Few-view computed tomography image reconstruction using mean curvature model with curvature smoothing and surface fitting

The edge and curve of an image surface are crucial visual cues in vision psychology. Studies show that human beings can effectively process curvature information, such as distinguishing the concavity and convexity of an image. This finding indicates that curvature is essential for a desired image to be felt authentic and real. In this paper, a novel few-view computed tomography (CT) image reconstruction model is proposed based on mean curvature (MC). Similar to the total variation model, the MC employs the $L_{1}$ -norm to utilize the sparse prior information. Constructing efficient numerical algorithms for minimizing the MC model is significant due to the associated high-order Euler–Lagrange equations. A two-step numerical method, including curvature smoothing and surface fitting, is presented to solve the proposed model, which can be stably and efficiently solved by the alternating direction minimization. By applying the variable splitting method, the explicit solutions of the corresponding subproblems can be efficiently and quickly approximated by fast Fourier transform and the proximal point method. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to verify the efficiency and feasibility of the proposed method. Comparisons with conventional algorithms demonstrate that the proposed approach has considerable advantages in few-view CT reconstruction problems.