Abstract

In X-ray computed tomography, the task of imaging only a local region of interest (ROI) inside a larger sample is very important. However, without a priori information, this ROI cannot be exactly reconstructed using only the image data limited to the ROI. We propose here an approach of region-of-interest tomography, which reconstructs a ROI within an object from projections of different fields of view acquired on a specific angular sampling scheme in the same tomographic experiment. We present a stable procedure that not only yields high-quality images of the ROI but keeps as well the quantitative contrast on the reconstructed images. In addition, we analyze the minimum number of projections required for ROI tomography from the point of view of the band region of the Radon transform, which confirms this number must be estimated based on the size of the entire object and not only on the size of the ROI.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Analysis and improvement in region-of-interest tomography

Nagaaki Ohyama, Akihiko Shiraishi, Toshio Honda, and Jumpei Tsujiuchi
Appl. Opt. 23(22) 4105-4110 (1984)

X-ray tomography of extended objects: a comparison of data acquisition approaches

Ming Du, Rafael Vescovi, Kamel Fezzaa, Chris Jacobsen, and Doğa Gürsoy
J. Opt. Soc. Am. A 35(11) 1871-1879 (2018)

Quantitative interior x-ray nanotomography by a hybrid imaging technique

Manuel Guizar-Sicairos, Jaap J. Boon, Kevin Mader, Ana Diaz, Andreas Menzel, and Oliver Bunk
Optica 2(3) 259-266 (2015)

References

  • View by:
  • |
  • |
  • |

  1. F. Natterer, The Mathematics of Computerized Tomography (SIAM, 2001).
    [Crossref]
  2. R. N. Bracewell and A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
    [Crossref]
  3. A. G. Ramm and A. Katsevich, The Radon Transform and Local Tomography (CRC, 1996).
  4. M. Müller and G. R. Arce, “Truncation artifacts in tomographic reconstructions from projections,” Appl. Opt. 35(20), 3902–3914 (1996).
    [Crossref] [PubMed]
  5. J. C. Gore and S. Leeman, “The reconstruction of objects from incomplete projections,” Phys. Med. Biol. 25(1), 129–136 (1980).
    [Crossref] [PubMed]
  6. A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography,” SIAM J. Appl. Math. 52, 459–484 (1992).
    [Crossref]
  7. A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography II,” SIAM J. Appl. Math. 57, 1095–1127 (1997).
    [Crossref]
  8. W. J. T. Spyra, A. Faridani, K. T. Smith, and E. L. Ritman, “Computed tomographic imaging of the coronary arterial tree - use of local tomography,” IEEE Trans. Med. Imag. 9(1), 1–4 (1990).
    [Crossref]
  9. G. Wang and H. Yu, “Can interior tomography outperform lambda tomography?” Proc. Natl. Acad. Sci. USA 107(22), E92–E93 (2010).
    [Crossref] [PubMed]
  10. R. Bates and R. Lewitt, “Image reconstruction from projections: I: General theoretical considerations, III:Projection completion methods (theory), IV: Projection completion methods (computational examples),” Optik 50, 269–278 (1978).
  11. M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
    [Crossref]
  12. F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
    [Crossref] [PubMed]
  13. T. Köhler and F. Noo, “Comment on “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 039801 (2009).
    [Crossref]
  14. Y. Ye, H. Yu, Y. Wei, and G. Wang, “A general local reconstruction approach based on a truncated Hilbert transform,” Int. J. Biomed. Imaging 2007, 63634 (2007).
    [Crossref]
  15. H. Kudo, M. Courdurier, F. Noo, and M. Defrise, “Tiny a priori knowledge solves the interior problem in computed tomography,” Phys. Med. Biol. 53, 2207–2231 (2008).
    [Crossref] [PubMed]
  16. K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
    [Crossref] [PubMed]
  17. N. Ohyama, A. Shiraishi, T. Honda, and J. Tsujiuchi, “Analysis and improvement in region-of-interest tomography,” Appl. Opt. 23(22), 4105–4110 (1984).
    [Crossref] [PubMed]
  18. O. Nalcioglu, Z.H. Cho, and R. Y. Lou, “Limited field of view reconstruction in computerized tomography,” IEEE Trans. Nucl. Sci. 26(1), 546–551 (1979).
    [Crossref]
  19. O. Nalcioglu, P. V. Sankar, and J. Sklansky, “Region-of-interest X-ray tomography (ROIT),” Proc. SPIE 0206, 98–102 (1979).
    [Crossref]
  20. W. Wagner, “Reconstructions from restricted region scan data - new means to reduce the patient dose,” IEEE Trans. Nucl. Sci. 26(2), 2866–2869 (1979).
    [Crossref]
  21. J. C. da Silva and A. Menzel, “Elementary signals in ptychography,” Opt. Express 23, 33812–33821 (2015).
    [Crossref]
  22. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
    [Crossref] [PubMed]
  23. M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from X-ray coherent diffractive imaging projections,” Opt. Express 19(22), 21345–21357 (2011).
    [Crossref] [PubMed]
  24. T. Olson and J. DeStefano, “Wavelet localization of the Radon transform,” IEEE Trans. Signal Process. 42(8), 2055–2067 (1994).
    [Crossref]
  25. T.-C. Hsung and D. P. K. Lun, “New sampling scheme for region-of-interest tomography,” IEEE Trans. Signal Process. 48(4), 1154–1163 (2000).
    [Crossref]
  26. M. Guizar-Sicairos, S. T. Thurman, and J. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008).
    [Crossref] [PubMed]
  27. P. A. Rattey and A. G. Lindgren, “Sampling the 2-D Radon transform,” IEEE Trans. Acoust. Speech Signal Process. 29(5), 994–1002 (1981).
    [Crossref]
  28. R. A. Crowther, D. J. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. Roy. Soc. Lond. A 317, 319–340 (1970).
    [Crossref]
  29. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
    [Crossref]
  30. A. Kyrieleis, V. Titarenko, M. Ibison, T. Connolley, and P. J. Withers, “Region-of-interest tomography using filtered backprojection: assessing the pratical limits,” J. Microsc. 241(1), 69–82 (2010).
    [Crossref] [PubMed]
  31. J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
    [Crossref] [PubMed]
  32. X. Xiao, F. de Carlo, and S. R. Stock, “Practical error estimation in zoom-in and truncated tomography reconstructions,” Rev. Sci. Instrum. 78(6), 063705 (2007).
    [Crossref] [PubMed]
  33. S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
    [Crossref]
  34. R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
    [Crossref]
  35. M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
    [Crossref] [PubMed]
  36. M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
    [Crossref] [PubMed]
  37. M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
    [Crossref] [PubMed]
  38. A. P. Kaestner, B. Munch, and P. Trtik, “Spatiotemporal computed tomography of dynamic processes,” Opt. Eng. 50(12), 123201 (2011).
    [Crossref]
  39. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
    [Crossref] [PubMed]
  40. P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14063004 (2012).
    [Crossref]
  41. A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
    [Crossref]
  42. A. Guinier, X-ray diffraction in crystals, imperfect crystals and amorphous bodies (Dover, 1994).
  43. ChemSpider database, “Melanin,” (ID 4884931). http://www.chemspider.com/Chemical-Structure.4884931.html (data of access February 01, 2018)
  44. M. L. Huggins, “The structure of alpha keratin,” Proc. Natl. Acad. Sci. U.S.A. 43(2), 204–209 (1957).
    [Crossref] [PubMed]
  45. M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151(3), 250–262 (2005).
    [Crossref] [PubMed]

