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.

Abstract: We present the ASTRA Toolbox as an open platform for 3D image reconstruction in tomography. Most of the software tools that are currently used in electron tomography offer limited flexibility with respect to the geometrical parameters of the acquisition model and the algorithms used for reconstruction. The ASTRA Toolbox provides an extensive set of fast and flexible building blocks that can be used to develop advanced reconstruction algorithms, effectively removing these limitations. We demonstrate this flexibility, the resulting reconstruction quality, and the computational efficiency of this toolbox by a series of experiments, based on experimental dual-axis tilt series.