Reconstruction Schemes Based on Uniform Angular Coverage

For completeness, two reconstruction schemes that rely on a uniform coverage of the space of orientations should be mentioned. Both use spherical harmonics as a means of representing the object and its relationship to the input projections. The requirement of statistical uniformity and the choice of the rather involved mathematical representation have restricted the use of these schemes to model computations and few demonstrations with experimental data. The first scheme, proposed by Zvi Kam (1980), is based on a sophisticated statistical approach difficult to paraphrase here. The second scheme, introduced by Provencher and Vogel (1983, 1988) and Vogel and Provencher (1988), is designed to determine the relative orientations of the projections of a set of particles by a least-squares method, but it requires approximate starting orientations. Thus far, only a single reconstruction of an asymmetric particle, the 50S ribosomal subunit, has been obtained with this latter method (Vogel and Provencher, 1988).

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