Objectives: The filtered backprojection is not able to cope with metal-induced inconsistencies in the Radon space which leads to artifacts in reconstructed CT images. A new algorithm is presented that reduces the drawbacks of existing artifact reduction strategies. Methods: Inconsistent projection data are bridged by directed interpolation. These projections are reconstructed using a weighted maximum likelihood algorithm (λ-MLEM). The correlation coefficient between images of a torso phantom marked with steel markers reconstructed with λ-MLEM and images of the same torso slice without markers quantifies the quality achieved. For clinical data, entropy maximization is presented to obtain appropriate weightings. Results: Different interpolation strategies have been applied. The quality of reconstruction sensitively depends on the complexity of interpolation. A directional interpolation gives best results. However, the quality of the images can be further improved by an appropriate weighing within λ-MLEM. This has been demonstrated with data from a torso phantom, a jaw with amalgam fillings and a hip prosthesis. Conclusions: λ-MLEM image reconstruction using data from directional Radon space interpolation is a new approach for metal artifact reduction. The weighting in this statistical approach is used to reduce the influence of residual inconsistencies in a way that optimal artifact suppression is obtained by optimizing a compromise between residual inconsistencies and void data. The image quality is superior compared with other artifact reduction strategies.