Abstract

Projection incompleteness in x-ray computed tomography (CT) often relates to sparse sampling or detector gaps and leads to degraded reconstructions with severe streak and ring artifacts. To suppress these artifacts, this study develops a new sinogram inpainting strategy based on sinusoid-like curve decomposition and eigenvector-guided interpolation, where each missing sinogram point is considered located within a group of sinusoid-like curves and estimated from eigenvector-guided interpolation to preserve the sinogram texture continuity. The proposed approach is evaluated on real two-dimensional fan-beam CT data, for which the projection incompleteness, due to sparse sampling and symmetric detector gaps, is simulated. A Compute Unified Device Architecture (CUDA)-based parallelization is applied on the operations of sinusoid fittings and interpolations to accelerate the algorithm. A comparative study is then conducted to evaluate the proposed approach with two other inpainting methods and with a compressed sensing iterative reconstruction. Qualitative and quantitative performances demonstrate that the proposed approach can lead to efficient artifact suppression and less structure blurring.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 177–201.
  2. J. L. Prince and A. S. Willsky, “Constrained sinogram restoration for limited-angle tomography,” Opt. Eng. 29, 535–544(1990).
    [CrossRef]
  3. P. M. Joseph and R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702(1980).
    [CrossRef] [PubMed]
  4. B. Ohnesorge, T. Flohr, K. Schwarz, J. P. Heiken, and K. T. Bae, “Efficient correction for CT image artifacts caused by objects extending outside the scan field of view,” Med. Phys. 27, 39–46(2000).
    [CrossRef] [PubMed]
  5. J. S. Maltz, S. Bose, H. P. Shukla, and A. R. Bani-Hashemi, “CT truncation artifact removal using water-equivalent thicknesses derived from truncated projection data,” in Proceedings of IEEE Conference on Engineering Medicine and Biology (IEEE, 2007), pp. 2907–2911.
  6. J. Xu, K. Taguchi, and B. M. W. Tsui, “Statistical projection completion in x-ray CT using consistency conditions,” IEEE Trans. Med. Imaging 29, 1528–40 (2010).
    [CrossRef] [PubMed]
  7. T. F. Chan and J. Shen, “Mathematical models for local nontexture inpaintings,” SIAM J. Appl. Math. 62, 1019–1043(2002).
    [CrossRef]
  8. H. Xue, L. Zhang, Y. Xiao, Z. Chen, and Y. Xing, “Metal artifact reduction in dual energy CT by sinogram segmentation based on active contour model and TV inpainting,” in 2009 IEEE Nuclear Science Symposium Conference Record (NSS/MIC) (IEEE, 2009), pp. 904–908.
    [CrossRef]
  9. J. Gu, L. Zhang, G. Yu, Y. Xing, and Z. Chen, “X-ray CT metal artifacts reduction through curvature based sinogram inpainting,” J. X-Ray Sci. Technol. 14, 73–82 (2006).
  10. H. Kostler, M. Prummer, U. Rude, and J. Hornegger, “Adaptive variational sinogram interpolation of sparsely sampled CT data,” in Proceedings of the 18th International Conference on Pattern Recognition (IEEE, 2006), pp. 778–781.
  11. M. Bertram, J. Wiegert, D. Schafer, T. Aach, and G. Rose, “Directional view interpolation for compensation of sparse angular sampling in cone-beam CT,” IEEE Trans. Med. Imaging 28, 1011–1022 (2009).
    [CrossRef] [PubMed]
  12. E. P. A. Constantino and K. B. Ozanyan, “Sinogram recovery for sparse angle tomography using sinusoidal Hough transform,” Meas. Sci. Technol. 19, 094015 (2008).
    [CrossRef]
  13. A. Zamyatin and N. Satoru, “Extension of the reconstruction field of view and truncation correction using sinogram decomposition,” Med. Phys. 34, 1593–1605 (2007).
    [CrossRef] [PubMed]
  14. R. Chityala, K. R. Hoffmann, S. Rudin, and D. R. Bednarek, “Artifact reduction in truncated CT using sinogram completion,” Proc. SPIE 5747, 2110–2117 (2005).
    [CrossRef]
  15. M. Oehler and T. M. Buzug, “Statistical image reconstruction for inconsistent CT projection data,” Methods Inf. Med. 46, 261–269 (2007).
    [CrossRef] [PubMed]
  16. W. Zbijewski, M. Defrise, M. Viergever, and F. Beekman, “Statistical reconstruction for x-ray CT systems with non-continuous detectors,” Phys. Med. Biol. 52, 403–418 (2007).
    [CrossRef] [PubMed]
  17. C. Lemmens, D. Faul, and J. Nuyts, “Suppression of metal artifacts in CT using a reconstruction procedure that combines MAP and projection completion,” IEEE Trans. Med. Imaging 28, 250–260 (2009).
    [CrossRef] [PubMed]
  18. E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
    [CrossRef] [PubMed]
  19. X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-view projection reconstruction with an iterative reconstruction re-projection algorithm a TV constraint,” IEEE Trans. Nucl. Sci. 56, 1377–1382 (2009).
    [CrossRef]
  20. L. Ritschl, F. Bergner, and M. Kachelriess, “A new approach to limited angle tomography using the compressed sensing framework,” Proc. SPIE 7622, 76222H (2010).
    [CrossRef]
  21. J. Tang, B. Nett, and G. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54, 5781–5804 (2009).
    [CrossRef] [PubMed]
  22. A. Kharlamov and V. Podlozhnyuk, “Image denoising,” Tech. Rep. (NVIDIA, Inc., 2007).
  23. NVIDIA CUDA Programming Guide (Version 3.0).
  24. “Accelerating MATLAB with CUDA using MEX files” (White Paper), http://developer.nvidia.com/object/matlab cuda.html.
  25. “GPU Acceleration in MATLAB,” http://arch.eece.maine.edu/superme/images/8/8c/Final report.pdf.
  26. U. Kothe, “Edge and junction detection with an improved structure tensor,” Lect. Notes Comput. Sci. 2781, 25–32(2003).
    [CrossRef]
  27. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd ed. (American Mathematical Society, 2002).

