| CT technique is of great value in every aspect of modern life,because of its revolutionary influence on medical diagnosis, industrial nondestructive testing and biological sensing. The essence of CT technique is X-ray imaging, namely through the effective projection data, design reconstruction algorithm and calculate the internal cross section information about objects. From the implementation respect Classic traditional CT image reconstruction algorithm is divided into image reconstruction algorithm and iterative image reconstruction algorithm. These two kinds of algorithm each has his strong point. In practical application, limited to the acquisition time, irradiation dose, imaging system scanning geometry and other factors, projection data can only be obtained in the limited angle range. The above situation is the so called the incomplete angle image reconstruction problem.Compressed sensing(CS) theory provides new strategies and ideas for incomplete Angle reconstruction research.Basing on the CS theory Image reconstruction algorithm breaks the conventional which reconstructs image directly and turns to sparse image representation instead. Isotropic TV minimization algorithm is one of the most representative algorithms which has satisfactory fidelity and prominent reconstructed image quality. According to the piecewise continuity of the reconstruction object, basing on the regularization framework and using alternating direction method Isotropic TV minimization algorithm realizes good reconstruction details. However Isotropic TV minimization algorithm reveals the huge gap of the reconstruction efficiency and storage capacity comparing with the traditional analytic reconstruction algorithm.Above all, this thesis mainly involves the following several aspects:1. To start a research around issues of incomplete Angle reconstruction, the Anisotropic TV minimization CT image reconstruction algorithm is proposed which improves the original Isotropic TV minimization algorithm from two aspects: One is to choose the anisotropy of minimizing the TV image vector which optimizes sparse discrete transform optimization; the second is to apply solving strategy of nonmonotone line search in the process of iteration to speed up the sub-problem optimization solution.Then this paper builds the simulation platform, continuously tuning parameters of algorithm and completed the full simulation test. Through a large number of sample size control experiments, precision and efficiency of the algorithm is verified. By comparing with Isotropic TV minimization algorithm, we find that the conver-gence performance of the proposed algorithm is outstanding.2. Quantitative analysis of sampling as an effective means of numerical analysis is of high practical value in the incomplete perspective study. In this paper, based on the theory of compressive sensing, research rebuilds the relationship between system matrix properties and incomplete projection angle. Based on the exact reconstruction of the necessary conditions of system matrix, the paper presents an accurate system matrix reconstruction analysis method for collecting point of quantitative estimation of lower boundary which is of great value. |
