of the ray that is back- projected, and apply this function during the backprojection. Numerous algorithms have been published that already use voxel-specific weighting [2–5]. Others assume some simplifi- cations to circumvent the problem of voxel-specific weighting and thereby compromise either dose usage or image quality [6–12]. Also implementations of quasiexact and exact recon- struction algorithms such as [13–15] may profit from our new approach. The paper proposes the new algorithm [16] and extends the paper [17] by implementation details for a filtered backprojec- tion. The new backprojection algorithm is able to perform the correct voxel weighting and that can be used together with 0169-2607/$ – see front matter © 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2009.08.003