Fig. 1.

A schematic interpretation of the approach. A structure is iteratively refined through a two-step procedure. The first step, which is called Expectation in mathematical terms, has been labeled “Alignment.” In this step, computer-generated projections of the structure are compared with the experimental images, resulting in information about the relative orientations of the images. Orientations are not assigned in a discrete manner, but probability distributions over all possible assignments [Γ_iϕ⁽ⁿ⁾] are calculated, and the sharpness of these distributions is determined by the power of the noise in the data. The second step is called Maximization and has been labeled “Smooth reconstruction.” In this step, the experimental images are combined with the prior information into a smooth, 3D reconstruction through Eq. (9), and updated estimates for the power of the noise and the signal in the data are obtained through Eqs. (10) and (11). The relative contributions of the data and the prior to the reconstruction are dictated by Bayes' law and depend on the power of the noise and the power of the signal in the data [see Eq. (9)]. The new structure and the updated estimates for the power of the noise and the signal are then used for a subsequent iteration. Iterations are typically stopped after a user-defined number or when the structures do not change anymore.