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In backprojection cone-beam CT the cone-beam projection images are first filtered, then 3D backprojected into the object space. In this paper the point spread function (PSF) for the filtering operation is studied. For the cases where the normalization matrix is a constant, i.e. all integration planes intersect the scan path the same number of times, the derivation of the PSF is extended to the general case of limited angular range for the Radon line integrals. It is found that the 2D component of the PSF can be reduced to the form of space-variant 1D Hilbert transforms. The application of the PSF to a number of aspects in long object imaging will be discussed.

We propose an algorithm to correct for the cupping artifact inherent in CT images due to the polychromatic nature of the spectrum. This method is empirical and does not require knowledge of the spectrum and of the attenuation coefficients. The method aims at linearizing the attenuation data using a precorrection function of polynomial form. The coefficients of the polynomial are determined from a fit of some linear combined reconstructed images of the polychromatic data with a defined template. This template is obtained from the reconstruction of the polychromatic raw data and does not make any assumptions on the phantom size or of its positioning. It is shown that the fit can be performed easily solving only a linear system, making the method very fast. An example of application is given as the water precorrection. For this particular case, practical considerations are given on the definition of the template when an attenuating object table of unknown density is within the images. The method can generally correct for any kind of cupping such as scatter as well.

The response of a point object in a cone beam (CB) spiral scan is analysed. Based on the result, a reconstruction algorithm for long object imaging in spiral scan cone beam CT is developed. A region-of-interest (ROI) of the long object is scanned with a detector smaller than the ROI, and a portion of it can be reconstructed without contamination from overlaying materials. The top and bottom surfaces of the ROI are defined by two sets of PI lines near the two ends of the spiral path. With this novel definition of the top and bottom ROI surfaces and through the use of projective geometry, it is straightforward to partition the cone beam image into regions corresponding to projections of the ROI, the overlaying objects or both. This also simplifies computation at source positions near the spiral ends, and makes it possible to reduce radiation exposure near the spiral ends substantially through simple hardware collimation. Simulation results to validate the algorithm are presented.

Presents a spiral scan cone beam reconstruction algorithm in which image reconstruction proceeds via backprojection in the object space. In principle the algorithm can reconstruct sectional ROI in a long object. The approach is a generalization of the cone beam backprojection technique developed by Kudo and Saito in two aspects: the resource-demanding normalization step in the Kudo and Saito's (1994) algorithm is eliminated through the technique of data combination which the authors published earlier, and the elimination of the restriction that the detector be big enough to capture the entire image of the ROI. Restricting the projection data to the appropriate angular range required by data combination can be accomplished by a masking process. Because of the simplification resulting from the elimination of the normalization step, the most time-consuming operations of the algorithm can be approximated by the efficient step of line-by-line ramp filtering the cone beam image in the direction of the scan path, plus a correction image. The correction image, which can be computed exactly, is needed because data combination is not properly matched at the mask boundary when ramp filtering is involved. Empirical 2D PSF, the Shepp-Logan filter, and a modified ramp filter are developed to improve matching with the correction image which is computed with finite samplings. The use of transition region to further improve matching is introduced. The results of testing the algorithm on simulated phantoms are presented.

A number of filtered-backprojection type quasi-exact algorithms have been recently developed to reconstruct images in cone beam spiral scan. A key common feature in these algorithms is a masking process employed in filtering the cone beam image. The masking process is an approximation to restrict the line integrals intersecting the cone beam image to the appropriate angular range required for data combination. Errors in the approximation are caused by portions of some integration line segments which do not conform to proper data combination. In this paper the line segments which constitute the major source of errors in the masking process are identified. It is found that these line segments are localized in the detector projection space. The errors can be corrected by applying the filtering process to this group of line segments. It is also shown in the paper that the correction procedure can be simplified by using 1D Hilbert transforms. Improvements in image quality brought about by the correction procedure are demonstrated in simulation reconstructions.

The authors present a (spiral + circles) scan cone beam reconstruction algorithm in which image reconstruction proceeds via backprojection in the object space. In principle, the algorithm can reconstruct sectional region-of-interest (ROI) in a long object. The approach is a generalization of the cone beam backprojection technique developed by Kudo and Saito (1994) in two aspects: the resource-demanding normalization step in the Kudo and Saito's algorithm is eliminated through the technique of data combination that the authors published earlier, and the elimination of the restriction that the detector be big enough to capture the entire cone beam projection of the ROI. Restricting the projection data to the appropriate angular range required by data combination can be accomplished by a masking process. Because of the simplification resulting from the elimination of the normalization step, the most time-consuming operations of the algorithm can be approximated by the efficient step of line-by-line ramp filtering the cone beam image in the direction of the scan path, plus a correction image. The correction image, which can be computed exactly, is needed because data combination is not properly matched at the mask boundary when ramp filtering is involved. Empirical two-dimensional (2-D) point spread function (PSF) is developed to improve matching with the correction image which is computed with finite samplings. The use of transition region to further improve matching is introduced. The results of testing the algorithm on simulated phantoms are presented.