CBCT reconstruction via a penalty combining total variation and its higher-degree term

Penalized weighted least-squares (PWLS) iterative algorithm with a total variation penalty (PWLS-TV) has shown potential to improve cone-beam CT (CBCT) image quality, particularly in suppressing noise and preserving edges. However, it sometimes suffers from the well-known staircase effect, which produces piece-wise constant areas in images. In order to remove the staircase effect, there is an increasing interest in replacing TV by higher-order derivative operations such as Hessian. Unfortunately, Hessian tends to blur the edges in the reconstruction results. In this study, we proposed a new penalty, namely the TV-H penalty, which combines the TV penalty and the Hessian penalty for CBCT reconstruction. The TV-H penalty retains some of the most favorable properties of the TV penalty like suppressing noise and preserving edges and has a better ability in preserving the structures of gradual intensity transition in images. The penalized weighted least-squares (PWLS) criterion with the majorization-minimization (MM) approach was used to minimize the objective function. Two simulated digital phantoms were used to compare the performance of TV, Hessian penalty and TV-H penalties. Our experiments indicated that the TV-H penalty outperformed the TV penalty and the Hessian penalty.