This work reports three reconstruction algorithms developed to address the practical issues encountered in 3D tomography diagnostics, such as the limited view angles available in many practical applications, the large scale and nonlinearity of the problems when they are in 3D, and the measurement uncertainty. These algorithms are: an algebraic reconstruction technique (ART) screening algorithm, a nonlinear iterative reconstruction technique (NIRT), and an iterative reconstruction technique integrating view registration optimization (IRT-VRO) algorithm. The ART screening algorithm was developed to enhance the performance of the traditional ART algorithm to solve linear tomography problems, the NIRT was to solve nonlinear tomography problems, and the IRT-VRO was to address the issue of view registration uncertainty in both linear and nonlinear problems. This dissertation describes the mathematical formulations, and the experimental and numerical validations for these algorithms. It is expected that the results obtained in this dissertation to lay the groundwork for their further development and expanded adaption in the deployment of tomography diagnostics in various practical applications.