• X-ray absorption computerized tomography;
  • laterally extended objects;
  • ring artefacts;
  • filtered back-projection;
  • inverse problem;
  • laminography

There are many objects for which the attenuation varies significantly as they are rotated during computerized X-ray tomography, for example plate samples. This can lead to significant ring artefacts in the subsequent tomographic reconstructions. In this paper a new method is presented that can successfully suppress such ring artefacts and is applicable to both parallel and cone-beam geometries. Rapid correction is achieved via an analytical formula which involves only a matrix-vector multiplication, for which the matrix is known and depends on a regularization parameter. The efficacy of the method is demonstrated for a paleontological sample (calcified shark cartilage) and a carbon–carbon composite/Ti–SiC metal matrix composite test sample.