Accurate real space iterative reconstruction (RESIRE) algorithm for tomography

Abstract

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at https://zenodo.org/record/7273314.

Nanoscale Three-Dimensional Network Structure of a Mesoporous Particle Unveiled via Adaptive Multidistance Coherent X-ray Tomography

“…The 3D electron density distribution of the particle was constructed from these 27 projection images via tomographic reconstruction using the RESIRE algorithm, as shown in Figure 3D and Movie S1. 25 The density map exhibits a high electron density at the intermediate area between the two spherical particles. During the spinodal decomposition, Marangoni flow causes an internal convection upon the merging of fluidic block copolymer (BCP)/silica droplets, leading to a rapid movement of the BCP/silica phase near the intermediate area from a significant buildup of capillary pressure there.…”

“…We collected projection images at 27 equally sloped angles from −69.44° to +69.44° to acquire the 3D density map of the specimen. The 3D electron density distribution of the particle was constructed from these 27 projection images via tomographic reconstruction using the RESIRE algorithm, as shown in Figure D and Movie S1 . The density map exhibits a high electron density at the intermediate area between the two spherical particles.…”

“…Next, 3D tomographic reconstruction was implemented using the RESIRE algorithm for tomography . First, a few reconstructions were conducted through 20 iterations of RESIRE for translation alignment .…”

“…Next, 3D tomographic reconstruction was implemented using the RESIRE algorithm for tomography. 25 First, a few reconstructions were conducted through 20 iterations of RESIRE for translation alignment. 53 We iteratively calibrated translational shifts by comparing the input projection images with projection images from the reconstructed volume, until the calculated shifts were below 0.01 pixel.…”

In Situ and Emerging Transmission Electron Microscopy for Catalysis Research

“…A tomographic tilt series of images are then collected by rotating the sample around a tilt axis. Methods to mitigate radiation damage during acquisition have been outlined previously. , After postdata processing, the tilt series is iteratively reconstructed to produce a 3D atomic structure by using advanced computational algorithms, ,, from which the 3D coordinates of the individual atoms in the sample are traced with high precision. Recently, Zhou et al advanced AET to study the 4D (3D space and time) dynamics of early stage nucleation in an ex situ experiment at atomic resolution .…”