2015 (3)

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

J. C. da Silva and A. Menzel, “Elementary signals in ptychography,” Opt. Express 23, 33812–33821 (2015).
[Crossref]

2014 (2)

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

2013 (1)

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

2012 (3)

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14063004 (2012).
[Crossref]

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
[Crossref]

2011 (4)

A. P. Kaestner, B. Munch, and P. Trtik, “Spatiotemporal computed tomography of dynamic processes,” Opt. Eng. 50(12), 123201 (2011).
[Crossref]

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
[Crossref]

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from X-ray coherent diffractive imaging projections,” Opt. Express 19(22), 21345–21357 (2011).
[Crossref] [PubMed]

2010 (3)

A. Kyrieleis, V. Titarenko, M. Ibison, T. Connolley, and P. J. Withers, “Region-of-interest tomography using filtered backprojection: assessing the pratical limits,” J. Microsc. 241(1), 69–82 (2010).
[Crossref] [PubMed]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

G. Wang and H. Yu, “Can interior tomography outperform lambda tomography?” Proc. Natl. Acad. Sci. USA 107(22), E92–E93 (2010).
[Crossref] [PubMed]

2009 (2)

T. Köhler and F. Noo, “Comment on “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 039801 (2009).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

2008 (3)

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

H. Kudo, M. Courdurier, F. Noo, and M. Defrise, “Tiny a priori knowledge solves the interior problem in computed tomography,” Phys. Med. Biol. 53, 2207–2231 (2008).
[Crossref] [PubMed]

M. Guizar-Sicairos, S. T. Thurman, and J. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008).
[Crossref] [PubMed]

2007 (2)

Y. Ye, H. Yu, Y. Wei, and G. Wang, “A general local reconstruction approach based on a truncated Hilbert transform,” Int. J. Biomed. Imaging 2007, 63634 (2007).
[Crossref]

X. Xiao, F. de Carlo, and S. R. Stock, “Practical error estimation in zoom-in and truncated tomography reconstructions,” Rev. Sci. Instrum. 78(6), 063705 (2007).
[Crossref] [PubMed]

2005 (1)

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151(3), 250–262 (2005).
[Crossref] [PubMed]

2000 (1)

T.-C. Hsung and D. P. K. Lun, “New sampling scheme for region-of-interest tomography,” IEEE Trans. Signal Process. 48(4), 1154–1163 (2000).
[Crossref]

1997 (1)

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography II,” SIAM J. Appl. Math. 57, 1095–1127 (1997).
[Crossref]

1996 (1)

1994 (1)

