Error bounds for discrete tomography

Discrete tomography deals with the problem of reconstructing a an image, with a few number of different grey values, from its projections. In particular, there is a focus on highly underdetermined reconstruction problems for which many solutions may exist. In such cases, it is important to have a quality measure for the reconstruction with respect to the unknown original image. In this thesis, we derive a series of computable upper bounds that can be used to guarantee the quality of a reconstructed binary image. This technique can be used with arbitrary projection model, number of projections and direction. This technique is also valid for bounding the error on higher resolution binary reconstructions from low resolution scans. When studying the problem of generating error bounds for binary tomography, we obtained a sufficient condition for the existence of binary solutions for the reconstruction problem. This condition allowed us to create a feature detection technique which is independent of a particular recontruction. We also developed and experimented a discrete reconstruction algorithm which guarantees that the projections of the reconstructed discrete image are close to the given set of projections

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