Robust Indexing for Challenging Serial X-ray Diffraction Patterns
Marc M Nasser, Frédéric Poitevin, Kevin M Dalton
TL;DR
The paper introduces a robust indexing method for serial X-ray diffraction patterns in the small-$N$ regime, formulating orientation determination as a symmetry-aware lattice decoding problem. It combines reciprocal-basis reduction, Babai's nearest-plane decoding, and a differential-evolution-based orientation search with a small-$N$-focused local refinement to improve robustness against noise and skewed unit cells. Across three CXIDB XFEL datasets, the method matches or surpasses state-of-the-art indexers like TORO and XGANDALF, with pronounced gains when patterns contain few reflections. The approach is memory-efficient and highly parallelizable on GPUs, making it well-suited for offline reprocessing and noisy datasets, with future work aimed at speeding up orientation search for online deployment.
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.