Preliminary studies on iterative transform algorithms for 3D reconstruction of 2D crystals

In this paper, we apply iterative transform algorithms, namely the error reduction algorithm and the hybrid input-output algorithm, to retrieve missing data in 3D reconstruction from 2D crystal images. 3D protein structures are determined using cryo-electron microscopy (cryo-EM). Extremely strong noise in cryo-EM brings in unreliable artifacts and a limited number of projections leave missing components in 3D Fourier space. We consider all these cases as missing data problems. The iterative transform algorithms aim at improving 3D resolution through applying constraints in Fourier space and real space. In Fourier space, the "true" signal components, which are either physically measured or assumed, are retained while the delusive components are updated iteratively. In real space, the protein has spatial limitation or "finite support" and possesses non-negativity values. Preliminary results of 3D reconstruction of membrane protein GlpF suggest that the iterative transform process improves 3D resolution.