Carazo J M, Carrascosa J L
J Microsc. 1987 Feb;145(Pt 2):159-77.
We consider the problem of the three-dimensional (3-D) reconstruction of objects by the direct Fourier method (DFM) and their restoration by the method of projections on to convex sets (POCS). The main discussion is centered on the case of specimens arranged in a two-dimensional (2-D) crystal and imaged by transmission electron microscopy, although the conclusions could be extended to more general cases. We present results of the restoration of the 3-D reconstruction of a computer generated 2-D crystal under different conditions of data collection limitation. A preliminary application with a real biological specimen (the connector of bacteriophage phi 29) is also presented. These results indicate that POCS can be used practically, in certain cases, to restore 3-D reconstructions obtained by the DFM, giving grounds for the proposal of the study of a combined DFM + POCS (reconstruction + restoration) method for the determination of biological structures by electron microscopy and 3-D image processing.
我们考虑了用直接傅里叶方法（DFM）对物体进行三维（3-D）重建以及通过凸集投影法（POCS）对其进行恢复的问题。主要讨论集中在二维（2-D）晶体中排列的标本通过透射电子显微镜成像的情况，尽管结论可扩展到更一般的情况。我们展示了在不同数据收集限制条件下对计算机生成的二维晶体进行三维重建恢复的结果。还展示了对真实生物标本（噬菌体φ29的连接器）的初步应用。这些结果表明，在某些情况下，POCS可实际用于恢复通过DFM获得的三维重建，为提出研究用于电子显微镜和三维图像处理确定生物结构的组合DFM + POCS（重建 + 恢复）方法提供了依据。
