The projection matrix model is used to describe the physical relationship between reconstructed object and projection.Such a model has a strong influence on projection and backprojection,two vital operations in iterative computed tomographic reconstruction.The distance-driven model（DDM） is a state-of-the-art technology that simulates forward and back projections.This model has a low computational complexity and a relatively high spatial resolution;however,it includes only a few methods in a parallel operation with a matched model scheme.This study introduces a fast and parallelizable algorithm to improve the traditional DDM for computing the parallel projection and backprojection operations.Our proposed model has been implemented on a GPU（graphic processing unit） platform and has achieved satisfactory computational efficiency with no approximation.The runtime for the projection and backprojection operations with our model is approximately 4.5 s and 10.5 s per loop,respectively,with an image size of 256×256×256 and 360 projections with a size of 512×512.We compare several general algorithms that have been proposed for maximizing GPU efficiency by using the unmatched projection/backprojection models in a parallel computation.The imaging resolution is not sacrificed and remains accurate during computed tomographic reconstruction.
The interior tomography is commonly met in practice, whereas the self-calibration method for geometric parameters remains far from explored. To determine the geometry of interior tomography, a modified interval subdividing based method, which was originally developed by Tan et al.,^[11] was presented in this paper. For the self-calibration method, it is necessary to obtain the reconstructed image with only geometric artifacts. Therefore, truncation artifacts reduction is a key problem for the self-calibration method of an interior tomography. In the method, an interior reconstruction algorithm instead of the Feldkamp-Davis-Kress （FDK） algorithm was employed for truncation artifact reduction. Moreover, the concept of a minimum interval was defined as the stop criterion of subdividing to ensure the geometric parameters are determined nicely. The results of numerical simulation demonstrated that our method could provide a solution to the self- calibration for interior tomography while the original interval subdividing based method could not. Furthermore, real data experiment results showed that our method could significantly suppress geometric artifacts and obtain high quality images for interior tomography with less imaging cost and faster speed compared with the traditional geometric calibration method with a dedicated calibration phantom.
