Natural and synthetic biological objects, e.g., Tobacco Mosaic Virus and tubes from bacteriophage P22 hexamers, form a large class of helically-symmetric biological nano-scale objects. Helical symmetry is a class of symmetries described by two relatively prime integers (u, v) and a period c. Typically u, v, and c are all unknown. Electron microscopy provides a method of visualizing such objects in 3-D via computational reconstruction from projection 2-D image measurements. Damage of the object by the electron beam restricts high-resolution studies to a single image of an unoriented object at low (? 0.2) SNR. This work considers the frequently-occurring case where multiple identical objects are available and so multiple images, one of each object, can be combined by computation to achieve a 3-D reconstruction of the object. Due to the poor SNR, the focus of this work is on maximum likelihood (ML) estimators to determine the reconstruction. The unknown orientation of the object in the microscope and the period of the helical symmetry are treated as nuisance parameters and the joint ML estimate of (u, v) and the parameters that describe the 3-D structure given the helical symmetry parameters is computed via an expectation maximization approach. This approach contrasts with a variety of current approaches which separate symmetry determination from reconstruction and which do not use explicit statistical models of the noise. Examples of the application of this approach to synthetic and experimental images from Tobacco Mosaic Virus are described.