Pham Minh, Lu Xingyuan, Rana Arjun, Osher Stanley, Miao Jianwei
Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, CA, 90095, USA.
Department of Mathematics, University of California, Los Angeles, CA, 90095, USA.
Sci Rep. 2024 Apr 25;14(1):9541. doi: 10.1038/s41598-024-59140-1.
Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method. To make the algorithm accessible to a broad user community, we have made our RESIRE-V MATLAB source codes and the data freely available at https://github.com/minhpham0309/RESIRE-V .
断层扫描技术对物理、生物和医学科学产生了重要影响。迄今为止，大多数断层扫描应用都集中在三维标量重建上。然而，在一些关键应用中，需要矢量断层扫描来重建三维矢量场，如电场和磁场。多年来，已经开发了几种矢量断层扫描方法。在这里，我们介绍用于矢量断层扫描的实空间迭代重建（REal Space Iterative REconstruction for Vector tomography，简称RESIRE-V）的数学基础和算法实现。RESIRE-V使用多个倾斜投影系列，并在投影和三维重建之间进行迭代。每次迭代包括一个使用拉东变换的前向步骤和一个使用其转置的后向步骤，然后通过梯度下降更新对象。结合三维支持约束，该算法迭代地最小化一个误差度量，该误差度量定义为测量投影和计算投影之间的差异。该算法还可用于优化倾斜角度并进一步改善三维重建。为了验证RESIRE-V，我们首先将其应用于一个三维磁化矢量场的模拟数据集，该数据集由两个正交倾斜系列组成，每个系列都有一个缺失楔形。我们的定量分析表明，重建的磁化矢量场的三个分量与真实对应分量吻合良好。然后，我们使用RESIRE-V重建由三个倾斜系列组成的铁磁元晶格的三维磁化矢量场。我们的三维矢量重建揭示了存在正负电荷的拓扑磁缺陷。我们期望RESIRE-V可以作为一种通用的矢量断层扫描方法纳入不同的成像模式。为了使广大用户群体能够使用该算法，我们已将RESIRE-V的MATLAB源代码和数据在https://github.com/minhpham0309/RESIRE-V上免费提供。