T. Olson and J. DeStefano, “Wavelet localization of the Radon transform,” IEEE Trans. Signal Process. 42(8), 2055–2067 (1994).
[Crossref]

1992 (1)

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography,” SIAM J. Appl. Math. 52, 459–484 (1992).
[Crossref]

1990 (1)

W. J. T. Spyra, A. Faridani, K. T. Smith, and E. L. Ritman, “Computed tomographic imaging of the coronary arterial tree - use of local tomography,” IEEE Trans. Med. Imag. 9(1), 1–4 (1990).
[Crossref]

1984 (1)

1981 (1)

P. A. Rattey and A. G. Lindgren, “Sampling the 2-D Radon transform,” IEEE Trans. Acoust. Speech Signal Process. 29(5), 994–1002 (1981).
[Crossref]

1980 (1)

J. C. Gore and S. Leeman, “The reconstruction of objects from incomplete projections,” Phys. Med. Biol. 25(1), 129–136 (1980).
[Crossref] [PubMed]

1979 (3)

O. Nalcioglu, Z.H. Cho, and R. Y. Lou, “Limited field of view reconstruction in computerized tomography,” IEEE Trans. Nucl. Sci. 26(1), 546–551 (1979).
[Crossref]

O. Nalcioglu, P. V. Sankar, and J. Sklansky, “Region-of-interest X-ray tomography (ROIT),” Proc. SPIE 0206, 98–102 (1979).
[Crossref]

W. Wagner, “Reconstructions from restricted region scan data - new means to reduce the patient dose,” IEEE Trans. Nucl. Sci. 26(2), 2866–2869 (1979).
[Crossref]

1978 (1)

R. Bates and R. Lewitt, “Image reconstruction from projections: I: General theoretical considerations, III:Projection completion methods (theory), IV: Projection completion methods (computational examples),” Optik 50, 269–278 (1978).

1970 (1)

R. A. Crowther, D. J. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. Roy. Soc. Lond. A 317, 319–340 (1970).
[Crossref]

1967 (1)

R. N. Bracewell and A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
[Crossref]

1957 (1)

M. L. Huggins, “The structure of alpha keratin,” Proc. Natl. Acad. Sci. U.S.A. 43(2), 204–209 (1957).
[Crossref] [PubMed]

Agah, M.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

Arce, G. R.

Barrett, R.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
[Crossref]

Bates, R.

R. Bates and R. Lewitt, “Image reconstruction from projections: I: General theoretical considerations, III:Projection completion methods (theory), IV: Projection completion methods (computational examples),” Optik 50, 269–278 (1978).

Bech, M.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

Bergamaschi, A.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Boon, J. J.

Bracewell, R. N.

R. N. Bracewell and A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
[Crossref]

Bravin, A.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

Bunk, O.

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
[Crossref]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from X-ray coherent diffractive imaging projections,” Opt. Express 19(22), 21345–21357 (2011).
[Crossref] [PubMed]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

Cheng, W.-C.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

Cho, Z.H.

O. Nalcioglu, Z.H. Cho, and R. Y. Lou, “Limited field of view reconstruction in computerized tomography,” IEEE Trans. Nucl. Sci. 26(1), 546–551 (1979).
[Crossref]

Cloetens, P.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

Connolley, T.

A. Kyrieleis, V. Titarenko, M. Ibison, T. Connolley, and P. J. Withers, “Region-of-interest tomography using filtered backprojection: assessing the pratical limits,” J. Microsc. 241(1), 69–82 (2010).
[Crossref] [PubMed]

Courdurier, M.

H. Kudo, M. Courdurier, F. Noo, and M. Defrise, “Tiny a priori knowledge solves the interior problem in computed tomography,” Phys. Med. Biol. 53, 2207–2231 (2008).
[Crossref] [PubMed]

Crowther, R. A.

R. A. Crowther, D. J. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. Roy. Soc. Lond. A 317, 319–340 (1970).
[Crossref]

da Silva, J. C.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

J. C. da Silva and A. Menzel, “Elementary signals in ptychography,” Opt. Express 23, 33812–33821 (2015).
[Crossref]

David, C.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
[Crossref]

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

de Carlo, F.

X. Xiao, F. de Carlo, and S. R. Stock, “Practical error estimation in zoom-in and truncated tomography reconstructions,” Rev. Sci. Instrum. 78(6), 063705 (2007).
[Crossref] [PubMed]

Defrise, M.

H. Kudo, M. Courdurier, F. Noo, and M. Defrise, “Tiny a priori knowledge solves the interior problem in computed tomography,” Phys. Med. Biol. 53, 2207–2231 (2008).
[Crossref] [PubMed]

DeRosier, D. J.

R. A. Crowther, D. J. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. Roy. Soc. Lond. A 317, 319–340 (1970).
[Crossref]

DeStefano, J.

T. Olson and J. DeStefano, “Wavelet localization of the Radon transform,” IEEE Trans. Signal Process. 42(8), 2055–2067 (1994).
[Crossref]

Diaz, A.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
[Crossref]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from X-ray coherent diffractive imaging projections,” Opt. Express 19(22), 21345–21357 (2011).
[Crossref] [PubMed]

Dierolf, M.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

Dinapoli, R.

