Application of natural basis functions to soft x-ray tomography
Natural basis functions (NBFs), also known as natural pixels in the literature, have been applied in tomographic reconstructions of simulated measurements for the JET soft x-ray system, which has a total of about 200 detectors spread over 6 directions. Various types of NBFs, i.e. normal, generalized and orthonormal NBFs, are reviewed. The number of basis functions is roughly equal to the number of measurements. Therefore, little a priori information is required as regularization and truncated singular-valve decomposition can be used for the tomographic inversion. The result of NBFs are compared with reconstructions by the same solution technique using local basis functions (LBFs), and with the reconstructions of a conventional constrained-optimization tomography method with many more LBFs that requires more a priori information. Although the results of the conventional method are superior due to the a priori information, the results of the NBF and other LBF methods are reasonable and show the main features. Therefore, NBFs are a promising way to assess whether features in reconstructions are real or artefacts resulting from the a priori information. Of the NBFs, regular triangular (generalized) NBFs give the most acceptable reconstructions, much better than traditional square pixel, although the reconstructions with pyramid-shaped LBFs are also reasonable and have slightly smaller reconstruction errors. A more-regular (virtual) viewing geometry improves the reconstructions. However, simulations with a viewing geometry with a total of 480 channels spread over 12 directions clearly show that a priori information still improves the reconstructions considerably.
Bibliographic Reference: Report: JET-R(99)07
Availability: Available from JET Joint Undertaking, Abingdon, Oxfordshire (GB)
Record Number: 200012772 / Last updated on: 2000-09-20
Original language: en
Available languages: en