Although three-dimensional electron microscopy (3D-EM) permits structural characterization of macromolecular assemblies in distinct functional states, the inability to classify projections from structurally heterogeneous samples has severely limited its application. We present a maximum likelihood-based classification method that does not depend on prior knowledge about the structural variability, and demonstrate its effectiveness for two macromolecular assemblies with different types of conformational variability: the Escherichia coli ribosome and Simian virus 40 (SV40) large T-antigen.

Summary. We investigate the behavior of Kaczmarz's method with relaxation for inconsistent systems. We show that when the relaxation parameter goes to zero, the limits of the cyclic subsequences generated by the method approach a weighted least squares solution of the system. This point minimizes the sum of the squares of the Euclidean distances to the hyperplanes of the system. If the starting point is chosen properly, then the limits approach the minimum norm weighted least squares solution. The Proof is given for a block-Kaczmarz method.

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