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Donath, T.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

Faridani, A.

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography II,” SIAM J. Appl. Math. 57, 1095–1127 (1997).
[Crossref]

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography,” SIAM J. Appl. Math. 52, 459–484 (1992).
[Crossref]

W. J. T. Spyra, A. Faridani, K. T. Smith, and E. L. Ritman, “Computed tomographic imaging of the coronary arterial tree - use of local tomography,” IEEE Trans. Med. Imag. 9(1), 1–4 (1990).
[Crossref]

Färm, E.

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

Fienup, J.

Gore, J. C.

J. C. Gore and S. Leeman, “The reconstruction of objects from incomplete projections,” Phys. Med. Biol. 25(1), 129–136 (1980).
[Crossref] [PubMed]

Gorelick, S.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
[Crossref]

Guinier, A.

A. Guinier, X-ray diffraction in crystals, imperfect crystals and amorphous bodies (Dover, 1994).

Guizar-Sicairos, M.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
[Crossref]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14063004 (2012).
[Crossref]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from X-ray coherent diffractive imaging projections,” Opt. Express 19(22), 21345–21357 (2011).
[Crossref] [PubMed]

M. Guizar-Sicairos, S. T. Thurman, and J. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008).
[Crossref] [PubMed]

Guzenko, V. A.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
[Crossref]

Haberthür, D.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

Härkönen, E.

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

Henrich, B.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Hoffman, E. A.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

Holler, M.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from X-ray coherent diffractive imaging projections,” Opt. Express 19(22), 21345–21357 (2011).
[Crossref] [PubMed]

Holzner, C.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

Honda, T.

Horisberger, R.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Hsung, T.-C.

T.-C. Hsung and D. P. K. Lun, “New sampling scheme for region-of-interest tomography,” IEEE Trans. Signal Process. 48(4), 1154–1163 (2000).
[Crossref]

Huggins, M. L.

M. L. Huggins, “The structure of alpha keratin,” Proc. Natl. Acad. Sci. U.S.A. 43(2), 204–209 (1957).
[Crossref] [PubMed]

Ibison, M.

A. Kyrieleis, V. Titarenko, M. Ibison, T. Connolley, and P. J. Withers, “Region-of-interest tomography using filtered backprojection: assessing the pratical limits,” J. Microsc. 241(1), 69–82 (2010).
[Crossref] [PubMed]

Jin, X.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

Johnson, I.

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Kaestner, A. P.

A. P. Kaestner, B. Munch, and P. Trtik, “Spatiotemporal computed tomography of dynamic processes,” Opt. Eng. 50(12), 123201 (2011).
[Crossref]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
[Crossref]

Karvinen, P.

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

Katsevich, A.

A. G. Ramm and A. Katsevich, The Radon Transform and Local Tomography (CRC, 1996).

Kewish, C. M.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Klug, A.

R. A. Crowther, D. J. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. Roy. Soc. Lond. A 317, 319–340 (1970).
[Crossref]

Köhler, T.

T. Köhler and F. Noo, “Comment on “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 039801 (2009).
[Crossref]

Kudo, H.

H. Kudo, M. Courdurier, F. Noo, and M. Defrise, “Tiny a priori knowledge solves the interior problem in computed tomography,” Phys. Med. Biol. 53, 2207–2231 (2008).
[Crossref] [PubMed]

Kyrieleis, A.

A. Kyrieleis, V. Titarenko, M. Ibison, T. Connolley, and P. J. Withers, “Region-of-interest tomography using filtered backprojection: assessing the pratical limits,” J. Microsc. 241(1), 69–82 (2010).
[Crossref] [PubMed]

Le Duc, G.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

Leeman, S.

J. C. Gore and S. Leeman, “The reconstruction of objects from incomplete projections,” Phys. Med. Biol. 25(1), 129–136 (1980).
[Crossref] [PubMed]

Lewitt, R.

R. Bates and R. Lewitt, “Image reconstruction from projections: I: General theoretical considerations, III:Projection completion methods (theory), IV: Projection completion methods (computational examples),” Optik 50, 269–278 (1978).

Lindgren, A. G.

P. A. Rattey and A. G. Lindgren, “Sampling the 2-D Radon transform,” IEEE Trans. Acoust. Speech Signal Process. 29(5), 994–1002 (1981).
[Crossref]

Lou, R. Y.

O. Nalcioglu, Z.H. Cho, and R. Y. Lou, “Limited field of view reconstruction in computerized tomography,” IEEE Trans. Nucl. Sci. 26(1), 546–551 (1979).
[Crossref]

Lucas, M. S.

Lun, D. P. K.

T.-C. Hsung and D. P. K. Lun, “New sampling scheme for region-of-interest tomography,” IEEE Trans. Signal Process. 48(4), 1154–1163 (2000).
[Crossref]

Mader, K.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

Menzel, A.

