Research On The Regularization Models And Algorithms For Computed Tomography

Computed tomography(CT) technology is an important technology in many application areas such as medical imaging and industrial inspection. The regularization CT image reconstruction models and algorithms are the main subjects in this field now. We proposed a second-order total variation regularization CT reconstruction model and an adaptive total variation regularization CT reconstruction model. We also studied the properties and primal-dual algorithms of the proposed two models.Firstly, we introduced the CT imaging principles, including the physical principles and mathematical principles; We then presented some definitions?propositions and theorems that will be used later; We also gave a brief introduction to regularization methods and Primal-Dual(PD) algorithm.Then, in order to eliminate the ‘staircase' effects caused by total variation(TV) regularization model, we proposed a regularization model based on second-order total variation(SOTV), then we studied the existence of solutions and the PD algorithm of this model. Numerical experiments showed that SOTV model can eliminate ‘staircase' effectively. We showed SOTV is also apply to interior CT and phantom with ghost by numerical experiments.Lastly, we proposed an adaptive total variation(ATV) CT image reconstruction model combining TV with SOTV in order to alleviate the blurring on boundary caused by SOTV.We focused on the choice of adaptive function, and proposed new adaptive functions and new method(lambda tomography) to compute the gradient of original image. We compared the numerical reconstruction results with different adaptive functions?different methods of compute gradient and different filters. These experiments demonstrated ATV model can get clearer results than SOTV and avoid the ‘staircase' at the same time. We also showed the feasibility of lambda tomography by interior CT.