Studies On Exact Katsevich Reconstruction Algorithm Of Spiral Cone-Beam Industrial CT

CT(Computed tomography) is the fruit by the combination of mathematics, physics, photoelectricity, mechanics and computer science, etc. It can be classified into two major practical fields: Medical CT (MCT) and Industrial CT (ICT). During the past forty years, the scan mode of ICT has been developed into the 3D spiral cone-beam from the 2D parallel-beam. Spiral cone-beam ICT now is a hot spot in the researching area. It possesses several strong points: not only it has shorter scan time, higher axis resolution and better ray's utilization, but also its scan locus satisfy necessary and sufficient condition for the 3D exact reconstruction. The reconstruction algorithms of spiral cone-beam can be divided into two sorts: algebraic algorithms and analytic algorithms. Algebraic algorithms need iteration many times, so it costs much time. There are two types of analytic algorithms: exact and approximate algorithms. Compared with approximate algorithms, the image reconstructed from exact algorithms rid itself of the influence of cone angle, and have no shadow in the aspect of theory. Also, there are mainly two types of exact algorithms: Grangeat algorithm and Katsevich algorithm. Due to higher efficiency of the algorithm implementation and better quality of the reconstructed image, the spiral cone-beam Katsevich exact reconstruction algorithm has attracted increasing attention.The exact reconstruction requires that the projections should be complete and without noise. Unfortunately, in spiral cone-beam ICT, the projections obtained from the practical engineering have a lot of noise. The noise is caused by maladjustment of some detectors, dispersion and cross-talk of X-rays, etc. In order to meet the exact reconstruction condition, the noised projections should be de-noised or the exact reconstruction algorithms should be improved. In this paper, two strategies were adopted to reduce the negative effects resulted from the noise when the Katsevich algorithm was applied to reconstruct the noised spiral cone-beam projections. The first strategy mainly improved the derivative method in Katsevich algorithm; the second strategy mainly removed the noise in the projections by means of improved adaptive mixed filter. The computer simulations validate that the first strategy could restrain the small abnormal noise and random noise in the projections, while the second strategy may be more suitable for the projections with more abnormal noise and random noise.In ICT, the projections may deviate to a certain extent due to many factors, such as shifts center of rotation, the inconsistency of the vertical height between the radial focus and the detector center, etc. The reconstructed image would be out of clarity if the practical projections were used directly. In this paper, correctional Katsevich algorithm was carried out to deal with the off-center spiral cone-beam CT. Firstly, the excursion of the projections were transformed to the excursion of the detector center. Then, in the process of the reconstruction, the filtering line, re-sampling, correction and backprojection were revised respectively according to the detector center excursion. Meanwhile, the traditional dichotomy algorithm for calculating PI line root was transformed to the method of calculating the root of the one variant function in course of the backprojection, which was also optimized by the high order iterative method. Computer simulations result validate that this method can reduce negative effects efficiently caused by the excursion of the projections. At the same time, the improved method for computing the root of the PI line can reduce the reconstruction time.Image edge mostly concludes the important feature of the image and plays an important role in recognition, segmentation and measurement. Acquiring the 3D edge of the object by ICT can generally be divided into two steps. First, a reconstruction method is utilized to reconstruct image from projections achieved by ICT. Second, a extraction method is used to extract 3D image edge. In this paper, the 3D enhanced image reconstruction method was investigated by modifying the spiral cone-beam Katsevich exact reconstruction algorithm. It could obtain the 3D enhanced image edge directly by reconstructing the projections from ICT. By this 3D enhanced image edge, we can identify the shape and type of the object inner structure. Furthermore, the time of 3D enhanced image edge reconstruction algorithm is equivalent to the Katsevich algorithm in spiral cone-beam ICT, which helps to economize the time of the 3D image extraction.