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

J. C. da Silva and A. Menzel, “Elementary signals in ptychography,” Opt. Express 23, 33812–33821 (2015).
[Crossref]

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions,” Opt. Express 22(12), 14859–14870 (2014).
[Crossref] [PubMed]

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
[Crossref]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from X-ray coherent diffractive imaging projections,” Opt. Express 19(22), 21345–21357 (2011).
[Crossref] [PubMed]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

Mozzanica, A.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Müller, M.

Munch, B.

A. P. Kaestner, B. Munch, and P. Trtik, “Spatiotemporal computed tomography of dynamic processes,” Opt. Eng. 50(12), 123201 (2011).
[Crossref]

Nalcioglu, O.

O. Nalcioglu, Z.H. Cho, and R. Y. Lou, “Limited field of view reconstruction in computerized tomography,” IEEE Trans. Nucl. Sci. 26(1), 546–551 (1979).
[Crossref]

O. Nalcioglu, P. V. Sankar, and J. Sklansky, “Region-of-interest X-ray tomography (ROIT),” Proc. SPIE 0206, 98–102 (1979).
[Crossref]

Narayanan, S.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

Natterer, F.

F. Natterer, The Mathematics of Computerized Tomography (SIAM, 2001).
[Crossref]

Noo, F.

T. Köhler and F. Noo, “Comment on “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 039801 (2009).
[Crossref]

H. Kudo, M. Courdurier, F. Noo, and M. Defrise, “Tiny a priori knowledge solves the interior problem in computed tomography,” Phys. Med. Biol. 53, 2207–2231 (2008).
[Crossref] [PubMed]

Ohyama, N.

Olson, T.

T. Olson and J. DeStefano, “Wavelet localization of the Radon transform,” IEEE Trans. Signal Process. 42(8), 2055–2067 (1994).
[Crossref]

Pfeiffer, F.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

Quitmann, C.

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

Raabe, J.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

Ramm, A. G.

A. G. Ramm and A. Katsevich, The Radon Transform and Local Tomography (CRC, 1996).

Rattey, P. A.

P. A. Rattey and A. G. Lindgren, “Sampling the 2-D Radon transform,” IEEE Trans. Acoust. Speech Signal Process. 29(5), 994–1002 (1981).
[Crossref]

Riddle, A. C.

R. N. Bracewell and A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
[Crossref]

Ritala, M.

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

Ritman, E. L.

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography II,” SIAM J. Appl. Math. 57, 1095–1127 (1997).
[Crossref]

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography,” SIAM J. Appl. Math. 52, 459–484 (1992).
[Crossref]

W. J. T. Spyra, A. Faridani, K. T. Smith, and E. L. Ritman, “Computed tomographic imaging of the coronary arterial tree - use of local tomography,” IEEE Trans. Med. Imag. 9(1), 1–4 (1990).
[Crossref]

Salome, M.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
[Crossref]

Sankar, P. V.

O. Nalcioglu, P. V. Sankar, and J. Sklansky, “Region-of-interest X-ray tomography (ROIT),” Proc. SPIE 0206, 98–102 (1979).
[Crossref]

Schatz, M.

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151(3), 250–262 (2005).
[Crossref] [PubMed]

Schmid, E.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Schmitt, B.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Schneider, P.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Schreiber, A.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Sharma, K. S.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

Shi, X.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Shiraishi, A.

Shu, Y.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

Sklansky, J.

O. Nalcioglu, P. V. Sankar, and J. Sklansky, “Region-of-interest X-ray tomography (ROIT),” Proc. SPIE 0206, 98–102 (1979).
[Crossref]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
[Crossref]

Smith, K. T.

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography II,” SIAM J. Appl. Math. 57, 1095–1127 (1997).
[Crossref]

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography,” SIAM J. Appl. Math. 52, 459–484 (1992).
[Crossref]

W. J. T. Spyra, A. Faridani, K. T. Smith, and E. L. Ritman, “Computed tomographic imaging of the coronary arterial tree - use of local tomography,” IEEE Trans. Med. Imag. 9(1), 1–4 (1990).
[Crossref]

Spyra, W. J. T.

W. J. T. Spyra, A. Faridani, K. T. Smith, and E. L. Ritman, “Computed tomographic imaging of the coronary arterial tree - use of local tomography,” IEEE Trans. Med. Imag. 9(1), 1–4 (1990).
[Crossref]

Stadler, H.-C.

Stock, S. R.

X. Xiao, F. de Carlo, and S. R. Stock, “Practical error estimation in zoom-in and truncated tomography reconstructions,” Rev. Sci. Instrum. 78(6), 063705 (2007).
[Crossref] [PubMed]

Theidel, G.

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Thibault, P.

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14063004 (2012).
[Crossref]

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
[Crossref]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

Thurman, S. T.

Titarenko, V.

A. Kyrieleis, V. Titarenko, M. Ibison, T. Connolley, and P. J. Withers, “Region-of-interest tomography using filtered backprojection: assessing the pratical limits,” J. Microsc. 241(1), 69–82 (2010).
[Crossref] [PubMed]

Trtik, P.

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
[Crossref]

A. P. Kaestner, B. Munch, and P. Trtik, “Spatiotemporal computed tomography of dynamic processes,” Opt. Eng. 50(12), 123201 (2011).
[Crossref]

Tsujiuchi, J.

van Bokhoven, J. A.

