Epipolar Consistency Guided Beam Hardening Reduction-ECC 2

Beam hardening is a problem arising in every computed tomography scan with a conventional X-ray tube. We describe a new calibration-free, computationally efficient algorithm for mono-material beam hardening reduction. It is based on optimization of the Epipolar consistency condition on computed tomography raw data. The efficiency of our approach is achieved by formulating the optimization problem directly on the Radon intermediate function conventionally used by these consistency conditions. We thus avoid recalculating the intermediate function and can solve a homogeneous least squares optimization problem. We regularize the ill-posed homogeneous problem by introduction of a regularizer which keeps the dynamic range of the projection data constant. The resulting constrained problem can be solved in closed form. To demonstrate the effectiveness of our approach we apply our method to simulation experiments. We additionally provide experimental insight to the robustness of our algorithm to image noise, geometrical noise and truncation. As a last experiment we apply our method to real data.