A regional adaptive variational PDE model for computed tomography image reconstruction

Improving CT images by increasing the number of scans, hence increasing the ionizing radiation dose, can increase the probability of inducing cancer in the patient. Using fewer images but improving them by accurate reconstruction is better solution. In this paper, an adaptive variational Partial Differential Equation (PDE) model is proposed for image reconstruction. L2 energy of the image gradient and the Total Variation (TV) are combined to form a new functional, which is introduced to an optimization problem. The dynamic behaviors of the model are formed by a threshold function, and then the L2 term is applied in the lower-density region to increase reconstruction speed, and the TV term is applied in the higher-density region to preserve the most important image features. The threshold function is asymptotically controlled by an evolutionary PDE and is more suitable for complex images. The efficiency and accuracy of the proposed model are demonstrated in numerical experiments. (C) 2019 Elsevier Ltd. All rights reserved.