Three-dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions instead of Fourier Transforms
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- G. N. Ramachandran
- Department of Biophysics, University of Chicago, Chicago, Illinois 60637
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- A. V. Lakshminarayanan
- Department of Biophysics, University of Chicago, Chicago, Illinois 60637
抄録
<jats:p>A new technique is proposed for the mathematical process of reconstruction of a three-dimensional object from its transmission shadowgraphs; it uses convolutions with functions defined in the real space of the object, without using Fourier transforms. The object is rotated about an axis at right angles to the direction of a parallel beam of radiation, and sections of it normal to the axis are reconstructed from data obtained by scanning the corresponding linear strips in the shadowgraphs at different angular settings.</jats:p> <jats:p>Since the formulae in the convolution method involve only summations over one variable at a time, while a two-dimensional reconstruction with the Fourier transform technique requires double summations, the convolution method is much faster (typically by a factor of 30); the relative increase in speed is larger where greater resolution is required. Tests of the convolution method with computer-simulated shadowgraphs show that it is also more accurate than the Fourier transform method. It has good potentialities for application in electron microscopy and x-radiography. A new method of reconstructing helical structures by this technique is also suggested.</jats:p>
収録刊行物
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- Proceedings of the National Academy of Sciences
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Proceedings of the National Academy of Sciences 68 (9), 2236-2240, 1971-09
Proceedings of the National Academy of Sciences
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詳細情報 詳細情報について
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- CRID
- 1360574094574986368
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- NII論文ID
- 30016259046
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- ISSN
- 10916490
- 00278424
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- データソース種別
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