Fast computation of 3D radon transform via a direct Fourier method

Bioinformatics

Volumn 14, Issue 2, 1998, Pages 212-216

  Lanzavecchia, Salvatore ^a   Bellon, Pier Luigi ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

RADON;

ALGORITHM; ARTICLE; FOURIER TRANSFORMATION; PRIORITY JOURNAL; THREE DIMENSIONAL IMAGING; TOMOGRAPHY;

EID: 0031853365     PISSN: 13674803     EISSN: 13674811     Source Type: Journal    
DOI: 10.1093/bioinformatics/14.2.212     Document Type: Article

References (29)

1. Bellon, P.L. and Lanzavecchia, S. (1995) A direct Fourier method (DFM) fox X-ray tomographic reconstructions and the accurate simulation of sinograms. Int. J. Bio-Med. Comp., 38, 55-69.
2. Bellon, P.L. and Lanzavecchia, S. (1997) Fast direct Fourier methods, based on 1- and 2-pass coordinates transformation, yields accurate reconstructions of X-ray CT clinical images. Phys. Med. Biol., 42, 443-463.
3. Brigham, O.E. (1974) The Fast Fourier Transform. Prentice-Hall, Englewood Cliffs, NJ.
4. Carazo, J.M. (1992) The fidelity of 3D reconstructions from incomplete data and the use of restoration methods. In Frank, J., (ed.), Electron Tomography. Plenum Press, New York, pp. 117-164.
5. Carazo, J.M. and Carrascosa, J.L. (1987) Information recovery in missing angular cases: an approach by convex projections method in three dimensions. J. Microsc., 145, 23-43.
6. Deans, S.R. (1993) The Radon Transform and Some of its Applications. Krieger Publishing, Malabar, FL.
7. Frank, J. (1996) Three-Dimensional Electron Microscopy of Macromolecular Assemblies. Academic Press, New York.
8. Helgason, S. (1984) Groups and Geometric Analysis. Academic Press, New York.
9. Karp, J.S., Muehllehner, G. and Lewitt, R.M. (1988) Constrained Fourier space method for compensation of missing data in emission computed tomography. IEEE Trans. Med. Imaging, 7, 21-25.
10. Lanzavecchia, S. and Bellon, P.L. (1994) A moving window Shannon reconstruction for image interpolation. J Vis. Commun Image Repres, 5, 255-264.
11. Lanzavecchia, S. and Bellon, P.L. (1995) A bevy of novel interpolating kernel for the Shannon reconstruction of high band pass images. J. Vis. Commun. Image Repres., 6, 122-131.
12. Lanzavecchia, S. and Bellon, P.L. (1996) Electron tomography in conical tilt geometry: the accuracy of a direct Fourier method (DFM) and the suppression of non tomographic noise. Ultramicroscopy, 63, 247-261.
13. Lanzavecchia, S. and Bellon, P.L. (1998) The moving window Shannon reconstruction in direct and Fourier domain: application in tomography. Scanning Microsc., in press.
14. Lanzavecchia, S., Bellon, P.L., Lupetti, P., Dallai, R., Rappuoli, R. and Telford, J.L. (1998) Three dimensional reconstruction of metal replicas of the H.pylori vacuolating cytotoxin. J. Struct. Biol., 121, in press.
15. Lanzavecchia, S., Tosoni, L. and Bellon, P.L. (1996) Fast sinogram computation and the sinogram-based alignment of images. Comput. Applic. Biosci., 12, 531-537.
16. Malzbender, T. (1993) Fourier volume rendering. ACM Trans. Graph., 12, 233-250.
17. Marr, R.B., Chen, C. and Lauterbur, P.C. (1981) On two approaches to 3D reconstruction in NMR zeugmatography. In Herman, G.T. and Natterer, F. (eds), Mathematical Aspects of Computerized Tomography. Springer Verlag, New York, pp. 225-240.
18. Penczek, P.A., Zhu, J. and Frank, J. (1996) A common-lines based method for determining orientations for N>3 particle projections simultaneously. Ultramicroscopy, 63, 205-218.
19. Radermacher, M. (1994) Three-dimensional reconstruction from random projections: orientational alignment via Radon transforms. Ultramicroscopy, 53, 121-136.
20. Radermacher, M. (1998) Radon transform technique for alignment and 3D-reconstruction from random projections. Scanning Microsc., in press.
21. Radermacher, M., Wagenknecht, T., Verschoor, A. and Frank, J. (1987) Three-dimensional reconstruction from a single-exposure, random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli. J. Microsc., 146, 113-136.
22. Radon, J. (1917) Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte über die Verhandlungen der Königlich Sächisischen Gesellshaft der Wissenschaften zu Luipzig. Math. Phys Klasse, 69, 262-277.
23. Radon, J. (1986) On the determination of functions from their integral values along certain manifolds. IEEE Trans Med. Imaging, 5, 170-176.
24. Sanz, J.L.C., Hinkle, E.B. and Jain, A.K. (1988) Radon and Projection Transform-Based Computer Vision. Springer-Verlag, Berlin.
25. Schatz, M., Orlova, E.V., Dube, P., Jäger, J. and van Heel, M. (1995) Structure of Lumbricus terrestris hemoglobin at 30 Å resolution determined using angular reconstitution. J. Struct. Biol., 114, 28-40.
26. Sezan, M.I. and Stark, H. (1984) Tomographic image reconstruction from incomplete view data by convex projections and direct Fourier inversion. IEEE Trans. Med. Imaging, 3, 91-98.
27. Tosoni, L., Lanzavecchia, S. and Bellon, P.L (1996) Image and voluma data rotation with 1- and 3-pass algorithms. Comput. Applic. Biosci., 12, 549-552.
28. van Heel, M. (1987) Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction. Ultramicroscopy, 21, 111-124.
29. van Heel, M., Winkler, H.P., Orlova, E.V. and Schatz, M. (1992) Structure analysis of ice-embedded single particles. Scanning Microsc. Suppl., 6, 23-42.