RESIRE: Accurate tomography with real space iterative reconstruction

Abstract Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundationof tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the numberof projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometricconstraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limitednumber of projections with noise. Over the years, a number of tomographic reconstruction methods have been developedincluding direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-spaceiterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of areconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step isimplemented 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 otherexisting tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be usedto reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of anamorphous 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 is freely availablefrom our group website.