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

van Heel, M.

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151(3), 250–262 (2005).
[Crossref] [PubMed]

Vasilescu, D. M.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

Vila-Comamala, J.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
[Crossref]

Wagner, W.

W. Wagner, “Reconstructions from restricted region scan data - new means to reduce the patient dose,” IEEE Trans. Nucl. Sci. 26(2), 2866–2869 (1979).
[Crossref]

Wang, G.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

G. Wang and H. Yu, “Can interior tomography outperform lambda tomography?” Proc. Natl. Acad. Sci. USA 107(22), E92–E93 (2010).
[Crossref] [PubMed]

Y. Ye, H. Yu, Y. Wei, and G. Wang, “A general local reconstruction approach based on a truncated Hilbert transform,” Int. J. Biomed. Imaging 2007, 63634 (2007).
[Crossref]

Wei, Y.

Y. Ye, H. Yu, Y. Wei, and G. Wang, “A general local reconstruction approach based on a truncated Hilbert transform,” Int. J. Biomed. Imaging 2007, 63634 (2007).
[Crossref]

Wepf, R.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Wepf, R. A.

Withers, P. J.

A. Kyrieleis, V. Titarenko, M. Ibison, T. Connolley, and P. J. Withers, “Region-of-interest tomography using filtered backprojection: assessing the pratical limits,” J. Microsc. 241(1), 69–82 (2010).
[Crossref] [PubMed]

Xiao, X.

X. Xiao, F. de Carlo, and S. R. Stock, “Practical error estimation in zoom-in and truncated tomography reconstructions,” Rev. Sci. Instrum. 78(6), 063705 (2007).
[Crossref] [PubMed]

Ye, Y.

Y. Ye, H. Yu, Y. Wei, and G. Wang, “A general local reconstruction approach based on a truncated Hilbert transform,” Int. J. Biomed. Imaging 2007, 63634 (2007).
[Crossref]

Yu, H.

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

G. Wang and H. Yu, “Can interior tomography outperform lambda tomography?” Proc. Natl. Acad. Sci. USA 107(22), E92–E93 (2010).
[Crossref] [PubMed]

Y. Ye, H. Yu, Y. Wei, and G. Wang, “A general local reconstruction approach based on a truncated Hilbert transform,” Int. J. Biomed. Imaging 2007, 63634 (2007).
[Crossref]

Appl. Opt. (2)

Astrophys. J. (1)

R. N. Bracewell and A. C. Riddle, “Inversion of fan-beam scans in radio astronomy,” Astrophys. J. 150, 427–434 (1967).
[Crossref]

ChemCatChem (1)

J. C. da Silva, K. Mader, M. Holler, D. Haberthür, A. Diaz, M. Guizar-Sicairos, W.-C. Cheng, Y. Shu, J. Raabe, A. Menzel, and J. A. van Bokhoven, “Assessment of the 3D Pore Structure and Individual Components of Preshaped Catalyst Bodies by X-Ray Imaging,” ChemCatChem 7(3), 413–416 (2015).
[Crossref] [PubMed]

IEEE Trans. Acoust. Speech Signal Process. (1)

P. A. Rattey and A. G. Lindgren, “Sampling the 2-D Radon transform,” IEEE Trans. Acoust. Speech Signal Process. 29(5), 994–1002 (1981).
[Crossref]

IEEE Trans. Med. Imag. (1)

W. J. T. Spyra, A. Faridani, K. T. Smith, and E. L. Ritman, “Computed tomographic imaging of the coronary arterial tree - use of local tomography,” IEEE Trans. Med. Imag. 9(1), 1–4 (1990).
[Crossref]

IEEE Trans. Nucl. Sci. (2)

O. Nalcioglu, Z.H. Cho, and R. Y. Lou, “Limited field of view reconstruction in computerized tomography,” IEEE Trans. Nucl. Sci. 26(1), 546–551 (1979).
[Crossref]

W. Wagner, “Reconstructions from restricted region scan data - new means to reduce the patient dose,” IEEE Trans. Nucl. Sci. 26(2), 2866–2869 (1979).
[Crossref]

IEEE Trans. Signal Process. (2)

T. Olson and J. DeStefano, “Wavelet localization of the Radon transform,” IEEE Trans. Signal Process. 42(8), 2055–2067 (1994).
[Crossref]

T.-C. Hsung and D. P. K. Lun, “New sampling scheme for region-of-interest tomography,” IEEE Trans. Signal Process. 48(4), 1154–1163 (2000).
[Crossref]

Int. J. Biomed. Imaging (1)

Y. Ye, H. Yu, Y. Wei, and G. Wang, “A general local reconstruction approach based on a truncated Hilbert transform,” Int. J. Biomed. Imaging 2007, 63634 (2007).
[Crossref]

J. Microsc. (1)

A. Kyrieleis, V. Titarenko, M. Ibison, T. Connolley, and P. J. Withers, “Region-of-interest tomography using filtered backprojection: assessing the pratical limits,” J. Microsc. 241(1), 69–82 (2010).
[Crossref] [PubMed]