2010 (2)

J. Xu, K. Taguchi, and B. M. W. Tsui, “Statistical projection completion in x-ray CT using consistency conditions,” IEEE Trans. Med. Imaging 29, 1528–40 (2010).
[CrossRef] [PubMed]

L. Ritschl, F. Bergner, and M. Kachelriess, “A new approach to limited angle tomography using the compressed sensing framework,” Proc. SPIE 7622, 76222H (2010).
[CrossRef]

2009 (4)

J. Tang, B. Nett, and G. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54, 5781–5804 (2009).
[CrossRef] [PubMed]

C. Lemmens, D. Faul, and J. Nuyts, “Suppression of metal artifacts in CT using a reconstruction procedure that combines MAP and projection completion,” IEEE Trans. Med. Imaging 28, 250–260 (2009).
[CrossRef] [PubMed]

M. Bertram, J. Wiegert, D. Schafer, T. Aach, and G. Rose, “Directional view interpolation for compensation of sparse angular sampling in cone-beam CT,” IEEE Trans. Med. Imaging 28, 1011–1022 (2009).
[CrossRef] [PubMed]

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-view projection reconstruction with an iterative reconstruction re-projection algorithm a TV constraint,” IEEE Trans. Nucl. Sci. 56, 1377–1382 (2009).
[CrossRef]

2008 (2)

E. P. A. Constantino and K. B. Ozanyan, “Sinogram recovery for sparse angle tomography using sinusoidal Hough transform,” Meas. Sci. Technol. 19, 094015 (2008).
[CrossRef]

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
[CrossRef] [PubMed]

2007 (3)

M. Oehler and T. M. Buzug, “Statistical image reconstruction for inconsistent CT projection data,” Methods Inf. Med. 46, 261–269 (2007).
[CrossRef] [PubMed]

W. Zbijewski, M. Defrise, M. Viergever, and F. Beekman, “Statistical reconstruction for x-ray CT systems with non-continuous detectors,” Phys. Med. Biol. 52, 403–418 (2007).
[CrossRef] [PubMed]

A. Zamyatin and N. Satoru, “Extension of the reconstruction field of view and truncation correction using sinogram decomposition,” Med. Phys. 34, 1593–1605 (2007).
[CrossRef] [PubMed]

2006 (1)

J. Gu, L. Zhang, G. Yu, Y. Xing, and Z. Chen, “X-ray CT metal artifacts reduction through curvature based sinogram inpainting,” J. X-Ray Sci. Technol. 14, 73–82 (2006).

2005 (1)

R. Chityala, K. R. Hoffmann, S. Rudin, and D. R. Bednarek, “Artifact reduction in truncated CT using sinogram completion,” Proc. SPIE 5747, 2110–2117 (2005).
[CrossRef]

2003 (1)

U. Kothe, “Edge and junction detection with an improved structure tensor,” Lect. Notes Comput. Sci. 2781, 25–32(2003).
[CrossRef]

2002 (1)

T. F. Chan and J. Shen, “Mathematical models for local nontexture inpaintings,” SIAM J. Appl. Math. 62, 1019–1043(2002).
[CrossRef]

2000 (1)

B. Ohnesorge, T. Flohr, K. Schwarz, J. P. Heiken, and K. T. Bae, “Efficient correction for CT image artifacts caused by objects extending outside the scan field of view,” Med. Phys. 27, 39–46(2000).
[CrossRef] [PubMed]

1990 (1)

J. L. Prince and A. S. Willsky, “Constrained sinogram restoration for limited-angle tomography,” Opt. Eng. 29, 535–544(1990).
[CrossRef]

1980 (1)

P. M. Joseph and R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702(1980).
[CrossRef] [PubMed]

Aach, T.

