In Cryo-EM 3D map refinement, popular software packages jointly reconstruct the 3D map while estimating orientations. The orientation estimation can roughly be categorised in two type of approaches: marginalisation and optimisation. While the former tends to be more robust to noise, the latter has better consistency with respect to the data. So far it appears difficult to obtain both data-consistency and noise-robustness in a single method. In this talk we will revisit the orientation estimation process. In particular, we develop an alternative that can be interpreted as being “in between marginalisation and optimisation” and argue that this new method is both robust to noise and data-consistent. Additionally, the framework of lifting-based global optimisation on manifolds allows analysis of the proposed methods that lead to several practical theoretical guarantees. Both theoretical results and performance on simulated data will be tested in numerical experiments.
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