Local and global uncertainty in binary tomographic reconstruction

• In binary tomography the projection data might be insufficient for an accurate reconstruction.
• We proposed methods to measure the reliability of the pixels of the reconstructions.
• We described a method for measuring the global uncertainty of the reconstructed image.
• We gave additional validation of the results.
• We proposed some possible applications of the given methods as well.

In binary tomography the goal is to reconstruct the inner structure of homogeneous objects from their projections. This is usually required from a low number of projections, which are also likely to be affected by noise and measurement errors. In general, the distorted and incomplete projection data holds insufficient information for the correct reconstruction of the original object.In this paper, we describe two methods for approximating the local uncertainty of the reconstructions, i.e., identifying how the information stored in the projections determine each part of the reconstructed image. These methods can measure the uncertainty of the reconstruction without any knowledge from the original object itself. Moreover, we provide a global uncertainty measure that can assess the information content of a projection set and predict the error to be expected in the reconstruction of a homogeneous object. We also give an experimental evaluation of our proposed methods, mention some of their possible applications, and describe how the uncertainty measure can be used to improve the performance of the DART reconstruction algorithm.