Limited-data x-ray CT for underwater pipeline inspection

Tomographic reconstruction from limited data is an important problem that arises in many applications and can be handled in many ways. Here we consider inspection of underwater oil pipelines via fan-beam x-ray CT where, due to restrictions in the measurement device, the beam cannot illuminate the full area to be reconstructed. Moreover, it is desirable to use only a small number of projections to save measurement time. We use microlocal analysis to determine a favorable scanning geometry, and propose a reconstruction method based on compactly supported shearlets with a weighted sparsity penalty. Numerical simulations and results on real data demonstrate the usefulness of our approach and that we are able to locate defects in the pipe from a small number of projections.