Discrete image reconstruction for material quantification

Imaging and quantifying elements of the internal structure of a sample is important for the analysis and engineering of materials. Electron tomography is a powerful technique that can reveal the three-dimensional structure of a sample at the nanometer scale. Unfortunately, the limited quantity and quality of electronic tomographic data produces artifacts in conventional reconstructions that can confound subsequent segmentation and quantitation. An alternative approach, termed discrete tomography, is to directly reconstruct only a limited and discrete set of pixel amplitudes. Recently, graph cut methods have been used with great success on such discrete-label problems in the domain of image segmentation. This work aims to develop such a graph-cut framework for discrete tomography. We analyze the structure of linear inverse problems, showing the relationship of the sensing structure to graph non-representability. We then propose a method that iteratively minimizes a surrogate energy functional that is always graph-representable. We show reconstruction results using synthetic phantom images for limited angle scenarios and compare them to a conventional reconstruction technique.