A solution to the long-object problem in helical cone-beam tomography

This paper presents a new algorithm for the long-object problem in helical cone-beam (CB) computerized tomography (CT). This problem consists in recon structing a region-of-interest (ROI) bounded by two given transaxial slices , using axially truncated CB projections corresponding to a helix segment l ong enough to cover the ROI, but not long enough to cover the whole axial e xtent of the object. The new algorithm is based on a previously published m ethod, referred to as CB-FBP (Kudo et al 1998 Phys. Med. Biol. 43 2885-909) , which is suitable for quasi-exact reconstruction when the helix extends w ell beyond the support of the object. We first show that the CB-FBP algorit hm simplifies dramatically, and furthermore constitutes a solution to the l ong-object problem, when the object under study has line integrals which va nish along all PI-lines. (A PI-line is a line which connects two points of the helix separated by less than one pitch.) Exploiting a geometric propert y of the helix, we then show how the image can be expressed as the sum of t wo images, where the first image can be reconstructed from the measured CB projections by a simple backprojection procedure, and the second image has zero PI-line integrals and hence can be reconstructed using the simplified CB-FBP algorithm. The resulting method is a quasi-exact solution to the lon g-object problem, called the ZB method. We present its implementation and i llustrate its performance using simulated CB data of the 3D Shepp phantom a nd of a more challenging head-like phantom.