The recent advent of tensor tomography techniques has enabled tomographic investigations of the 3D nanostructure organization of biological and material science samples. These techniques extended the concept of conventional X-ray tomography by reconstructing not only a scalar value such as the attenuation coefficient per voxel, but also a set of parameters that capture the local anisotropy of nanostructures within every voxel of the sample. Tensor tomography data sets are intrinsically large as each pixel of a conventional X-ray projection is substituted by a scattering pattern, and projections have to be recorded at different sample angular orientations with several tilts of the rotation axis with respect to the X-ray propagation direction. Currently available reconstruction approaches for such large data sets are computationally expensive. Here, a novel, fast reconstruction algorithm, named iterative reconstruction tensor tomography (IRTT), is presented to simplify and accelerate tensor tomography reconstructions. IRTT is based on a second-rank tensor model to describe the anisotropy of the nanostructure in every voxel and on an iterative error backpropagation reconstruction algorithm to achieve high convergence speed. The feasibility and accuracy of IRTT are demonstrated by reconstructing the nanostructure anisotropy of three samples: a carbon fiber knot, a human bone trabecula specimen and a fixed mouse brain. Results and reconstruction speed were compared with those obtained by the small-angle scattering tensor tomography (SASTT) reconstruction method introduced by Liebiet al.[Nature(2015),527, 349–352]. The principal orientation of the nanostructure within each voxel revealed a high level of agreement between the two methods. Yet, for identical data sets and computer hardware used, IRTT was shown to be more than an order of magnitude faster. IRTT was found to yield robust results, it does not require prior knowledge of the sample for initializing parameters, and can be used in cases where simple anisotropy metrics are sufficient,i.e.the tensor approximation adequately captures the level of anisotropy and the dominant orientation within a voxel. In addition, by greatly accelerating the reconstruction, IRTT is particularly suitable for handling large tomographic data sets of samples with internal structure or as a real-time analysis tool during the experiment for online feedback during data acquisition. Alternatively, the IRTT results might be used as an initial guess for models capturing a higher complexity of structural anisotropy such as spherical harmonics based SASTT in Liebiet al.(2015), improving both overall convergence speed and robustness of the reconstruction.

中文翻译：

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高速张量断层扫描：迭代重建张量断层扫描（IRTT）算法


张量断层扫描技术的最新出现使得能够对生物和材料科学样品的 3D 纳米结构组织进行断层扫描研究。这些技术扩展了传统 X 射线断层扫描的概念，不仅重建了标量值（例如每个体素的衰减系数），还重建了一组捕获样本每个体素内纳米结构局部各向异性的参数。张量断层扫描数据集本质上很大，因为传统 X 射线投影的每个像素都被散射图案取代，并且必须以不同的样本角方向记录投影，并且旋转轴相对于 X 射线传播有多个倾斜方向。目前针对如此大的数据集可用的重建方法在计算上是昂贵的。这里，提出了一种新颖的快速重建算法，称为迭代重建张量断层扫描（IRTT），以简化和加速张量断层扫描重建。 IRTT基于二阶张量模型来描述每个体素中纳米结构的各向异性，并基于迭代误差反向传播重建算法来实现高收敛速度。通过重建碳纤维结、人体骨小梁标本和固定小鼠大脑三个样本的纳米结构各向异性，证明了IRTT的可行性和准确性。将结果和重建速度与Liebiet等人[Nature(2015),527,349–352]提出的小角散射张量断层扫描(SASTT)重建方法进行比较。每个体素内纳米结构的主要方向揭示了两种方法之间的高度一致性。 然而，对于使用相同的数据集和计算机硬件，IRTT 的速度要快一个数量级以上。 IRTT 被发现可以产生稳健的结果，它不需要样本的先验知识来初始化参数，并且可以在简单的各向异性度量就足够的情况下使用，即张量近似充分捕获各向异性水平和体素内的主导方向。此外，通过大大加速重建，IRTT特别适合处理具有内部结构的样本的大型断层扫描数据集，或作为实验过程中的实时分析工具，用于数据采集过程中的在线反馈。或者，IRTT 结果可以用作捕获更高复杂性结构各向异性的模型的初始猜测，例如 Liiebiet al.(2015) 中基于球谐函数的 SASTT，从而提高整体收敛速度和重建的鲁棒性。