M. Bertram, J. Wiegert, D. Schafer, T. Aach, and G. Rose, “Directional view interpolation for compensation of sparse angular sampling in cone-beam CT,” IEEE Trans. Med. Imaging 28, 1011–1022 (2009).
[CrossRef] [PubMed]

Bae, K. T.

B. Ohnesorge, T. Flohr, K. Schwarz, J. P. Heiken, and K. T. Bae, “Efficient correction for CT image artifacts caused by objects extending outside the scan field of view,” Med. Phys. 27, 39–46(2000).
[CrossRef] [PubMed]

Bani-Hashemi, A. R.

J. S. Maltz, S. Bose, H. P. Shukla, and A. R. Bani-Hashemi, “CT truncation artifact removal using water-equivalent thicknesses derived from truncated projection data,” in Proceedings of IEEE Conference on Engineering Medicine and Biology (IEEE, 2007), pp. 2907–2911.

Bednarek, D. R.

R. Chityala, K. R. Hoffmann, S. Rudin, and D. R. Bednarek, “Artifact reduction in truncated CT using sinogram completion,” Proc. SPIE 5747, 2110–2117 (2005).
[CrossRef]

Beekman, F.

W. Zbijewski, M. Defrise, M. Viergever, and F. Beekman, “Statistical reconstruction for x-ray CT systems with non-continuous detectors,” Phys. Med. Biol. 52, 403–418 (2007).
[CrossRef] [PubMed]

Bergner, F.

L. Ritschl, F. Bergner, and M. Kachelriess, “A new approach to limited angle tomography using the compressed sensing framework,” Proc. SPIE 7622, 76222H (2010).
[CrossRef]

Bertram, M.

M. Bertram, J. Wiegert, D. Schafer, T. Aach, and G. Rose, “Directional view interpolation for compensation of sparse angular sampling in cone-beam CT,” IEEE Trans. Med. Imaging 28, 1011–1022 (2009).
[CrossRef] [PubMed]

Bose, S.

J. S. Maltz, S. Bose, H. P. Shukla, and A. R. Bani-Hashemi, “CT truncation artifact removal using water-equivalent thicknesses derived from truncated projection data,” in Proceedings of IEEE Conference on Engineering Medicine and Biology (IEEE, 2007), pp. 2907–2911.

Buzug, T. M.

M. Oehler and T. M. Buzug, “Statistical image reconstruction for inconsistent CT projection data,” Methods Inf. Med. 46, 261–269 (2007).
[CrossRef] [PubMed]

Chan, T. F.

T. F. Chan and J. Shen, “Mathematical models for local nontexture inpaintings,” SIAM J. Appl. Math. 62, 1019–1043(2002).
[CrossRef]

Chen, G.

J. Tang, B. Nett, and G. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54, 5781–5804 (2009).
[CrossRef] [PubMed]

Chen, Z.

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-view projection reconstruction with an iterative reconstruction re-projection algorithm a TV constraint,” IEEE Trans. Nucl. Sci. 56, 1377–1382 (2009).
[CrossRef]

J. Gu, L. Zhang, G. Yu, Y. Xing, and Z. Chen, “X-ray CT metal artifacts reduction through curvature based sinogram inpainting,” J. X-Ray Sci. Technol. 14, 73–82 (2006).

H. Xue, L. Zhang, Y. Xiao, Z. Chen, and Y. Xing, “Metal artifact reduction in dual energy CT by sinogram segmentation based on active contour model and TV inpainting,” in 2009 IEEE Nuclear Science Symposium Conference Record (NSS/MIC) (IEEE, 2009), pp. 904–908.
[CrossRef]

Cheney, W.

D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd ed. (American Mathematical Society, 2002).

Cheng, J.

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-view projection reconstruction with an iterative reconstruction re-projection algorithm a TV constraint,” IEEE Trans. Nucl. Sci. 56, 1377–1382 (2009).
[CrossRef]

Chityala, R.

R. Chityala, K. R. Hoffmann, S. Rudin, and D. R. Bednarek, “Artifact reduction in truncated CT using sinogram completion,” Proc. SPIE 5747, 2110–2117 (2005).
[CrossRef]

Constantino, E. P. A.

E. P. A. Constantino and K. B. Ozanyan, “Sinogram recovery for sparse angle tomography using sinusoidal Hough transform,” Meas. Sci. Technol. 19, 094015 (2008).
[CrossRef]

Defrise, M.

W. Zbijewski, M. Defrise, M. Viergever, and F. Beekman, “Statistical reconstruction for x-ray CT systems with non-continuous detectors,” Phys. Med. Biol. 52, 403–418 (2007).
[CrossRef] [PubMed]

Duan, X.

