To compensate for sparse angular sampling in cone-beam computed tomography causing characteristic streak artifacts, we propose to increase the number of projected views by means of nonlinear directional interpolation. For this purpose, a specific method for accurate interpolation of 3D sinogram data based on a structure tensor approach has been developed. Quantitative evaluation of the interpolation error shows that our method clearly outperforms conventional interpolation schemes. Using a set of simulated cone-beam CT projection data, it is demonstrated that inclusion of interpolated projections into the reconstruction process significantly reduces streak artifacts and noise while preserving spatial resolution to a high degree.