Electron tomography, a powerful imaging tool for studying 3D structures of macromolecular assemblies, always suffers from imperfect reconstruction with limited resolution due to the intrinsic low signal-to-noise ratio (SNR) and inaccessibility to certain tilt angles induced by radiation damage or mechanical limitation. In order to compensate for such insufficient data with low SNR and further improve imaging resolution, prior knowledge constraints about the objects in both real space and reciprocal space are thus exploited during tomographic reconstruction. However, direct Fast Fourier transform (FFT) between real space and reciprocal space remains extraordinarily challenging owing to their inconsistent grid sampling modes, e.g. regular and uniform grid sampling in real space whereas radial or polar grid sampling in reciprocal space. In order to solve such problem, a technique of non-uniform fast Fourier transform (NFFT) has been developed to transform efficiently between non-uniformly sampled grids in real and reciprocal space with sufficient accuracy. In this work, a Non-Uniform fast Fourier transform based Dual-space constraint Iterative reconstruction Method (NUDIM) applicable to biological electron tomography is proposed with a combination of basic concepts from equally sloped tomography (EST) and NFFT based reconstruction. In NUDIM, the use of NFFT can circumvent such grid sampling inconsistency and thus alleviate the stringent equally-sloped sampling requirement in EST reconstruction, while the dual-space constraint iterative procedure can dramatically enhance reconstruction quality. In comparison with conventional reconstruction methods, NUDIM is numerically and experimentally demonstrated to produce superior reconstruction quality with higher contrast, less noise and reduced missing wedge artifacts. More importantly, it is also capable of retrieving part of missing information from a limited number of projections.

电子断层扫描是一种用于研究大分子组装体 3D 结构的强大成像工具，但由于固有的低信噪比 (SNR) 以及辐射损伤或机械限制引起的某些倾斜角无法接近，因此总是存在分辨率有限的不完美重建问题. 为了补偿这种低信噪比的数据不足并进一步提高成像分辨率，因此在层析重建过程中利用了关于真实空间和倒易空间中对象的先验知识约束。然而，真实空间和倒易空间之间的直接快速傅里叶变换（FFT）由于其不一致的网格采样模式（例如，在真实空间中的规则和均匀网格采样而在倒易空间中的径向或极坐标网格采样），仍然非常具有挑战性。为了解决这个问题，已经开发了一种非均匀快速傅里叶变换 (NFFT) 技术，以足够的精度在实空间和倒易空间中的非均匀采样网格之间进行高效变换。在这项工作中，一个基于N on- Uniform快速傅里叶变换的双空间约束迭代重建M提出了适用于生物电子断层扫描的方法（NUDIM），它结合了等斜断层扫描（EST）和基于NFFT的重建的基本概念。在 NUDIM 中，使用 NFFT 可以规避这种网格采样不一致，从而缓解 EST 重建中严格的等斜率采样要求，而双空间约束迭代过程可以显着提高重建质量。与传统的重建方法相比，NUDIM 在数值和实验上被证明可以产生具有更高对比度、更少噪声和减少丢失楔形伪影的卓越重建质量。更重要的是，它还能够从有限数量的预测中检索部分缺失信息。