Algorithms for sorting and reconstructing heterogeneous nanoscale biological objects from cryo electron microscopy images

Statistical algorithms are described for 2- and 3-D signal reconstruction and classification problems based on electron microscopy images where the objects displayed in the images are heterogeneous. Both discrete heterogeneity (there exist classes of objects but all objects within one class are identical) and continuous heterogeneity (there exist classes of objects but, in addition, the objects within a class differ). With continuous heterogeneity, the idea of reconstruction is generalized from reconstruction of a unique 2- or 3-D object to reconstruction of the statistics of the 2- or 3-D object. The basic process is reconstruction by maximum likelihood estimation computed by an expectation-maximization algorithm with classification following as postprocessing given the reconstruction. Two examples are considered, one focusing on classification and one on reconstruction.