Research On CT Reconstruction Using Proximal Algorithms With Incomplete Projection Data

In this thesis,we proposed a three dimensional(two dimension also included)computed tomography reconstruction framework,which is based on recently very popular proximal algorithms in machine learning and signal processing.This framework is quite flexible and robust.There are two typical classes of methods for CT reconstruction: transform-based algorithms(e.g.FDK),and iterative algorithms(e.g.ART).Even though the better reconstruction quality can be obtained by iterative algorithms,the softwares that deployed on medical system in practice are still based on transform-based algorithms,because of their nice features(e.g.the lower computational cost,and faster speed for reconstruction etc.).With the rapid development of super computing and distributed computing over the last decade,the cost of computing caused by algorithms is not the first concern in CT community,gradually.Under this circumstance,the iterative algorithms again gain more and more attentions.For each iterative algorithm,there are two kinds of implementation in the perspective of the way rays casted: Ray-based method and Voxel-based method.In this thesis,the detailed comparison will be given for these two kinds of methods with incomplete projection data as input.Proximal algorithm consists of proximal operators.In this thesis,we introduce existing popular proximal algorithms such as ADMM,linear ADMM,primal-dual,etc.Besides,we derived the operators for data term solver(such as proximal operator of ART,or PART)algorithm,and implemented the ATV,ITV,and SAD priors in both 2D and 3D.To validate the effectiveness of the proposed framework,we compared it with popular open source in CT community named RTK.In the thesis,compared to the methods integrated in RTK(such as FDK,and ADMM with TV prior),we show that the methods from our framework can reconstruct volumes with unprecedented quality and the framework's high efficiency,flexibility,and robustness.