Low-pass filtering revisited: ramped phase randomization for cryo-EM map comparison and data augmentation

Conventional low-pass filters attenuate or remove high-frequency Fourier amplitudes but leave the phases intact wherever the amplitude response stays above zero. As a result, fine-scale detail of the original signal can persist beyond the target resolution. A sharp cutoff removes this detail but produces ringing artifacts. To address both limitations, this work introduces ramped phase randomization, which extends a conventional low-pass filter by adding random offsets to Fourier phases that increase smoothly with spatial frequency. For cryo-EM maps, the correlation between a map at the target resolution and an ideal, noiseless map sets the levels of the phase offsets, with a correction for the finite resolution of the input map. On three published map pairs, ramped phase filtering reduced the higher resolution parent's fine detail to a level similar to that of independently determined maps at the lower target resolution, whereas amplitude-only filtering kept the parent's sharp features. The FSCs between the filtered maps and their parents closely resembled those of the experimental maps. The same filter also serves as a data augmentation approach for neural network-based machine learning. With ramped phase randomization, each augmented copy keeps the power spectrum and low-frequency content of the original example but has a different high-frequency pattern. For simulated CryoBench particles of 16 ribosome assembly states, phase augmentation raised mean test accuracy in all 20 combinations of training-set size and latent dimension, by 20.8 percentage points on average (range from 3.3 points to 44.2 points). On two general deep learning benchmarks, mean test accuracy rose from 92.15% to 96.99% with 60 labelled UCI Synthetic Control traces and from 53.44% to 74.27% with 500 labelled noisy MNIST images. The ramped phase randomization is implemented in an open-source Python package, with a companion browser application for interactive visualization of cryo-EM maps and filtering effects.