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Large patient anatomies and limited imaging fleld-of-view (FOV) lead to truncation of CT projections. Truncation introduces serious artifacts into reconstructed images, including central cupping and bright external rings. FOV may be increased using laterally offset detectors, but this requires sophisticated imaging hardware and full angular scanning. We propose a novel method to complete truncated projections based on the observation that the thickness of the patient may be estimated along the projection rays by calculating water-equivalent thicknesses (WET). These values are not at all affected by truncation and thus constitute valuable auxiliary information. We parameterize pairs of points along each ray that intersects the unknown object boundary. These points are separated by the measured WET value (obtained from projections that have been corrected for scatter and beam-hardening). We assume, for all large body parts, that the patient outline may be roughly approximated as an ellipse. Using a deterministic optimization algorithm, we simultaneously estimate the point positions and ellipse parameters by minimizing the distance between point sets and the ellipse boundary. The optimal ellipse is used to complete the truncated projections. Reconstruction then ensues. We apply the algorithm to a severely truncated CT dataset of a typical abdomen. The RMS error between complete data and truncated reconstructions (corrected using an empirical extrapolation approach) is 20.4% for an abdominal dataset. The new algorithm reduces this error to 1.0%. Even thought the algorithm assumes an elliptical patient cross-section, truly impressive increases in quantitative image quality are observed. The presence of pelvic bone in the image does not appreciably bias the ellipse position even though it does bias the thickness estimates for some rays. The algorithm incurs low computational cost and is suitable for on-line clinical workflows.