Fast and Accurate Three-Dimensional Reconstruction from Projections with Random 
Orientations via Radon Transforms

Lanzavecchia, Salvatore; Bellon, Pier Luigi; Radermacher, Michael

doi:10.1006/jsbi.1999.4185

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Fast and Accurate Three-Dimensional Reconstruction from Projections with Random Orientations via Radon Transforms

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Radermacher, Michael
Department of Structural Biology, Max Planck Institute of Biophysics, Max Planck Society;

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Citation

Lanzavecchia, S., Bellon, P. L., & Radermacher, M. (1999). Fast and Accurate Three-Dimensional Reconstruction from Projections with Random Orientations via Radon Transforms. Journal of Structural Biology, 128(2), 152-164. doi:10.1006/jsbi.1999.4185.

Cite as: https://hdl.handle.net/21.11116/0000-0007-EB33-7

Abstract

A new algorithm for three-dimensional reconstruction from randomly oriented projections has been developed. The algorithm recovers the 3D Radon transform from the 2D Radon transforms (sinograms) of the projections. The structure in direct space is obtained by an inversion of the 3D Radon transform. The mathematical properties of the Radon transform are exploited to design a special filter that can be used to correct inconsistencies in a data set and to fill the gaps in the Radon transform that originate from missing projections. Several versions of the algorithm have been implemented, with and without a filter and with different interpolation methods for merging the sinograms into the 3D Radon transform. The algorithms have been tested on analytical phantoms and experimental data and have been compared with a weighted back projection algorithm (WBP). A quantitative analysis of phantoms reconstructed from noise-free and noise-corrupted projections shows that the new algorithms are more accurate than WBP when the number of projections is small. Experimental structures obtained by the new methods are strictly comparable to those obtained by WBP. Moreover, the algorithm is more than 10 times faster than WPB when applied to a data set of 1000–5000 projections.