The Theoretical Study And Realization Of New Iterative Image Reconstruction Algorithms

Computer tomography(CT) is widely applied not only in the medical radiodiagnosis, but also in the industry inspection. Transformation based imaging technique is generally adopted in the medical CT, because a large number of projections can be obtained and analytic algorithm is then used to quickly reconstruct image with high quality. In industry application, however, incomplete projections can only be obtained, so the situation is not appropriate to the transformed imaging technique and then the iterative algorithm has to be applied so that better reconstructed image can be got. Unfortunately, up to now, there is no an efficient algorithm to deal with the iterative reconstruction algorithm, especially from fan-scanned projections. How to balance the quality and the speed of reconstructed image is always a goal that many investigators pursue.The main disadvantage of iterative algorithm is its slow speed and the time cost of image reconstruction is directly proportional to the number of projections and the size of reconstruction image. One of the restricting factors is the obtainment of projection matrix. To fan-scanned projections, they are commonly rearranged into parallel projections, which, however, occupy a great deal of memory. A fast and real-time algorithm to obtain some vectors of the projection matrix is proposed in this dissertation to solve the conflict of time cost by matrix obtainment and memory occupied by matrix, and speed the iterative algorithm.As for single objective optimization algorithm, a fast iterative algorithm based on conjugate gradient algorithm is presented, which makes use of extent limit of iterative optimization step in conjugate gradient with the idea of least square. In order to express imaging problem accurately, moreover, projection equations are introduced as the restricted condition of single objective optimization, and then a restricted least-square iteration algorithm for image reconstruction from projections is proposed to get the reconstructed results with little artifact quickly and concisely.In view of the fact that there is inevitably noise in actual projections, single objective can't express reconstruction characteristic accurately, so the author pays more attention to other objectives of reconstruction image to make full use of the mutual information among the incomplete projections and the vector mathematic programming is presented to solve the imaging problem. During the process ofseeking the solution, three conditions are considered: [1] each objective is guaranteed comparable, namely each objective is guaranteed to have the same scalar measure; [2] The weight of each objective is determined according to its contribution to the final reconstructed image; [3] the whole algorithm was guaranteed to be convergent, and the solution is the tradeoff of problem to be solved.Because there is lots of uncertain information in optimization based image reconstruction from projections, fuzzy vector mathematic programming algorithm for image reconstruction from projections is therefore proposed. That is to say, express each objective function as a membership function to form a new mathematic mode] and a recurrent max-min method is put forward to solve the model. The proposed algorithm can not only predigests the seeking process, but also finds the available solution of original problem automatically.The results of all proposed algorithms for image reconstruction from computer-generated noisy projections and real projections (Industry part scanner data and SIEMENS SOMATOM DR3 head scanner data) have been given in the dissertation and the reconstructed results and the subsequent data analysis have shown validity of the algorithms.