HeteroTomo3D.jl

Welcome to the documentation for HeteroTomo3D.

This package provides nonparametric estimation of conformational variability from 3D tomographic data using tensorized Krylov methods in a Reproducing Kernel Hilbert Space (RKHS).

🚀 Key Features

• RKHS Framework: Employs a functional estimation framework tailored for statistical inverse problems.
• 3D Heterogeneity: Facilitates the estimation of mean and covariance structures for non-identical 3D objects.
• Matrix-Free Operators: Implicitly implements Khatri-Rao products, minimizing memory overhead for covariance estimation.
• Singularity-Free Geometry: Utilizes UnitQuaternion to ensure robust 3D rotations without gimbal lock.

📚 References

If you use this package in your research, please cite the following papers:

• Yun, H., & Panaretos, V. M. (2025). Computerized Tomography and Reproducing Kernels. SIAM Review, 67(2), 321–350. https://doi.org/10.1137/23M1616716
• Yun, H., Caponera, A., & Panaretos, V. M. (2025). Low-Dose Tomography of Random Fields and the Problem of Continuous Heterogeneity. arXiv preprint arXiv:2507.10220. https://doi.org/10.48550/arXiv.2507.10220
• Yun, H., & Panaretos, V. M. (2026). Fast and Cheap Covariance Smoothing. Journal of Computational and Graphical Statistics. https://doi.org/10.1080/10618600.2026.2615054