Abstract: Quantitative electron tomography is proposed to characterize porous materials at a nanoscale. To achieve reliable three-dimensional (3D) quantitative information, the influence of missing wedge artifacts and segmentation methods is investigated. We are presenting the Discrete Algebraic Reconstruction Algorithm as the most adequate tomography method to measure porosity at the nanoscale. It provides accurate 3D quantitative information, regardless the presence of a missing wedge. As an example, we applied our approach to nanovoids in La2Zr2O7 thin films.

Abstract: We introduce single-shot x-ray tomography that aims to estimate the target image from a single cone-beam projection measurement. This linear inverse problem is extremely under-determined since the measurements are far fewer than the number of unknowns. Moreover, it is more challenging than conventional tomography, where a sufficiently large number of projection angles forms the measurements, allowing for a simple inversion process. However, single-shot tomography becomes less severe if the target image is only composed of known shapes. This paper restricts analysis to target image function that can be decomposed into known compactly supported non-negative-valued functions termed shapes. Hence, the shape prior transforms a linear ill-posed image estimation problem to a non-linear problem of estimating the roto-translations of the shapes. We circumvent the non-linearity by using a dictionary of possible roto-translations of the shapes. We propose a convex program CoShaRP, to recover the dictionary coefficients successfully. CoShaRP relies on simplex-type constraints and can be solved quickly using a primal-dual algorithm. The numerical experiments show that CoShaRP recovers shape stably from moderately noisy measurements.