The invention relates to a computed tomography apparatus comprising a radiation source (2) and a detector (6) for generating detection values depending on a conical radiation beam (4). A weight providing unit (12) provides, for combinations of voxels of an image and detection values, weights for weighting the detection values, and a beam shaper shapes the conical radiation beam (4) such that for at least a part of the detection values the inverse of the variance of a respective detection value is positively correlated with an average of the weights corresponding to the combinations of the voxels, which correspond to the respective detection value, and the respective detection value. This shaping of the conical radiation beam improves the signal-to-noise ratio of the weighted detection values.
