Marabini R, Herman G T, Carazo J M
Centro Nacional de Biotecnología, Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain.
Ultramicroscopy. 1998 Apr;72(1-2):53-65. doi: 10.1016/s0304-3991(97)00127-7.
Algebraic reconstruction techniques (ART) are iterative procedures for solving systems of linear equations. They have been used in tomography to recover objects from their projections. In this work we apply an ART approach in which the basis functions used to describe the objects are not based on voxels, but are much smoother functions named "blobs". The data collection studied in this work follows the so-called "conical tilt geometry" that is commonly used in many applications of three-dimensional electron microscopy of biological macromolecules. The performance of ART with blobs is carefully compared with a currently well-known three dimensional (3D) reconstruction algorithm (weighted back projection) using a methodology which assigns a level of statistical significance to a claim of relative superiority of one algorithm over another for a particular task. The conclusion we reach is that ART with blobs produces high-quality reconstructions and is, in particular, superior to weighted backprojection in recovering features along the "vertical" direction. For the exact implementation recommended in this paper, the computational costs of ART are almost an order of magnitude smaller than those of WBP.
代数重建技术（ART）是用于求解线性方程组的迭代过程。它们已被用于断层扫描中，以便从投影中恢复物体。在这项工作中，我们应用了一种ART方法，其中用于描述物体的基函数不是基于体素，而是更平滑的函数，称为“斑点”。这项工作中研究的数据采集遵循所谓的“锥形倾斜几何”，这在生物大分子的三维电子显微镜的许多应用中常用。使用一种方法将一种算法相对于另一种算法在特定任务中的相对优势声明赋予统计显著性水平，将带斑点的ART性能与当前著名的三维（3D）重建算法（加权反投影）进行了仔细比较。我们得出的结论是，带斑点的ART产生高质量的重建，特别是在沿“垂直”方向恢复特征方面优于加权反投影。对于本文推荐的精确实现，ART的计算成本几乎比WBP小一个数量级。