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-view projection reconstruction with an iterative reconstruction re-projection algorithm a TV constraint,” IEEE Trans. Nucl. Sci. 56, 1377–1382 (2009).
[CrossRef]

Faul, D.

C. Lemmens, D. Faul, and J. Nuyts, “Suppression of metal artifacts in CT using a reconstruction procedure that combines MAP and projection completion,” IEEE Trans. Med. Imaging 28, 250–260 (2009).
[CrossRef] [PubMed]

Flohr, T.

B. Ohnesorge, T. Flohr, K. Schwarz, J. P. Heiken, and K. T. Bae, “Efficient correction for CT image artifacts caused by objects extending outside the scan field of view,” Med. Phys. 27, 39–46(2000).
[CrossRef] [PubMed]

Gu, J.

J. Gu, L. Zhang, G. Yu, Y. Xing, and Z. Chen, “X-ray CT metal artifacts reduction through curvature based sinogram inpainting,” J. X-Ray Sci. Technol. 14, 73–82 (2006).

Heiken, J. P.

B. Ohnesorge, T. Flohr, K. Schwarz, J. P. Heiken, and K. T. Bae, “Efficient correction for CT image artifacts caused by objects extending outside the scan field of view,” Med. Phys. 27, 39–46(2000).
[CrossRef] [PubMed]

Hoffmann, K. R.

R. Chityala, K. R. Hoffmann, S. Rudin, and D. R. Bednarek, “Artifact reduction in truncated CT using sinogram completion,” Proc. SPIE 5747, 2110–2117 (2005).
[CrossRef]

Hornegger, J.

H. Kostler, M. Prummer, U. Rude, and J. Hornegger, “Adaptive variational sinogram interpolation of sparsely sampled CT data,” in Proceedings of the 18th International Conference on Pattern Recognition (IEEE, 2006), pp. 778–781.

Joseph, P. M.

P. M. Joseph and R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702(1980).
[CrossRef] [PubMed]

Kachelriess, M.

L. Ritschl, F. Bergner, and M. Kachelriess, “A new approach to limited angle tomography using the compressed sensing framework,” Proc. SPIE 7622, 76222H (2010).
[CrossRef]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 177–201.

Kharlamov, A.

A. Kharlamov and V. Podlozhnyuk, “Image denoising,” Tech. Rep. (NVIDIA, Inc., 2007).

Kincaid, D.

D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd ed. (American Mathematical Society, 2002).

Kostler, H.

H. Kostler, M. Prummer, U. Rude, and J. Hornegger, “Adaptive variational sinogram interpolation of sparsely sampled CT data,” in Proceedings of the 18th International Conference on Pattern Recognition (IEEE, 2006), pp. 778–781.

Kothe, U.

U. Kothe, “Edge and junction detection with an improved structure tensor,” Lect. Notes Comput. Sci. 2781, 25–32(2003).
[CrossRef]

Lemmens, C.

C. Lemmens, D. Faul, and J. Nuyts, “Suppression of metal artifacts in CT using a reconstruction procedure that combines MAP and projection completion,” IEEE Trans. Med. Imaging 28, 250–260 (2009).
[CrossRef] [PubMed]

Maltz, J. S.

J. S. Maltz, S. Bose, H. P. Shukla, and A. R. Bani-Hashemi, “CT truncation artifact removal using water-equivalent thicknesses derived from truncated projection data,” in Proceedings of IEEE Conference on Engineering Medicine and Biology (IEEE, 2007), pp. 2907–2911.

Nett, B.

J. Tang, B. Nett, and G. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54, 5781–5804 (2009).
[CrossRef] [PubMed]

Nuyts, J.

C. Lemmens, D. Faul, and J. Nuyts, “Suppression of metal artifacts in CT using a reconstruction procedure that combines MAP and projection completion,” IEEE Trans. Med. Imaging 28, 250–260 (2009).
[CrossRef] [PubMed]

Oehler, M.

M. Oehler and T. M. Buzug, “Statistical image reconstruction for inconsistent CT projection data,” Methods Inf. Med. 46, 261–269 (2007).
[CrossRef] [PubMed]

Ohnesorge, B.

B. Ohnesorge, T. Flohr, K. Schwarz, J. P. Heiken, and K. T. Bae, “Efficient correction for CT image artifacts caused by objects extending outside the scan field of view,” Med. Phys. 27, 39–46(2000).
[CrossRef] [PubMed]

Ozanyan, K. B.

E. P. A. Constantino and K. B. Ozanyan, “Sinogram recovery for sparse angle tomography using sinusoidal Hough transform,” Meas. Sci. Technol. 19, 094015 (2008).
[CrossRef]

Pan, X.

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
[CrossRef] [PubMed]

Podlozhnyuk, V.

A. Kharlamov and V. Podlozhnyuk, “Image denoising,” Tech. Rep. (NVIDIA, Inc., 2007).

Prince, J. L.

