Restoration of direct Fourier three-dimensional reconstructions of crystalline specimens by the method of convex projections

Abstract

We consider the problem of the three-dimensional (3-D) reconstruction of objects by the direct Fourier method (DFM) and their restoration by the method of projections on to convex sets (POCS). The main discussion is centered on the case of specimens arranged in a two-dimensional (2-D) crystal and imaged by transmission electron microscopy, although the conclusions could be extended to more general cases. We present results of the restoration of the 3-D reconstruction of a computer generated 2-D crystal under different conditions of data collection limitation. A preliminary application with a real biological specimen (the connector of bacteriophage phi 29) is also presented. These results indicate that POCS can be used practically, in certain cases, to restore 3-D reconstructions obtained by the DFM, giving grounds for the proposal of the study of a combined DFM + POCS (reconstruction + restoration) method for the determination of biological structures by electron microscopy and 3-D image processing.