Reconstructing Crystalline Structures from Few Images Under High Resolution Transmission Electron Microscopy

The present paper is motivated by the demand from material sciences to reconstruct crystalline structures given through their images under high resolution transmission electron microscopy (HRTEM) in a certain limited number of directions. In particular, [31] and [22] show how a quantitative analysis of images from high resolution transmission electron microscopy can be used to determine the number of atoms on atomic columns in certain directions; see Sects. 2 and 3. Mathematically, this leads to the problem of reconstructing finite lattice sets from certain of their marginal sums; see Sect. 4.