Statistical Interior Tomography via L₁ Norm Dictionary Learning without Assuming an Object Support

Interior tomography of X-ray computed tomography (CT) has many advantages, such as a lower radiation dose and lower detector hardware cost compared to traditional CT. However, this imaging technique only uses the projection data passing through the region of interest (ROI) for imaging; accordingly, the projection data are truncated at both ends of the detector, so the traditional analytical reconstruction algorithm cannot satisfy the demand of clinical diagnosis. To solve the above limitations, in this paper we propose a high-quality statistical iterative reconstruction algorithm that uses the zeroth-order image moment as novel prior knowledge; the zeroth-order image moment can be estimated in the projection domain using the Helgason-Ludwig consistency condition. Then, the L₁norm of sparse representation, in terms of dictionary learning, and the zeroth-order image moment constraints are incorporated into the statistical iterative reconstruction framework to construct an objective function. Finally, the objective function is minimized using an alternating minimization iterative algorithm. The chest CT image simulated and CT real data experimental results demonstrate that the proposed approach can remove shift artifacts effectively and has superior performance in removing noise and persevering fine structures than the total variation (TV)-based approach.