J. L. Prince and A. S. Willsky, “Constrained sinogram restoration for limited-angle tomography,” Opt. Eng. 29, 535–544(1990).
[CrossRef]

Prummer, M.

H. Kostler, M. Prummer, U. Rude, and J. Hornegger, “Adaptive variational sinogram interpolation of sparsely sampled CT data,” in Proceedings of the 18th International Conference on Pattern Recognition (IEEE, 2006), pp. 778–781.

Ritschl, L.

L. Ritschl, F. Bergner, and M. Kachelriess, “A new approach to limited angle tomography using the compressed sensing framework,” Proc. SPIE 7622, 76222H (2010).
[CrossRef]

Rose, G.

M. Bertram, J. Wiegert, D. Schafer, T. Aach, and G. Rose, “Directional view interpolation for compensation of sparse angular sampling in cone-beam CT,” IEEE Trans. Med. Imaging 28, 1011–1022 (2009).
[CrossRef] [PubMed]

Rude, U.

H. Kostler, M. Prummer, U. Rude, and J. Hornegger, “Adaptive variational sinogram interpolation of sparsely sampled CT data,” in Proceedings of the 18th International Conference on Pattern Recognition (IEEE, 2006), pp. 778–781.

Rudin, S.

R. Chityala, K. R. Hoffmann, S. Rudin, and D. R. Bednarek, “Artifact reduction in truncated CT using sinogram completion,” Proc. SPIE 5747, 2110–2117 (2005).
[CrossRef]

Satoru, N.

A. Zamyatin and N. Satoru, “Extension of the reconstruction field of view and truncation correction using sinogram decomposition,” Med. Phys. 34, 1593–1605 (2007).
[CrossRef] [PubMed]

Schafer, D.

M. Bertram, J. Wiegert, D. Schafer, T. Aach, and G. Rose, “Directional view interpolation for compensation of sparse angular sampling in cone-beam CT,” IEEE Trans. Med. Imaging 28, 1011–1022 (2009).
[CrossRef] [PubMed]

Schulz, R. A.

P. M. Joseph and R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702(1980).
[CrossRef] [PubMed]

Schwarz, K.

B. Ohnesorge, T. Flohr, K. Schwarz, J. P. Heiken, and K. T. Bae, “Efficient correction for CT image artifacts caused by objects extending outside the scan field of view,” Med. Phys. 27, 39–46(2000).
[CrossRef] [PubMed]

Shen, J.

T. F. Chan and J. Shen, “Mathematical models for local nontexture inpaintings,” SIAM J. Appl. Math. 62, 1019–1043(2002).
[CrossRef]

Shukla, H. P.

J. S. Maltz, S. Bose, H. P. Shukla, and A. R. Bani-Hashemi, “CT truncation artifact removal using water-equivalent thicknesses derived from truncated projection data,” in Proceedings of IEEE Conference on Engineering Medicine and Biology (IEEE, 2007), pp. 2907–2911.

Sidky, E. Y.

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
[CrossRef] [PubMed]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 177–201.

Taguchi, K.

J. Xu, K. Taguchi, and B. M. W. Tsui, “Statistical projection completion in x-ray CT using consistency conditions,” IEEE Trans. Med. Imaging 29, 1528–40 (2010).
[CrossRef] [PubMed]

Tang, J.

J. Tang, B. Nett, and G. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54, 5781–5804 (2009).
[CrossRef] [PubMed]

Tsui, B. M. W.

J. Xu, K. Taguchi, and B. M. W. Tsui, “Statistical projection completion in x-ray CT using consistency conditions,” IEEE Trans. Med. Imaging 29, 1528–40 (2010).
[CrossRef] [PubMed]

Viergever, M.

W. Zbijewski, M. Defrise, M. Viergever, and F. Beekman, “Statistical reconstruction for x-ray CT systems with non-continuous detectors,” Phys. Med. Biol. 52, 403–418 (2007).
[CrossRef] [PubMed]

Wiegert, J.

M. Bertram, J. Wiegert, D. Schafer, T. Aach, and G. Rose, “Directional view interpolation for compensation of sparse angular sampling in cone-beam CT,” IEEE Trans. Med. Imaging 28, 1011–1022 (2009).
[CrossRef] [PubMed]

Willsky, A. S.

J. L. Prince and A. S. Willsky, “Constrained sinogram restoration for limited-angle tomography,” Opt. Eng. 29, 535–544(1990).
[CrossRef]

Xiao, Y.

H. Xue, L. Zhang, Y. Xiao, Z. Chen, and Y. Xing, “Metal artifact reduction in dual energy CT by sinogram segmentation based on active contour model and TV inpainting,” in 2009 IEEE Nuclear Science Symposium Conference Record (NSS/MIC) (IEEE, 2009), pp. 904–908.
[CrossRef]

Xing, Y.

