Research On The Reconstruction Algorithms Of Limited-angle Reverse Helical Cone-beam CT

Computed Tomography(CT) technology has the advantages of nondestructive, high precision and 3D visualization, etc. It has been very popular in in many areas such as medical treatment, industry and safety inspection since its advent. CT image reconstruction problem refers to the process of obtaining the inner cross-sectional images of object with the projection data from multi-directions. CT technology is composed of two important parts: the acquisition of projection data and the selection of reconstruction method. Given fairly sufficient projection data, high quality CT images can be obtained with proper reconstruction algorithms. While in some practical situations, there will arise some problems caused by insufficient projection data, such as limited-angle problem that the range of rotation angle of ray souce is restricted. Currently, limited-angle problem is still of great value for research.As a common device, pipeline has been widely utilized in many areas such as petrochemical engineering, oceaneering and metallurgy. Meanwhile, nondestructive testing for the pipeline is significant for ensuring the safety of transportation and manufacture. Limited-angle problem has been the primary problem in practical operation of nondestructive testing for pipeline which is in service with CT due to the limitations of scanning configuration and circumstances of pipeline. In the process of limited-angle scanning, every point in the object can only be covered by the rays under limited angular range, thus complete projection data of the object can’t be available. The lack of projection data may not lead to the acquisition of an ideal reconstruction image. Two important characteristics regarding the pipeline are that the transformed image is sparse and the sectional slices of pipeline are highly similar in structure, then the limited-angle reverse helical cone-beam CT reconstruction method based on 1-norm and nuclear norm minimization is developed. The method mainly involves two aspects, including scanning strategy and reconstruction method. In the aspect of scanning strategy, different from the traditional helical scanning, a limited-angle reverse helical cone-beam CT is developed. The specific scanning strategy is practical for the acquisition of projection and the angular range of scanning can be adjusted flexibly according to practical situations. In the aspect of reconstruction method, some related theory about matrix and optimization are combined. First, the slices of 3D pipeline are rearranged in the columns of a matrix sequentially, and the matrix is representing the 3D pipeline is obtained. Because the slices of 3D pipeline are similar in structure, thus the column space of matrix is approximately low-rank. Second, the mentioned matrix is decomposed into the superposition of a low-rank matrix and a sparse matrix, where the low-rank matrix denotes the similarity among slices and the sparse matrix denotes the differences among slices. Finally, inspired by the robust principal component analysis based four dimensional CT(RPCA-4DCT) in medical CT for dynamic imaging problems, the nuclear norm and 1-norm are utilized as the measure for the low-rank matrix and sparse matrix respectively to build the reconstruction model. Results of numerical simulation show that the developed specific scanning strategy and reconstruction method are effective and feasible in the limited-angle problem for pipeline which is in service.In practical CT nondestructive testing for pipeline, there may appear adverse situations such as the angular range is too small for scanning, which will introduce distorted artifacts into the reconstructed image with traditional reconstruction methods. To obtain high quality reconstruction image by suppressing the artifacts under the condition of maintaining spatial resolution, a method based on the aforementioned work is developed. Taking the prior image as the constraint, then the prior image constrained Schatten p( 0 <p <1)-norm minimization based limited-angle reverse helical cone-beam CT reconstruction method is developed. In the aspect of scanning strategy, a composite scanning trajectory including the limited-angle reverse helix and traditional helix is adopted for the projection data acquisition. The specific scanning strategy is practical for the acquisition of projection and the angular range of scanning can be adjusted flexibly according to practical situations. What’s more, this scanning strategy can improve efficiency and extend the angular range of scanning to a certain degree. Complete helical scanning can be implemented for the pipeline which is offline or the specific part where complete scan be available locally. With these projection data under helical scanning, a preliminary result is reconstructed. And the slices with less or no defects can be selected to constitute the prior image. Once the prior image is available, the reverse helical scanning strategy can be adopted as a subsequent scanning strategy for any other part of the pipeline which is in service. In the aspect of reconstruction method, under the constraint of prior image, nuclear norm is replaced by Schatten p( 0 <p <1)-norm to derive a more accurate solution. Results of numerical simulation show that the method is significant in suppressing artifact and the spatial resolution can be maintained to a certain degree.The two aforementioned methods turn to explore the similarity among the slices of pipeline, that is, the matrix form of CT image of pipeline is low-rank. While sparsity is another important characteristic and it has been widely utilized in image reconstruction problems as the effective and feasible prior information. Exploring the sparsity of pipeline adequately and utilizing it properly in reconstruction is very significant for the improvement of the image quality. Related theoretical researches demonstrate thatp( 0 <p <1)-norm is superior to 1-norm in representing sparse data, and the adaptive tight frame can also construct the optimal sparse approximation method according to different objects. Under the limited-angle reverse helical cone-beam CT scanning, a reconstruction method based on the p( 0 <p <1)-norm minimization and tensor framelet is developed. The method has two separate steps including adaptive tensor framelet construction and p( 0 <p <1)-norm minimization based image reconstruction. In the first step for construction of adaptive tight frame, images with similar structures are utilized as the prior image for training. Then the constructed tight frame is utilized to implement sparse transform. In the second step, image reconstruction is the procedure of p( 0 <p <1)-norm minimization. Results of numerical simulation of this method show the superiority from the some traditional analytic reconstruction method such as filtered backprojection type FDK(Feldkamp–Davis–Kress) and algebraic reconstruction method such as simultaneous algebraic reconstruction technique(SART) in suppressing artifacts and maintaining spatial resolution, and the image quality is improved. Meanwhile, the method not only can be utilized for the testing of objects with similar structures among slices such as pipeline, but also can be utilized for the testing of other objects with more general structures.