Robust Indexing for Challenging Serial X-ray Diffraction Patterns

Abstract

Serial crystallography experiments routinely produce thousands of diffraction patterns from crystals in random orientations. To turn this stream of images into a usable dataset, each pattern must be indexed before integration and merging can proceed. In practice, diffraction patterns may contain only a small number of reliable peaks, be contaminated by background or spuriously detected reflections, or arise from crystals with highly skewed unit cells. These factors make indexing unstable in the small-N regime. We introduce a robust indexing algorithm tailored to this setting. We formulate indexing as a symmetry-aware lattice decoding problem and design a loss that explicitly incorporates lattice symmetries while trimming outlier peaks that are inconsistent with any plausible orientation. We combine this objective with a reciprocal-space basis reparameterization that stabilizes decoding for skewed or poorly conditioned lattices, and we develop a dedicated small-N objective mode that couples refined peak scoring with a method to recover orientations from very few reflections. The resulting method is memory-efficient and suitable for robust indexing. We evaluate our approach on three protein datasets from the Coherent X-ray Imaging Data Bank collected at XFEL facilities, using identical preprocessing and unit-cell information across methods. Across all datasets, our algorithm matches or outperforms established indexers such as XGANDALF and TORO, with particularly large gains for patterns with few indexed peaks and for crystals with skewed unit cells. While slower, our method is extremely memory-efficient, and its structure allows high-parallelism on CPUs or larger batch sizes on GPUs. These results show that exploiting lattice structure, symmetry, and small-N-aware search yields substantial improvements in indexing robustness.