Theoretical Study And Improvement Of Superiorization Algorithm And Its Applications In CT And MRI

Image reconstruction technique is a kind of technique which can get image of the internal structure or function of object without damage. The incomplete data reconstruction and rapid imaging problems are hot spots in the image reconstruction technology. Both problems can be ascribed to ill-posed problems. Regularization method is a common way to solve ill-posed problems. It has very important application values to research the algorithms of these problem, which have been widely used in medical, industrial and other fields. This article aimed at solving incomplete data reconstruction and rapid imaging problems, studied a superiorization algorithm for large-scale constrained regularization model, proposed two new improved algorithms and proved convergence of the first improved algorithm.This paper first briefly introduced the research background, significance and research status at home and abroad of medical image reconstruction, regularization reconstruction techniques and superiorization algorithm; then introduces the basic principle, reconstruction models, reconstruction algorithms and related regularized reconstruction models of the computed tomography,(computed tomography, CT), magnetic resonance imaging(magnetic resonance imaging,MRI) and parallel magnetic resonance imaging(partially parallel imaging, PPI).In addition, the superiorization algorithm was researched. The idea of superiorization algorithm is added perturbation parameter during the iterative process to solve a approximate optimal solution of constrained minimization model. For the algorithm, from the theoretical analysis and a large number of numerical experiments we found the following problems: the iteration results of the algorithm need to meet two conditions:(1) the objective function decline,(2) in constraint set. If the results meet the two conditions, the iteration was performed one time, otherwise we adjusted the size of the parameters. This is not only time-consuming but also affect the iteration results. In addition, because the function of regularization parameter become small in the late iteration. It will increase the reconstruction time and affect the final result. In order to solve these problems, two improved algorithms were proposed.Two improved algorithms are as follows:(1) The superiorization algorithm of optimal parameter —–the method of changing parameter. Its main idea is to use the solution of unconstrained minimization model instead of the perturbed iteration results of the original algorithm.Then the result of the replacement can make the target function decline, and we don't need to verify this condition. Therefore it can save a lot of time, improve the quality of reconstruction.We also proved the convergence of the algorithm.(2) The superiorization algorithm of threshold constraint, whose main idea is restricting the perturbation parameter to some threshold value during the process of iteration. When the perturbation parameter is less than the threshold value, let parameter is equal to this value. This method makes the regularization has played a role in the whole iterative process, so as to save the calculation time and improve the quality of the reconstruction. In addition, this paper also proved that the projection iterative algorithm based on the PPI imaging satisfy BPR(Bounded perturbation resilience, BPR). It means that superiorization algorithm also applies to PPI imaging.Finally, the improved algorithms were applied to regularization reconstruction model based on total variation(TV) of CT and PPI. We analysed, compared the simulation results, verified the validity of the improved algorithms, the experimental results shown that the improved superiorization algorithms are better than the original algorithm, they not only shorten the time of reconstruction but also improved the quality of reconstruction images.