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In 3-D reconstruction problems, the image data obtained from cryo electron microscopy is the projection of many heterogeneous instances of the object under study (e.g., a virus). When the object is heterogeneous but has an overall symmetry, it is natural to describe the object as stochastic with symmetrical statistics. This paper presents a maximum likelihood reconstruction approach which allows each object to lack symmetry while constraining the {\it statistics} of the ensemble of objects to have symmetry. This algorithm is demonstrated on bacteriophage HK97 and is contrasted with an existing algorithm in which each object, while still heterogeneous, has the symmetry. Reconstruction results show that the proposed algorithm eliminates long-standing distortions in previous heterogeneity calculations associated with symmetry axes, and provides estimates that make more biologically sense than the estimates of existing algorithms.