J. Struct. Biol. (1)

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151(3), 250–262 (2005).
[Crossref] [PubMed]

J. Synchrotron Rad. (1)

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Rad. 18, 442–446 (2011).
[Crossref]

Nature (1)

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

New J. Phys. (1)

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14063004 (2012).
[Crossref]

Nucl. Instrum. Methods Phys. Res. A (1)

R. Dinapoli, A. Bergamaschi, B. Henrich, R. Horisberger, I. Johnson, A. Mozzanica, E. Schmid, B. Schmitt, A. Schreiber, X. Shi, and G. Theidel, “EIGER: next generation single photon counting detector for X-ray applications,” Nucl. Instrum. Methods Phys. Res. A 650, 79–83 (2011).
[Crossref]

Opt. Eng. (1)

A. P. Kaestner, B. Munch, and P. Trtik, “Spatiotemporal computed tomography of dynamic processes,” Opt. Eng. 50(12), 123201 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optica (1)

Optik (1)

R. Bates and R. Lewitt, “Image reconstruction from projections: I: General theoretical considerations, III:Projection completion methods (theory), IV: Projection completion methods (computational examples),” Optik 50, 269–278 (1978).

Phys Med Biol. (1)

K. S. Sharma, C. Holzner, D. M. Vasilescu, X. Jin, S. Narayanan, M. Agah, E. A. Hoffman, H. Yu, and G. Wang, “Scout-view Assisted Interior Micro-CT,” Phys Med Biol. 58(12), 4297–4314 (2013).
[Crossref] [PubMed]

Phys. Med. Biol. (2)

H. Kudo, M. Courdurier, F. Noo, and M. Defrise, “Tiny a priori knowledge solves the interior problem in computed tomography,” Phys. Med. Biol. 53, 2207–2231 (2008).
[Crossref] [PubMed]

J. C. Gore and S. Leeman, “The reconstruction of objects from incomplete projections,” Phys. Med. Biol. 25(1), 129–136 (1980).
[Crossref] [PubMed]

Phys. Rev. B (1)

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative X-ray phase nanotomography,” Phys. Rev. B 85, 020104(R) (2012).
[Crossref]

Phys. Rev. Lett. (2)

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 168101 (2008).
[Crossref] [PubMed]

T. Köhler and F. Noo, “Comment on “Region-of-Interest Tomography for Grating-Based X-Ray Differential Phase-Contrast Imaging,” Phys. Rev. Lett. 101, 039801 (2009).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. L. Huggins, “The structure of alpha keratin,” Proc. Natl. Acad. Sci. U.S.A. 43(2), 204–209 (1957).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

G. Wang and H. Yu, “Can interior tomography outperform lambda tomography?” Proc. Natl. Acad. Sci. USA 107(22), E92–E93 (2010).
[Crossref] [PubMed]

Proc. Roy. Soc. Lond. A (1)

R. A. Crowther, D. J. DeRosier, and A. Klug, “The reconstruction of a three-dimensional structure from projections and its application to electron microscopy,” Proc. Roy. Soc. Lond. A 317, 319–340 (1970).
[Crossref]

Proc. SPIE (1)

O. Nalcioglu, P. V. Sankar, and J. Sklansky, “Region-of-interest X-ray tomography (ROIT),” Proc. SPIE 0206, 98–102 (1979).
[Crossref]

Rev. Sci. Instrum. (2)

X. Xiao, F. de Carlo, and S. R. Stock, “Practical error estimation in zoom-in and truncated tomography reconstructions,” Rev. Sci. Instrum. 78(6), 063705 (2007).
[Crossref] [PubMed]

M. Holler, J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk, “An instrument for 3D x-ray nano-imaging,” Rev. Sci. Instrum. 83, 073703 (2012).
[Crossref] [PubMed]

Sci. Rep. (1)

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution.,” Sci. Rep. 4, 3857 (2014).
[Crossref] [PubMed]

SIAM J. Appl. Math. (2)

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography,” SIAM J. Appl. Math. 52, 459–484 (1992).
[Crossref]

A. Faridani, E. L. Ritman, and K. T. Smith, “Local Tomography II,” SIAM J. Appl. Math. 57, 1095–1127 (1997).
[Crossref]

Ultramicroscopy (1)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

Other (5)

A. Guinier, X-ray diffraction in crystals, imperfect crystals and amorphous bodies (Dover, 1994).

ChemSpider database, “Melanin,” (ID 4884931). http://www.chemspider.com/Chemical-Structure.4884931.html (data of access February 01, 2018)

