ESTIMATION OF VARIANCE DISTRIBUTION IN 3-DIMENSIONAL RECONSTRUCTION .1. THEORY

A theory is developed for estimating the three-dimensional (3-D) varia nce of a 3-D image reconstructed from projections by weighted backproj ection. The theory is applicable for any data-collection schemes that produce partially redundant sampling of the angular space. The particu lar data collection considered here, the single-exposure random-conica l scheme, is used for the reconstruction of macromolecules in electron microscopy. In this context, the purpose of the 3-D Variance estimati on is to detect and localize the conformational variability, to assess the significance of structural differences between two experimentally related 3-D images, and to assess the significance of local features in a 3-D image. The 3-D variance estimate of each reconstruction voxel is obtained by (i) the comparison of closest points on Fourier sectio ns associated with difference projections, (ii) the comparison of neig hbor projections in real space, or (iii) the comparison of projections with reprojections of the reconstruction. (C) 1995 Optical Society of America