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Cryo electron microscopy is a measurement modality which provides images from which 3-D reconstructions of biological particles such as viruses can be estimated. When the specimen is composed of mixtures of particles of different types, the 3-D reconstruction problem must be solved jointly with a pattern classification problem. The performance of the estimators is not well understood because the computations are not suitable for analytical results and are too large for extensive Monte Carlo results. The problem formulation typically has nuisance parameters and different treatments of the nuisance parameters lead to different estimators. In this paper two types of estimators and two model problems are studied with the conclusion that it is difficult to improve upon maximum likelihood estimators based on integrating out the nuisance parameters.

Model Calculations for Joint Pattern Recognition and Signal Reconstruction in Cyro Electron Microscopy