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

Ali Punjani; Haowei Zhang; David J. Fleet

There is a long line of cryo-EM research aimed at estimating the local resolution at each voxel of a 3D structure once a refinement is complete [2, 17, 29] . These methods are generally based on statistical tests applied to the coefficients of a windowed Fourier transform [2] or some form of wavelet transform [17, 29] . Although the aim of non-uniform refinement is not to estimate resolution per se, the regularizer parameter θ(x) does correspond to a local frequency band-limit at each voxel. As such, it might be viewed as a proxy for local resolution, but with some important differences. Notably, our formulation defines θ(x) as the optimum of a cross-validation objective that removes noise. It does not depend on a particular definition of "local resolution" nor on an explicit resolution estimator.