Non-uniform refinement: Adaptive regularization improves single particle cryo-EM reconstruction

Ali Punjani; Haowei Zhang; David J. Fleet

To improve signal detection, we further constrain θ * to be smooth. That is, although in some regions θ should change quickly (solvent-protein boundaries), in most regions we expect it to change slowly (solvent and regions of rigid protein mass). Smoothness effectively limits the number of degrees of freedom in θ, which is important to ensure θ itself does not overfit during iterative refinement (see Sec. 7). One can encourage smoothness in θ by explicitly penalizing spatial derivatives of θ in the objective (Eqn. 3), but this yields a Markov random field problem that is hard to optimize. Alternatively, one can express θ in a low-dimensional basis (e.g., radial basis functions), but this requires prior knowledge of the expected degree of smoothness. Instead, we adopt a simple but effective approach. Assuming that θ is smoothly varying, we treat measurements in the local neighborhood of x as additional constraints on 5 . CC-BY-NC-ND 4.0 International license author/funder. It is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2019.12.15.877092 doi: bioRxiv preprint