A sufficient condition for spiral cone beam long object imaging via backprojection

The response of a point object in cone beam spiral scan is analysed. Based on the result a sufficient condition for the spiral scan long object problem employing backprojection is formulated. By making use of the sufficient condition a general class of exact, backprojection based reconstruction algorithms for spiral scan cone beam CT is developed which are capable of reconstructing a sectional ROI of the long object without contamination from overlaying materials using spiral scan cone beam data irradiating the particular ROI and its immediate vicinity only. Also, at each source position the minimum size of the region on the detector plane required for 3D backprojection is reduced, which in term brings about reduction in the amount of 3D backprojection computation. I. 2D filtering and masking Spiral scan computed tomography with large area detectors is of increasing interest for rapidly scanning spacious volumes. As the cone angle increases the artifacts generated in the reconstructed images by the approximate reconstruction algorithms will become more and more serious, and exact reconstruction algorithms are required. It is known that if the spiral path is long enough so that every plane intersecting the object also intersects the spiral path, the object can be reconstructed. For long objects, however, it is highly desirable to scan only the portion of the object that is of interest, for the sake of reduction in scan time as well as radiation protection of the patient in medical imaging. However, as a consequence of the divergent nature of the X-ray cone-beams different regions of the object are correlated. To reconstruct only a region-of-interest (ROI) from a spiral scan which covers the particular ROI and its immediate vicinity only poses a challenge for the imaging community. This is referred to as the long object problem in the literature. The first solution to the long object problem in spiral cone beam CT is the Radon space driven (spiral + 2 circles) algorithm reported in [1,2]. A key part of the reconstruction algorithm is the data-combination technique in which the radial Radon derivative for each plane intersecting the ROI is obtained by combining the partial results computed from the cone beam data at the various source positions that the plane intersects. The method is illustrated in Figure 1 which represents a plane Q intersecting the ROI and the scan path. Since the partial planes do not overlap and together they completely cover the portion of plane Q that lies within the ROI, the Radon derivative for plane Q can be obtained exactly by summing the Radon derivatives for the partial planes. From Figure 1 it is evident that the portions of the object outside the ROI do not need to be irradiated. Therefore during scanning collimators can be used to block off radiation from reaching those portions. Restricting the cone beam projection data to the appropriate angular range for data combination can be accomplished by a masking process. The mask consists of a top curve and a bottom curve formed by projecting on the detector the spiral turn above and the turn below from the current source position. It can be easily seen that such masking procedure corresponds exactly to the angular range bound by the prior and the subsequent source positions as indicated in Figure 1. We shall refer to this mask as the datacombination mask. For a flat detector located at the rotation axis such that the line connecting the source to the detector origin is normal to the Figure 1. A typical integration plane covering the ROI defined by the source positions. Other integration planes may have more or less spiral scan path intersections, and may not intersect either the top or the bottom circle scan paths. detector plane, the equation for the top curve for the spiral scan is given by:           + − = 2 2 1 1 tan 2 R u h v u R