RECONSTRUCTION OF A 3-DIMENSIONAL STRUCTURE FROM PROJECTIONS AND ITS APPLICATION TO ELECTRON-MICROSCOPY .2. DIRECT METHODS
RECONSTRUCTION OF A 3-DIMENSIONAL STRUCTURE FROM PROJECTIONS AND ITS APPLICATION TO ELECTRON-MICROSCOPY .2. DIRECT METHODS
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DOI：
10.1098/rspb.1972.0068
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发表时间：
1972-01-01
期刊：
影响因子：
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通讯作者：
GILBERT, PFC
中科院分区：
文献类型：
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作者：
GILBERT, PFC
在某些条件下，可以从电子显微照片中获得样品的近似投影密度，并且通过在不同方向上拍摄电子显微照片，可以确定样品的许多不同投影。已经提出了几种方法，用于从一系列投影重建物体的三维密度分布，这些投影的平面围绕轴等角度地间隔开。这些方法之一使用投影的傅立叶变换，而其他方法直接对投影数据进行操作。讨论了“反投影”的直接方法的局限性，并且示出了如何通过从修改的投影密度的反投影来实现有效的重建。这种直接的方法被证明是等效的傅立叶方法，也为解决类似的问题，在其他领域的重建开发的某些方法。给出了一个表达式的分辨率的重建可从有限数量的投影。由于其计算简单，该方法非常适合于旋转或螺旋对称物体的密度重建。
Under certain conditions it is possible to obtain the approximate projected density of a specimen from an electron micrograph, and by taking electron micrographs in different directions a number of different projections of a specimen can be determined. Several methods have been proposed for reconstructing the three-dimensional density distribution of an object from a series of projections whose planes are equally spaced in angle about an axis. One of these methods uses the Fourier transforms of the projections, while other methods operate directly on the projection data. The limitations of the direct method of ‘back-projection’ are discussed, and it is shown how a valid reconstruction may be achieved by back-projection from modified projected densities. This direct method is shown to be equivalent to the Fourier method and also to certain methods of reconstruction developed for the solution of analogous problems in other fields. An expression is given for the resolution of the reconstruction obtainable from a finite number of projections. Because of its computational simplicity this method is very suitable for reconstructing the density of objects with rotational or helical symmetry.