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-view projection reconstruction with an iterative reconstruction re-projection algorithm a TV constraint,” IEEE Trans. Nucl. Sci. 56, 1377–1382 (2009).
[CrossRef]

J. Gu, L. Zhang, G. Yu, Y. Xing, and Z. Chen, “X-ray CT metal artifacts reduction through curvature based sinogram inpainting,” J. X-Ray Sci. Technol. 14, 73–82 (2006).

H. Xue, L. Zhang, Y. Xiao, Z. Chen, and Y. Xing, “Metal artifact reduction in dual energy CT by sinogram segmentation based on active contour model and TV inpainting,” in 2009 IEEE Nuclear Science Symposium Conference Record (NSS/MIC) (IEEE, 2009), pp. 904–908.
[CrossRef]

Xu, J.

J. Xu, K. Taguchi, and B. M. W. Tsui, “Statistical projection completion in x-ray CT using consistency conditions,” IEEE Trans. Med. Imaging 29, 1528–40 (2010).
[CrossRef] [PubMed]

Xue, H.

H. Xue, L. Zhang, Y. Xiao, Z. Chen, and Y. Xing, “Metal artifact reduction in dual energy CT by sinogram segmentation based on active contour model and TV inpainting,” in 2009 IEEE Nuclear Science Symposium Conference Record (NSS/MIC) (IEEE, 2009), pp. 904–908.
[CrossRef]

Yu, G.

J. Gu, L. Zhang, G. Yu, Y. Xing, and Z. Chen, “X-ray CT metal artifacts reduction through curvature based sinogram inpainting,” J. X-Ray Sci. Technol. 14, 73–82 (2006).

Zamyatin, A.

A. Zamyatin and N. Satoru, “Extension of the reconstruction field of view and truncation correction using sinogram decomposition,” Med. Phys. 34, 1593–1605 (2007).
[CrossRef] [PubMed]

Zbijewski, W.

W. Zbijewski, M. Defrise, M. Viergever, and F. Beekman, “Statistical reconstruction for x-ray CT systems with non-continuous detectors,” Phys. Med. Biol. 52, 403–418 (2007).
[CrossRef] [PubMed]

Zhang, L.

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-view projection reconstruction with an iterative reconstruction re-projection algorithm a TV constraint,” IEEE Trans. Nucl. Sci. 56, 1377–1382 (2009).
[CrossRef]

J. Gu, L. Zhang, G. Yu, Y. Xing, and Z. Chen, “X-ray CT metal artifacts reduction through curvature based sinogram inpainting,” J. X-Ray Sci. Technol. 14, 73–82 (2006).

H. Xue, L. Zhang, Y. Xiao, Z. Chen, and Y. Xing, “Metal artifact reduction in dual energy CT by sinogram segmentation based on active contour model and TV inpainting,” in 2009 IEEE Nuclear Science Symposium Conference Record (NSS/MIC) (IEEE, 2009), pp. 904–908.
[CrossRef]

IEEE Trans. Med. Imaging (3)

J. Xu, K. Taguchi, and B. M. W. Tsui, “Statistical projection completion in x-ray CT using consistency conditions,” IEEE Trans. Med. Imaging 29, 1528–40 (2010).
[CrossRef] [PubMed]

M. Bertram, J. Wiegert, D. Schafer, T. Aach, and G. Rose, “Directional view interpolation for compensation of sparse angular sampling in cone-beam CT,” IEEE Trans. Med. Imaging 28, 1011–1022 (2009).
[CrossRef] [PubMed]

C. Lemmens, D. Faul, and J. Nuyts, “Suppression of metal artifacts in CT using a reconstruction procedure that combines MAP and projection completion,” IEEE Trans. Med. Imaging 28, 250–260 (2009).
[CrossRef] [PubMed]

IEEE Trans. Nucl. Sci. (1)

X. Duan, L. Zhang, Y. Xing, Z. Chen, and J. Cheng, “Few-view projection reconstruction with an iterative reconstruction re-projection algorithm a TV constraint,” IEEE Trans. Nucl. Sci. 56, 1377–1382 (2009).
[CrossRef]

J. X-Ray Sci. Technol. (1)

J. Gu, L. Zhang, G. Yu, Y. Xing, and Z. Chen, “X-ray CT metal artifacts reduction through curvature based sinogram inpainting,” J. X-Ray Sci. Technol. 14, 73–82 (2006).

