Low-pass filtering revisited: ramped phase randomization for cryo-EM map comparison and data augmentation
- 1The Pennsylvania State University
Abstract
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.
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BibTeX
@misc{dang2026lowpass,
title = {{Low-pass filtering revisited: ramped phase randomization for cryo-EM map comparison and data augmentation}},
author = {L. Y. Dang and W. Jiang},
howpublished = {bioRxiv},
year = {2026},
month = oct,
doi = {10.64898/2026.10.30.763149},
url = {https://www.biorxiv.org/content/10.64898/2026.10.30.763149v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Low-pass filtering revisited: ramped phase randomization for cryo-EM map comparison and data augmentation
AU - L. Y. Dang
AU - W. Jiang
PY - 2026
DA - 2026/10/30
PB - bioRxiv
DO - 10.64898/2026.10.30.763149
UR - https://www.biorxiv.org/content/10.64898/2026.10.30.763149v1
AB - 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.
ER -