A. G. Ramm and A. Katsevich, The Radon Transform and Local Tomography (CRC, 1996).

F. Natterer, The Mathematics of Computerized Tomography (SIAM, 2001).
[Crossref]

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 Schematic representation of the PRofIT approach. (a) Shepp-Logan head phantom where the different sizes of the regions in different levels, named L0 (ROI), L1, L2, and L3. (b) The corresponding sinogram where the different levels are indicated by colors. The size of the projections are 20, 21, 22, and 23 for the levels L0, L1, L2 and L3, respectively, and are related to the colored circles in (a). (c) Angular sampling of the different levels. Each level contains equally spaced projections in the angular range. Their spacings are indicated and Δθ is the angular resolution when combining all the levels.
Fig. 2
Fig. 2 The bowtie-like band region of the Radon transform. (a) The representation of the band region of the Radon transform of an object of size 2 × R and maximum spatial frequency W. This band region is called RW-bowtie and is obtained by the Fourier transform of the sinogram. The slope of the limits of the bowtie-like band region depends on 1/R. (b) Sampling of the projections in a rectangular grid with Δr in the radial direction and Δθ in the angular direction. (c) Representation of the discrete Fourier transform of the rectangularly sampled Radon transform of (b) generated from equispaced projections from 0 to π. Periodic replications of the RW-bowtie will appear and proper angular sampling is needed to avoid aliasing errors. (d) Representation of the aliasing errors affecting the bowtie-like band region of the Radon transform in case of angular undersampling. The affected areas are illustrated by checkerboard regions.
Fig. 3
Fig. 3 Results of the simulations with the Shepp-Logan head phantom using PRofIT approach. Tomographic reconstruction using (a) 4-level projections, (b) 2-level projections, and (c) only truncated projections and the sinogram extension approach. An offset of 9 × 10−3 was added to the gray level in (c) to compensate for the loss of quantitative contrast of the approach. The images of the absolute value of the difference between the original tomographic reconstruction from non-truncated projections and the reconstruction in (a), (b), and (c) are shown in (d), (e), and (f), respectively. The images are zoomed-in of the ROI (dashed yellow lines) with a region around to shown the transition from the region away the ROI to the ROI. (g) The gray level profiles across the blue, red, and green lines in (a), (b), and (c), respectively, along with the one from the original reconstruction from non-truncated projections. The dashed black lines limit the region-of-interest.
Fig. 4
Fig. 4 The RW-bowtie shaped support of the 2D Fourier transform of the Radon transform for the 4-level decomposition of the sinogram. The different sinograms corresponding to the levels L0 (372 projections), L1 (186 projections), L2 (93 projections) and L3 (93 projections) are shown in (a), (d), (g), and (j), respectively. They are undersampled in the angular range. The RW-bowtie support for each of this level of decomposition is shown in (b), (e), (h) and (k) for L0, L1, L2 and L3 projections, respectively. In the third column, the RW-bowtie support for each level is shown again, but this time with a finer angular sampling considering the entire object size according to Eq. (3).
Fig. 5
Fig. 5 Representation of the digital truncation of the PXCT projections of a FCC catalyst sample. (a) One phase projection acquired from the pillar porous material where the 4 colored square regions represent a 4-level decomposition for PRofIT. Blue for L3, green for L2, yellow for L1, and red for L0. (b) A representation of the set of truncated projections for the 4 levels. The levels are indicated on the right side of each projection.
Fig. 6
Fig. 6 PRofIT results obtained by truncating the original experimental projections from the 3D volumes of the FCC catalyst sample. (a) Reconstructed slice from non-truncated ptychographic projections. (b) Reconstructed slice from truncated projection using the PRofIT approach with four levels. (c) Reconstructed slice from truncated projections using the sinogram extension approach. An offset of 0.65 × 10−5 was added to the gray level in (c) to compensate the loss of quantitative contrast of the approach. (d), (e) and (f) show the zoomed-in images of the corresponding ROIs reconstructed in (a), (b) and (c), respectively. The yellow dashed circles represent the region-of-interest. (g) The gray level profiles across the blue, red and green lines in (a), (b), and (c), respectively. The dashed black lines limit the region-of-interest. The colormap of the images is given in units of refractive index decrement δ.
Fig. 7
Fig. 7 3D volume of the hair shaft reconstructed using PRofIT with 2 levels decomposition. (a) Reconstructed slice displaying the entire hair cross section. The gray level is given in units of refractive index decrement δ. The yellow circle highlights the off-centered ROI. (b) Zoom-in of the ROI where the red arrows indicate the cuticles, one melanin grain, and a part of the cortex. (c) Gray level profile across the solid blue line in (a), which crosses a melanin grain as indicated by the red arrow. The dashed lines limit the region-of-interest.
Fig. 8
Fig. 8 Fourier Shell correlation curve obtained for the images in Fig. 6 to estimate of spatial resolution of the reconstructions. All curves intersect the threshold curve at about the same value of ∼ 0.365 of the axis of abscissae. The pixel size of figures is 14.3 nm.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

θ L 0 ( n ) = θ 1 + ( 2 n 1 ) Δ θ , θ L 1 ( n ) = θ 1 + ( 4 n 2 ) Δ θ , θ L 2 ( n ) = θ 1 + ( 8 n 4 ) Δ θ , θ L 3 ( n ) = θ 1 + ( 8 n 8 ) Δ θ ,
1 = 0 ( 1 + k ) , 2 = 1 ( 1 + k ) ,
M > π 2 × N + 1 ,
δ 1.35 × 10 6 ρ λ 2 ,

Metrics