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The exposure of normal tissues to high radiation during cone-beam CT (CBCT) imaging increases the risk of cancer and genetic defects. Statistical iterative algorithms with the total variation (TV) penalty have been widely used for low dose CBCT reconstruction, with state-of-the-art performance in suppressing noise and preserving edges. However, TV is a first-order penalty and sometimes leads to the so-called staircase effect, particularly over regions with smooth intensity transition in the reconstruction images. A second-order penalty known as the Hessian penalty was recently used to replace TV to suppress the staircase effect in CBCT reconstruction at the cost of slightly blurring object edges. In this study, we proposed a new penalty, the TV-H, which combines TV and Hessian penalties for CBCT reconstruction in a structure-adaptive way. The TV-H penalty automatically differentiates the edges, gradual transition …