Lect. Notes Comput. Sci. (1)

U. Kothe, “Edge and junction detection with an improved structure tensor,” Lect. Notes Comput. Sci. 2781, 25–32(2003).
[CrossRef]

Meas. Sci. Technol. (1)

E. P. A. Constantino and K. B. Ozanyan, “Sinogram recovery for sparse angle tomography using sinusoidal Hough transform,” Meas. Sci. Technol. 19, 094015 (2008).
[CrossRef]

Med. Phys. (3)

A. Zamyatin and N. Satoru, “Extension of the reconstruction field of view and truncation correction using sinogram decomposition,” Med. Phys. 34, 1593–1605 (2007).
[CrossRef] [PubMed]

P. M. Joseph and R. A. Schulz, “View sampling requirements in fan beam computed tomography,” Med. Phys. 7, 692–702(1980).
[CrossRef] [PubMed]

B. Ohnesorge, T. Flohr, K. Schwarz, J. P. Heiken, and K. T. Bae, “Efficient correction for CT image artifacts caused by objects extending outside the scan field of view,” Med. Phys. 27, 39–46(2000).
[CrossRef] [PubMed]

Methods Inf. Med. (1)

M. Oehler and T. M. Buzug, “Statistical image reconstruction for inconsistent CT projection data,” Methods Inf. Med. 46, 261–269 (2007).
[CrossRef] [PubMed]

Opt. Eng. (1)

J. L. Prince and A. S. Willsky, “Constrained sinogram restoration for limited-angle tomography,” Opt. Eng. 29, 535–544(1990).
[CrossRef]

Phys. Med. Biol. (3)

W. Zbijewski, M. Defrise, M. Viergever, and F. Beekman, “Statistical reconstruction for x-ray CT systems with non-continuous detectors,” Phys. Med. Biol. 52, 403–418 (2007).
[CrossRef] [PubMed]

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
[CrossRef] [PubMed]

J. Tang, B. Nett, and G. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54, 5781–5804 (2009).
[CrossRef] [PubMed]

Proc. SPIE (2)

L. Ritschl, F. Bergner, and M. Kachelriess, “A new approach to limited angle tomography using the compressed sensing framework,” Proc. SPIE 7622, 76222H (2010).
[CrossRef]

R. Chityala, K. R. Hoffmann, S. Rudin, and D. R. Bednarek, “Artifact reduction in truncated CT using sinogram completion,” Proc. SPIE 5747, 2110–2117 (2005).
[CrossRef]

SIAM J. Appl. Math. (1)

T. F. Chan and J. Shen, “Mathematical models for local nontexture inpaintings,” SIAM J. Appl. Math. 62, 1019–1043(2002).
[CrossRef]

Other (9)

H. Xue, L. Zhang, Y. Xiao, Z. Chen, and Y. Xing, “Metal artifact reduction in dual energy CT by sinogram segmentation based on active contour model and TV inpainting,” in 2009 IEEE Nuclear Science Symposium Conference Record (NSS/MIC) (IEEE, 2009), pp. 904–908.
[CrossRef]

H. Kostler, M. Prummer, U. Rude, and J. Hornegger, “Adaptive variational sinogram interpolation of sparsely sampled CT data,” in Proceedings of the 18th International Conference on Pattern Recognition (IEEE, 2006), pp. 778–781.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988), pp. 177–201.

J. S. Maltz, S. Bose, H. P. Shukla, and A. R. Bani-Hashemi, “CT truncation artifact removal using water-equivalent thicknesses derived from truncated projection data,” in Proceedings of IEEE Conference on Engineering Medicine and Biology (IEEE, 2007), pp. 2907–2911.

D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd ed. (American Mathematical Society, 2002).

A. Kharlamov and V. Podlozhnyuk, “Image denoising,” Tech. Rep. (NVIDIA, Inc., 2007).

NVIDIA CUDA Programming Guide (Version 3.0).

“Accelerating MATLAB with CUDA using MEX files” (White Paper), http://developer.nvidia.com/object/matlab cuda.html.

“GPU Acceleration in MATLAB,” http://arch.eece.maine.edu/superme/images/8/8c/Final report.pdf.

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 (12)

Fig. 1
Fig. 1

Fan-beam geometry and sinogram decomposition.

Fig. 2
Fig. 2

Illustration of sine curve decomposition.

Fig. 3
Fig. 3

Family of S-curves going though point ( β , γ ) in the sinogram.

Fig. 4
Fig. 4

Eigenvalue analysis of one patch P in the sinogram. β and γ characterize the projection view and the detector coordinate, respectively. e L ( β , γ ) and e S ( β , γ ) correspond to the direction of the largest and smallest intensity variation, respectively.

Fig. 5
Fig. 5

Inpainting process at one unmeasured point. (a) Original sinogram: the patch P is centered at the unmeasured point; (b) the family of S-curves going through the unmeasured point are fitted and interpolated using the fitting method and cubic spline interpolation; (c) the estimation of the central point is determined from the eigenvector-guided interpolation process.

Fig. 6
Fig. 6

Reconstruction of incomplete sinograms. (a) Original complete sinogram; (b) simulated sinogram with a sparse sampling: 90 projection views on 360 are available; (c) simulated sinogram containing two symmetric detector gaps: two 10-row detector gaps are located at each side of the center-of-detector; (d) image reconstructed from the complete sinogram in (a); (e) image reconstructed from the sparse sampling sinogram in (c); (f) image reconstructed from the sinogram including detector gaps in (d). We can note that the missing data from sparse sampling and detector gaps leads to degraded reconstructions with severe cyclic and streak artifacts.

