Research On Algorithms For Cone-beam Ct Image Reconstruction From Limited-view Projections

Computed Tomography (CT) is widely used in medicine and industrial non-destructive testing, the core technology of which—the image reconstruction—is always the research focus. However, in practical applications, the projection data often are acquired only in a limited angle range, because of the factors of the dose, contrast and so on. This situation is referred to as the limited-view problem.The research of this dissertation is the three dimensions image reconstruction algorithm for limited-view problem. In this dissertation, a new algorithm for limited-view problem using iterative method, named reconstruction-reference difference (RRD), is introduced and discussed. The most basic idea of this algorithm is to build a sparse representation for the object and then solving it with the regularization method. The existence and uniqueness of minimal element of the regularization function based on l₁-norm is discussed, and the restricted orthonormality hypothesis to a kind of CT projection matrix is proved. Based on the conclusion above and compressive sensing theory, we develop the RRD algorithm using regularization. Moreover, high performance computing to RRD algorithm is studied. Generally the work consists of the following three parts.Firstly, based on compressive sensing theory, the theory for reconstruction of sparse image is developed in the frame of regularization. The existence and uniqueness of minimal element of the regularization function based on l₁-norm is discussed, and the restricted orthonormality hypothesis to a kind of CT projection matrix is proved. Secondly, making use of the theory for reconstruction of sparse image, a reconstruction algorithm based on regularization function discussed above is developed in order to solve limited-view problem. In order to use the algorithm in real data reconstruction, the RRD algorithm is proposed with some improvements. The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data. Moreover, all the studies showed the satisfactory results in accuracy.In the third part, high performance computing to RRD algorithm is studied to use the algorithm in real more easily. We analyze the Processing-Memory-Communication (PMC) properties of the algorithm, and give a project for parallel computing. Taking into account PMC analyses, some advice is proposed for hardware design and architecture.In the last part the dissertation is summarized, and prospected directions for the research of CT image reconstruction are proposed and discussed.