On the bayesian reconstruction method for randomly oriented particles in cryo-EM

In this work, we address the problem of reconstructing the 3D structure of an object from a set of transmission electron microscopy (TEM) images, taken at unknown, random directions around the object. We use the expectation maximisation (EM) algorithm for finding the maximum a posteriori (MAP) estimates for the 3D structure from the marginal posterior, where the view orientations are integrated out. In comparison to previous work related to this single particle reconstruction application, we have made the following novel contributions. (1) We use Monte Carlo integration to approximate the expected complete data log posterior to reduce the computational complexity; (2) we use a uniform prior in the space of rotations instead of the space of rotation angles; (3) we use the positivity constraint for the reconstructed density that is both a physical constraint as well as it acts as a natural sparsity prior; (4) on the M-step we use a large scale, subspace trust-region method based on the interior-reflective Newton method for efficient computation of the reconstruction. We experimented the approach on cryo-electron microscopy (cryo-EM) protein images. The results are promising and show that the 3D structure can be robustly recovered with the proposed method in spite of the very low signal-to-noise ratio (SNR).