References
1. J. Babaud, A. Witkin, M. Baudin, R. Duda, Uniqueness of the Gaussian kernel for scale-space
filtering. IEEE Trans. Pattern Anal. Machine Intell. 8(1), 26–33 (1986)
2. K. Batenburg, S. Bals, J. Sijbers, C. Kübel, P. Midgley, J. Hernandez, U. Kaiser, E. Encina, E.
Coronado, G.V. Tendeloo, 3D imaging of nanomaterials by discrete tomography.
Ultramicroscopy 109, 730–740 (2009)
3. K. Batenburg, J. Sijbers, Dart: a practical reconstruction algorithm for discrete tomography.
IEEE Trans. Image Process. 20, 2542–2553 (2011)
4. E. Brigham, The Fast Fourier Transform and Its Applications (Prentice-Hall, UK, 1988)
5. L. Calder, S. Wasilewski, J. Berriman, P. Rosenthal, Structural organization of a filamentous
influenza A virus. PNAS 107(10), 685–690 (2010)
6. M. Cao, H. Zhang, Y. Lu, R. Nishi, A. Takaoka, Formation and reduction of streak artefacts
in electron tomography. J. Microsc. 239, 66–71 (2010)
7. H. Chapman, C. Jacobsen, S. Williams, A characterisation of dark-field imaging of colloidal
gold labels in a scanning transmission x-ray microscope. Ultramicroscopy 62(3), 191–213
(1996)
8. Y. Dong, S. Xu, A new directional weighted median filter for removal of random-valued
impulse noise. IEEE Signal Process. Lett. 14(3), 193–196 (2007)
9. A. Duerinckx, A. Macovski, Polychromatic streak artifacts in computed tomography images.
J. Comput. Assist. Tomogr. 2, 481–487 (1978)
10. H. Engl, M. Hanke, A. Neubauer, Regularization of Inverse Prob. (Springer, Berlin, 2000)
(31 Mar 200)
11. D. Fanelli, O. Öktem, Electron tomography: a short overview with an emphasis on the
absorption potential model for the forward problem. Inverse Prob. 24(1), 1–51 (1997)
12. J. Fernández, S. Li, An improved algorithm for anisotropic nonlinear diffusion for denoising
cryo-tomograms. J. Struct. Biol. 144(1–2), 152–161 (2003)
13. J. Fernandez, S. Li, Anisotropic nonlinear filtering of cellular structures in cryoelectron
tomography. Comput. Sci. Eng. 7(5), 54–61 (2005)
14. L. Florack, R. Duits, J. Bierkens, Tikhonov regularization versus scale space: A new result.
ICIP (2004) pp. 271–274
15. A. Frangakis, R. Hegerl, Noise reduction in electron tomographic reconstructions using
nonlinear anisotropic diffusion. J. Struct. Biol. 135(3), 239–250 (2001)
16. J. Frank, Introduction: Principles of electron tomography, in Electron Tomography, 2nd edn.
(Springer, New York, 2006)
17. B. Goris, W.V. den Broek, K. Batenburg, H.H. Mezerji, S. Bals, Electron tomography based
on a total variation minimization reconstruction technique. Ultramicroscopy 113, 120–130
(2012)
18. R. Gray, J. Goodman, Fourier Transforms (Kluwer, Alphen aan den Rijn, 1995)
19. A. Guesdon, S. Blestel, C. Kervrann, D. Chretien, Single versus dual-axis cryo-electron
tomography of microtubules assembled in vitro: limits and perspectives. J. Struct. Biol. 181,
169–178 (2013)
20. G. Harauz, M. van Heel, Exact filters for general geometry three-dimensional reconstruction.
Optik 73, 146–156 (1986)
21. R. Hegerl, A. Frangakis, Denoising of electron tomograms, in Electron Tomography, vol.
2006, 2nd edn. (Springer, New York, 2006), pp. 331–352
22. P. van der Heide, X. Xu, B. Marsh, D. Hanein, N. Volkmann, Efficient automatic noise
reduction of electron tomographic reconstructions based on iterative median filtering.
J. Struct. Biol. 158(2), 196–204 (2007)
23. P. Henrici, Applied and Computational Complex Analysis, Discrete Fourier Analysis, Cauchy
Integrals, Construction of Conformal Maps, Univalent Functions (Wiley, Hoboken, 1993)
24. W. Jiang, M. Baker, Q. Wu, C. Bajaj, W. Chiu, Applications of a bilateral denoising filter in
biological electron microscopy. J. Struct. Biol. 144, 114–122 (2003)
11 Signal Optimization in Electron Tomography
299
1. J. Babaud, A. Witkin, M. Baudin, R. Duda, Uniqueness of the Gaussian kernel for scale-space
filtering. IEEE Trans. Pattern Anal. Machine Intell. 8(1), 26–33 (1986)
2. K. Batenburg, S. Bals, J. Sijbers, C. Kübel, P. Midgley, J. Hernandez, U. Kaiser, E. Encina, E.
Coronado, G.V. Tendeloo, 3D imaging of nanomaterials by discrete tomography.
