The industrial nondestructive testing (NDT) of objects seems to be an ideal application of discrete tomography. In many cases, the objects consist of known materials, and a lot of a priori information is available (e.g., the description of an ideal object, which is similar to the actual one under investigation). One of the frequently used methods in NDT is to take projection images of the objects by some transmitting ray (e.g., X- or neutron-ray) and reconstruct the cross sections. But it can happen that only a few number of projections can be collected, because of long and/or expensive data acquisition, or the projections can be collected only from a limited range of directions. The chapter describes two DT reconstruction methods used in NDT experiments, shows the results of a DT procedure applied in the reconstruction of oblong objects having projections only from a limited range of angles, and, finally, suggests a few further possible NDT applications of DT.

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}, isbn = {978-0-8176-3614-2}, doi = {10.1007/978-0-8176-4543-4_14}, author = {Joachim Baumann and Zolt{\'a}n Kiss and Sven Krimmel and Attila Kuba and Antal Nagy and Lajos Rodek and Burkhard Schillinger and Juergen Stephan}, editor = {G{\'a}bor T Herman and Attila Kuba} } @article {1854, title = { Image reconstruction and correction methods in neutron and X-ray tomography}, journal = {Acta Cybernetica}, volume = {17}, year = {2006}, pages = {557-587}, publisher = {University of Szeged}, type = {Journal Article}, address = {Szeged, Hungary}, abstract = {Neutron and X-ray tomography are imaging techniques for getting information about the interior of objects in a non-destructive way. They reconstruct cross-sections from projection images of the object being investigated. Due to the properties of the image acquisition system, the projection images are distorted by several artifacts, and these reduce the quality of the reconstruction. In order to eliminate these harmful effects the projection images should be corrected before reconstruction. Taking projections is usually an expensive and time consuming procedure. One of our main goals has been to try to minimize the number of projections - for example, by exploiting more a priori information. A possible way of reducing the number of projections is by the application of discrete tomographic methods. In this case a special class of objects can be reconstructed, consisting of only a few homogenous materials that can be characterized by known discrete absorption values. To this end we have implemented two reconstruction methods. One is able to reconstruct objects consisting of cylinders and spheres made of homogeneous materials only. The other method is a general one in the sense that it can be used for reconstructing any shape. Simulations on phantoms and physical measurements were carried out and the results are presented here. ` `

Discrete tomography (DT) is a new technique to reconstruct discrete images from their projections (like neutron images). The reconstruction methods in DT are different from the conventional ones, because the created images may contain only a few numbers of given discrete values. One of the main reasons to apply DT is that hopefully we need only a few numbers of projections. In many applications we have a situation where we know the material components of the object to be studied, that is, we know the discrete values of the image to be reconstructed. Using discreteness and some a priori information we can apply several DT methods in neutron imaging. Most of the DT reconstruction methods are reducing the problem to an optimization task. We tried two such methods on software and physical phantoms. In these experiments we investigated the effects of the following parameters: number of projections, noise levels, and complexity of the object to be reconstructed. We also developed a software system, called DIRECT, for testing different DT methods, to compare them and to present the reconstructed objects. ` `