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

Fast and Accurate Three-Dimensional Reconstruction from Projections with Random Orientations via... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Structural Biology Elsevier

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

Loading next page...
 
/lp/elsevier/fast-and-accurate-three-dimensional-reconstruction-from-projections-dnASHnNxq2
Publisher
Elsevier
Copyright
Copyright © 1999 Academic Press
ISSN
1047-8477
eISSN
1095-8657
DOI
10.1006/jsbi.1999.4185
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Structural BiologyElsevier

Published: Dec 1, 1999

References

  • Novel properties of the Fourier decomposition of the sinogram
    Edholm, P.R.; Lewitt, R.M.; Lindholm, B.
  • Fast computation of 3D Radon transform via a direct Fourier method
    Lanzavecchia, S.; Bellon, P.L.
  • Fast sinogram computation and the sinogram-based alignment of images
    Lanzavecchia, S.; Tosoni, L.; Bellon, P.L.
  • The correlation averaging of a regularly arranged bacterial cell envelope protein
    Saxton, W.O.; Baumeister, W.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off