Variance in three-dimensional reconstructions from projections

Methods for estimation of variance for the three-dimensional (3D) reconstruction from projections are introduced. First, a Fourier space variance for a class of 3D reconstruction algorithms that involve interpolation is derived. It is used to construct a test for the validity of the single particle analysis process. Second, a real space variance/covariance for an arbitrary reconstruction algorithm is introduced. It is calculated using a bootstrap technique and used to investigate conformational variability of biological macromolecules.