Ultramicroscopy 109, 730–740 (2009)
3. K. Batenburg, J. Sijbers, Dart: a practical reconstruction algorithm for discrete tomography.
IEEE Trans. Image Process. 20, 2542–2553 (2011)
4. E. Brigham, The Fast Fourier Transform and Its Applications (Prentice-Hall, UK, 1988)
5. L. Calder, S. Wasilewski, J. Berriman, P. Rosenthal, Structural organization of a filamentous
influenza A virus. PNAS 107(10), 685–690 (2010)
6. M. Cao, H. Zhang, Y. Lu, R. Nishi, A. Takaoka, Formation and reduction of streak artefacts
in electron tomography. J. Microsc. 239, 66–71 (2010)
7. H. Chapman, C. Jacobsen, S. Williams, A characterisation of dark-field imaging of colloidal
gold labels in a scanning transmission x-ray microscope. Ultramicroscopy 62(3), 191–213
(1996)
8. Y. Dong, S. Xu, A new directional weighted median filter for removal of random-valued
impulse noise. IEEE Signal Process. Lett. 14(3), 193–196 (2007)
9. A. Duerinckx, A. Macovski, Polychromatic streak artifacts in computed tomography images.
J. Comput. Assist. Tomogr. 2, 481–487 (1978)
10. H. Engl, M. Hanke, A. Neubauer, Regularization of Inverse Prob. (Springer, Berlin, 2000)
(31 Mar 200)
11. D. Fanelli, O. Öktem, Electron tomography: a short overview with an emphasis on the
absorption potential model for the forward problem. Inverse Prob. 24(1), 1–51 (1997)
12. J. Fernández, S. Li, An improved algorithm for anisotropic nonlinear diffusion for denoising
cryo-tomograms. J. Struct. Biol. 144(1–2), 152–161 (2003)
13. J. Fernandez, S. Li, Anisotropic nonlinear filtering of cellular structures in cryoelectron
tomography. Comput. Sci. Eng. 7(5), 54–61 (2005)
14. L. Florack, R. Duits, J. Bierkens, Tikhonov regularization versus scale space: A new result.
ICIP (2004) pp. 271–274
15. A. Frangakis, R. Hegerl, Noise reduction in electron tomographic reconstructions using
nonlinear anisotropic diffusion. J. Struct. Biol. 135(3), 239–250 (2001)
16. J. Frank, Introduction: Principles of electron tomography, in Electron Tomography, 2nd edn.
(Springer, New York, 2006)
17. B. Goris, W.V. den Broek, K. Batenburg, H.H. Mezerji, S. Bals, Electron tomography based
on a total variation minimization reconstruction technique. Ultramicroscopy 113, 120–130
(2012)
18. R. Gray, J. Goodman, Fourier Transforms (Kluwer, Alphen aan den Rijn, 1995)
19. A. Guesdon, S. Blestel, C. Kervrann, D. Chretien, Single versus dual-axis cryo-electron
tomography of microtubules assembled in vitro: limits and perspectives. J. Struct. Biol. 181,
169–178 (2013)
20. G. Harauz, M. van Heel, Exact filters for general geometry three-dimensional reconstruction.
Optik 73, 146–156 (1986)
21. R. Hegerl, A. Frangakis, Denoising of electron tomograms, in Electron Tomography, vol.
2006, 2nd edn. (Springer, New York, 2006), pp. 331–352
22. P. van der Heide, X. Xu, B. Marsh, D. Hanein, N. Volkmann, Efficient automatic noise
reduction of electron tomographic reconstructions based on iterative median filtering.
J. Struct. Biol. 158(2), 196–204 (2007)
23. P. Henrici, Applied and Computational Complex Analysis, Discrete Fourier Analysis, Cauchy
Integrals, Construction of Conformal Maps, Univalent Functions (Wiley, Hoboken, 1993)
24. W. Jiang, M. Baker, Q. Wu, C. Bajaj, W. Chiu, Applications of a bilateral denoising filter in
biological electron microscopy. J. Struct. Biol. 144, 114–122 (2003)
11 Signal Optimization in Electron Tomography
299