CT imaging is a widespread technique in both medicine and industry. However, the classic algorithms used are often not good enough for the desired quality, as they have high sensitivity to errors and noise. Iterative algorithms are minimization algorithms that are proven to give considerably better images, specially in high noise and low data cases. However, the computational costs of nowadays 3D CT images is too high for stadard computers to handle. In our work we developed a GPU toolbox to accelerate CT image reconstruction, implementing and studying a wide variety of iterative algorithms with it. Furthermore, new research in low projection algorithms has lead to a better understanding and a proposal of a new algorithm. Additionally, a full 4D imaging technique has been proposed, potentially helping imaging patients with lung injuries.