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<p>Atomic electron tomography (AET) is a powerful technique for determining the three-dimensional atomic structure of matter in real space. However, conventional AET requires numerous projections across a wide angular range. The high dose and prolonged acquisition severely limit its application. Here, we propose an interpretable and universal algorithm for low-dose, fast and tilt-constrained AET: null-space iterative reconstruction (NSIRE), which uses an unsupervised diffusion model to iteratively compute null-space solutions of projection equations, thereby generating tomograms consistent with both projection constraints and atomic potential prior. NSIRE can resolve a wide range of complex materials under 6–12° sparse projection or within ±29° small tilt-range without retraining. Using the NSIRE, we determine the three-dimensional atomic structures of a 4-nm Pt nanoparticle with grain boundaries and a 3-nm PtCo nanoalloy (the smallest one resolved so far), achieving a root-mean-square displacement of &lt;20 pm and high projection consistency, overcoming the scale, dose and time limitations of AET.</p>

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Generative-model-based null-space iterative reconstruction for atomic electron tomography with sparse data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月16日

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  • Han Li,
  • Wenting Cui,
  • Wenda Su,
  • Huan Lei,
  • Kuang Yu,
  • Jiali Yang,
  • Jia Li,
  • Lin Gan

摘要

Atomic electron tomography (AET) is a powerful technique for determining the three-dimensional atomic structure of matter in real space. However, conventional AET requires numerous projections across a wide angular range. The high dose and prolonged acquisition severely limit its application. Here, we propose an interpretable and universal algorithm for low-dose, fast and tilt-constrained AET: null-space iterative reconstruction (NSIRE), which uses an unsupervised diffusion model to iteratively compute null-space solutions of projection equations, thereby generating tomograms consistent with both projection constraints and atomic potential prior. NSIRE can resolve a wide range of complex materials under 6–12° sparse projection or within ±29° small tilt-range without retraining. Using the NSIRE, we determine the three-dimensional atomic structures of a 4-nm Pt nanoparticle with grain boundaries and a 3-nm PtCo nanoalloy (the smallest one resolved so far), achieving a root-mean-square displacement of <20 pm and high projection consistency, overcoming the scale, dose and time limitations of AET.