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© Oxford University Press

Three-dimensional reconstruction of helical structures with fast inversion of very large Fourier transforms

Salvatore Lanzavecchia 1, Laura Tosoni and Pier Luigi Bellon

Università degli Studi, Dipartimento di Chimica Strutturale e Stereochimica Inorganica via Venezian 21. 20133 Milan, Italy

1To whom correspondence should be addressed. Email: salvator{at}stinch9.csmtbo.mi.cnr.it

A single projection of a helical distribution of matter allows one to obtain the complete three-dimensional reconstruction of the structure. This task is usually performed by a Fourier-Bessel algorithm, which is more efficient than a customary fast Fourier transform inversion. This article describes how to achieve such a result by a direct Fourier method in a reasonable time. Once the two-dimensional transform of the projection is obtained from the source image, it is possible to build up the three-dimensional transform array, in Cartesian coordinates, that yields the reconstruction by a straightforward Fourier inversion. Images of projected helices should be studied with high sampling rates to enhance the resolution, and the segments of helix should be long enough to give a satisfactory signal-to-noise ratio. These conditions result in three-dimensional transform arrays that would require one or more gigabytes of storage. The strategy proposed here requires much less storage and is fast enough to allow the reconstruction to be performed with dfferent parameters and filters in a very short time without any sacrfice in resolution.


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