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

Ali Punjani; Haowei Zhang; David J. Fleet

estimation of the spatial regularization parameters in Algorithm 2 effectively partitions each half-dataset into quarter-datasets, and we often refer to the raw reconstructions in Algorithm 2 as quarter-maps. The non-uniform refinements on half-maps are therefore entirely independent, satisfying the assumptions of a "gold-standard" refinement [28] . By contrast, conventional uniform refinement uses FSC between halfmaps to determine regularization parameters at each iteration, thereby sharing masks and regularization parameters, both of which contaminate final FSC-based assessment because the two half-maps are no longer reconstructed independently. Most importantly, non-uniform refinement uses Eqn. 6 to define the optimal parameters with which to regularize each half-set reconstruction at each refinement iteration. Figure 2 shows an example of the difference between uniform filtering (FSC-based) and the new CV-optimal regularizer used in non-uniform refinement. Uniform regularization removes signal and noise from all parts of the 3D map equally. Nonuniform regularization, on the other hand, removes more noise from disordered regions, while retaining the high-resolution signal in well-structured regions that is critical for aligning 2D particle images in the next iteration.