Iterative CBCT reconstruction using Hessian penalty

Statistical iterative reconstruction algorithms have shown potential to improve cone-beam CT (CBCT) image quality. Most iterative reconstruction algorithms utilize prior knowledge as a penalty term in the objective function. The penalty term greatly affects the performance of a reconstruction algorithm. The total variation (TV) penalty has demonstrated great ability in suppressing noise and improving image quality. However, calculated from the first-order derivatives, the TV penalty leads to the well-known staircase effect, which sometimes makes the reconstructed images oversharpen and unnatural. In this study, we proposed to use a second-order derivative penalty that involves the Frobenius norm of the Hessian matrix of an image for CBCT reconstruction. The second-order penalty retains some of the most favorable properties of the TV penalty like convexity, homogeneity, and rotation and translation invariance, and has a better ability in preserving the structures of gradual transition in the reconstructed images. An effective algorithm was developed to minimize the objective function with the majorization-minimization (MM) approach. The experiments on a digital phantom and two physical phantoms demonstrated the priority of the proposed penalty, particularly in suppressing the staircase effect of the TV penalty.