Fig. 7
Fig. 7

Inpainting results in the experiment of sparse sampling after application of (a) the linear interpolation, (b) the TV inpainting method in [7], and (c) our proposed method; (a1)–(c1) the zoomed ROI from (a)–(c); (d1) the zoomed region from the original complete reference sinogram in Fig. 6a.

Fig. 8
Fig. 8

Reconstruction results in the experiment of sparse sampling (a)–(c) from the corresponding inpainted sinograms in Figs. 7a, 7b, 7c and (d) from the TV-based CS method. We can note that the proposed inpainting can lead to reconstruction with better artifact suppression and structure preservation than the other inpainting methods, and reconstruction comparable to the TV-based CS reconstruction can be obtained from the inpainted sinogram using the proposed method.

Fig. 9
Fig. 9

Illustration of the profiles along the 245th rows in the reconstructed images in Fig. 8.

Fig. 10
Fig. 10

Inpainting results in the experiment of symmetric detector gaps. Sinogram restoration using (a) the linear interpolation, (b) the TV inpainting method in [7], and (c) the proposed method; (a1)–(c1) the zoomed ROIs from (a)–(c); (d1) the zoomed region from the original complete reference sinogram in Fig. 6a.

Fig. 11
Fig. 11

Reconstruction results in the experiment of symmetric detector gaps (a)–(c) from the inpainted sinograms in Figs. 10a, 10b, 10c and (d) from the TV-based CS reconstruction. We can note that the proposed inpainting can lead to reconstruction [(c)] with better artifact suppression and structure preservation than other inpainting methods and the iterative CS reconstruction.

Fig. 12
Fig. 12

Illustration of the profiles along the 100th row in the reconstructed images in Fig. 11.

Tables (6)

Tables Icon

Table 1 Parameter Definitions for the 2D Fan-Beam CT Geometrya

Tables Icon

Table 2 Parameter Settings in the Experiments on Sparse Sampling Sinograms

Tables Icon

Table 3 MSE of the Inpainted Sinograms and Reconstructed Images of Figs. 7, 8, Respectively

Tables Icon

Table 4 Parameter Settings in the Experiments on Detector Gaps

Tables Icon

Table 5 MSE Calculations for the Inpainted Sinograms and Reconstructed Images in Figs. 11, 12

Tables Icon

Table 6 CPU Computation Costs (in CPU Seconds) for Different Methods

Equations (14)

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

y ( β ) = ( R cos β , R sin β ) T .
g ( β , γ ) = 0 + μ ( y ( β ) + t θ ) d t ,
| O P | = R sin γ , | O M | = | O N | = R v , θ m = arccos | O P | | O N | = R R v ( π 2 γ ) .
φ 0 = ( π / 2 β γ ) , φ 1 = ( φ 0 + θ m ) , φ 2 = ( φ 0 θ m ) .
sin ( β + γ φ ) = | O P | | O X | = R sin γ r φ r φ = R sin γ sin ( β + γ φ ) .
| O X | = | O X | cos ( β φ ) = r φ cos ( β φ ) | O X | = R | O X | | Q X | = Q X 2 + X X 2 } | Q X | = R r φ cos ( β φ ) | X X | = r φ sin ( β φ ) | Q X | = Q X 2 + X X 2 } | Q X | = Q X 2 + X X 2 = ( r φ sin ( β φ ) ) 2 + ( R r φ cos ( β φ ) ) 2 = r φ 2 + R 2 2 R r φ cos ( β φ ) .
sin γ = | X X | | Q X | = r φ sin ( β φ ) r φ 2 + R 2 2 R r φ cos ( β φ ) γ = arcsin r φ sin ( β φ ) r φ 2 + R 2 2 R r φ cos ( β φ ) .
S ( β , γ ) { ( β̑ , γ̑ ) | γ̑ = arcsin r φ sin ( β̑ φ ) r φ 2 + R 2 2 R r φ cos ( β̑ φ ) } ,
T = K ( P P T ) = K ( ( P ( x ) x P ( x ) y ) ( P ( x ) x P ( x ) y ) ) = K ( P ( x ) x P ( x ) x P ( x ) x P ( x ) y P ( x ) y P ( x ) x P ( x ) y P ( x ) y ) = ( T 11 T 1 2 T 2 1 T 22 ) ,
y = y e x e x + y k y e x e x k ,
μ ^ = arg max ( 1 2 ( g A μ ) T D ( g A μ ) + β U T V ( μ ) ) ,
U T V ( μ ) = j ( Δ j h μ ) 2 + ( Δ j v μ ) 2 + ε 2 ,
MSE g = 1 N g j ( g j g j o ) 2 ,
MSE μ = 1 N μ j ( μ j μ j o ) 2 ,

Metrics