Improving Cryo-EM Optimization Robustness with an Optimal Transport Loss Function for Noisy Images

Abstract

Many tasks in single-particle cryo-electron microscopy (cryo-EM), such as 2D/3D classification and homo/heterogeneous reconstruction, require optimizing model parameters to minimize the discrepancy between observed data and a forward model. The standard Mean Squared Error (MSE) loss function is computationally efficient but suffers from a non-convex rugged loss landscape, particularly for high-resolution heterogeneity inference. In this work, we investigate the practical utility of Sliced Wasserstein (SW) distances. We implement exact W2 estimators (inverse-CDF and greedy matching) of projections alongside a computationally efficient proxy based on the L2 norm of CDFs, a formulation akin to the sliced Cramer-von Mises distance. We establish the latter as a robust, fully differentiable workhorse for the cryo-EM forward model. We evaluate its performance against the MSE in joint inference tasks recovering pose, CTF parameters, and conformational heterogeneity. Our results demonstrate that SW significantly broadens the basin of attraction, enabling robust gradient-based optimization from distant initializations where MSE fails. Using a helical spiral toy model, we highlight how SW losses are sensitive to per-particle contrast, where background noise level miscalibration can induce geometric bias in the inferred structure. We show that this bias is manageable through a joint optimization strategy that treats background contrast as a learnable parameter. Finally, we validate the approach on a synthetic dataset using the Zernike3D framework, showing that the SW loss works and yields an accurate landscape representations, comparable with MSE. These findings establish SW as a powerful tool for navigating the rugged landscapes of cryo-EM forward model parameters. SynopsisThe Sliced Wasserstein loss provides a smoother optimization landscapes than mean squared error for single particle cryo-EM joint inference of pose, CTF defocus and conformational heterogeneity. Estimating background contrast is essential to avoid biasing other parameters.