Abstract

The 3D reconstruction of coronary artery from X-ray angiograms rotationally acquired on C-arm has great clinical value. While cardiac-gated reconstruction has shown promising results, it suffers from the problem of residual motion. This work proposed a new local motion-compensated reconstruction method to handle this issue. An initial image was firstly reconstructed using a regularized iterative reconstruction method. Then a 3D/2D registration method was proposed to estimate the residual vessel motion. Finally, the residual motion was compensated in the final reconstruction using the extended iterative reconstruction method. Through quantitative evaluation, it was found that high-quality 3D reconstruction could be obtained and the result was comparable to state-of-the-art method.

© 2016 Optical Society of America

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2016 (1)

S. Çimen, A. Gooya, M. Grass, and A. F. Frangi, “Reconstruction of Coronary Arteries from X-ray Angiography: A Review,” Med. Image Anal. 32, 46–68 (2016).
[Crossref] [PubMed]

2015 (2)

H. Guo, J. Yu, X. He, Y. Hou, F. Dong, and S. Zhang, “Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization,” Biomed. Opt. Express 6(5), 1648–1664 (2015).
[Crossref] [PubMed]

F. Yang, M. Ding, X. Zhang, W. Hou, and C. Zhong, “Non-rigid multi-modal medical image registration by combining L-BFGS-B with cat swarm optimization,” Inf. Sci. 316, 440–456 (2015).
[Crossref]

2014 (3)

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

G. Cao, B. Liu, H. Gong, H. Yu, and G. Wang, “A Stationary-Sources and Rotating-Detectors Computed Tomography Architecture for Higher Temporal Resolution and Lower Radiation Dose,” IEEE Access 2, 1263–1271 (2014).
[Crossref]

B. Liu, F. Zhou, and X. Bai, “Improved C-arm cardiac cone beam CT based on alternate reconstruction and segmentation,” Biomed. Signal Process. Control 13, 113–122 (2014).
[Crossref]

2013 (1)

C. Schwemmer, C. Rohkohl, G. Lauritsch, K. Müller, and J. Hornegger, “Residual motion compensation in ECG-gated interventional cardiac vasculature reconstruction,” Phys. Med. Biol. 58(11), 3717–3737 (2013).
[Crossref] [PubMed]

2012 (2)

T. Pengpan, W. Qiu, N. D. Smith, and M. Soleimani, “Cone Beam CT using motion-compensated algebraic reconstruction methods with limited data,” Comput. Methods Programs Biomed. 105(3), 246–256 (2012).
[Crossref] [PubMed]

M. F. Kraus, B. Potsaid, M. A. Mayer, R. Bock, B. Baumann, J. J. Liu, J. Hornegger, and J. G. Fujimoto, “Motion correction in optical coherence tomography volumes on a per A-scan basis using orthogonal scan patterns,” Biomed. Opt. Express 3(6), 1182–1199 (2012).
[Crossref] [PubMed]

2010 (4)

E. Hansis, J. D. Carroll, D. Schäfer, O. Dössel, and M. Grass, “High-quality 3-D coronary artery imaging on an interventional C-arm x-ray system,” Med. Phys. 37(4), 1601–1609 (2010).
[Crossref] [PubMed]

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

C. Rohkohl, G. Lauritsch, L. Biller, M. Prümmer, J. Boese, and J. Hornegger, “Interventional 4D motion estimation and reconstruction of cardiac vasculature without motion periodicity assumption,” Med. Image Anal. 14(5), 687–694 (2010).
[Crossref] [PubMed]

W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
[Crossref] [PubMed]

2009 (3)

G. Schoonenberg, A. Neubauer, and M. Grass, “Three-Dimensional Coronary Visualization, Part 2: 3D Reconstruction,” Cardiol. Clin. 27(3), 453–465 (2009).
[Crossref] [PubMed]

E. Hansis, H. Schomberg, K. Erhard, O. Dössel, and M. Grass, “Four-dimensional cardiac reconstruction from rotational x-ray sequences: first results for 4D coronary angiography,” Proc. SPIE 7258, 72580B (2009).

A. Keil, J. Vogel, G. Lauritsch, and N. Navab, “Dynamic cone beam reconstruction using a new level set formulation,” Med Image Comput Comput Assist Interv 12(2), 389–397 (2009).
[PubMed]

2008 (4)

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Projection-based motion compensation for gated coronary artery reconstruction from rotational x-ray angiograms,” Phys. Med. Biol. 53(14), 3807–3820 (2008).
[Crossref] [PubMed]

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27(11), 1548–1555 (2008).
[Crossref] [PubMed]

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman, “An image-based modeling framework for patient-specific computational hemodynamics,” Med. Biol. Eng. Comput. 46(11), 1097–1112 (2008).
[Crossref] [PubMed]

M. Chen, W. Lu, Q. Chen, K. J. Ruchala, and G. H. Olivera, “A simple fixed-point approach to invert a deformation field,” Med. Phys. 35(1), 81–88 (2008).
[Crossref] [PubMed]

2006 (2)

D. Schäfer, J. Borgert, V. Rasche, and M. Grass, “Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography,” IEEE Trans. Med. Imaging 25(7), 898–906 (2006).
[Crossref] [PubMed]

G. Shechter, J. R. Resar, and E. R. McVeigh, “Displacement and velocity of the coronary arteries: cardiac and respiratory motion,” IEEE Trans. Med. Imaging 25(3), 369–375 (2006).
[Crossref] [PubMed]

2004 (1)

M. Li, H. Kudo, J. Hu, and R. H. Johnson, “Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data,” IEEE Trans. Nucl. Sci. 51(3), 659–666 (2004).
[Crossref]

2003 (1)

T. Rohlfing, C. R. Maurer, D. A. Bluemke, and M. A. Jacobs, “Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint,” IEEE Trans. Med. Imaging 22(6), 730–741 (2003).
[Crossref] [PubMed]

2002 (1)

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47(15), 2599–2609 (2002).
[Crossref] [PubMed]

1999 (1)

D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18(8), 712–721 (1999).
[Crossref] [PubMed]

1994 (1)

J. J. Moré and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,” ACM Trans. Math. Softw. 20(3), 286–307 (1994).
[Crossref]

1989 (1)

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45(1-3), 503–528 (1989).
[Crossref]

1984 (1)

Antiga, L.

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman, “An image-based modeling framework for patient-specific computational hemodynamics,” Med. Biol. Eng. Comput. 46(11), 1097–1112 (2008).
[Crossref] [PubMed]

Bai, X.

B. Liu, F. Zhou, and X. Bai, “Improved C-arm cardiac cone beam CT based on alternate reconstruction and segmentation,” Biomed. Signal Process. Control 13, 113–122 (2014).
[Crossref]

Baumann, B.

Biller, L.

C. Rohkohl, G. Lauritsch, L. Biller, M. Prümmer, J. Boese, and J. Hornegger, “Interventional 4D motion estimation and reconstruction of cardiac vasculature without motion periodicity assumption,” Med. Image Anal. 14(5), 687–694 (2010).
[Crossref] [PubMed]

Bluemke, D. A.

T. Rohlfing, C. R. Maurer, D. A. Bluemke, and M. A. Jacobs, “Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint,” IEEE Trans. Med. Imaging 22(6), 730–741 (2003).
[Crossref] [PubMed]

Bock, R.

Boese, J.

C. Rohkohl, G. Lauritsch, L. Biller, M. Prümmer, J. Boese, and J. Hornegger, “Interventional 4D motion estimation and reconstruction of cardiac vasculature without motion periodicity assumption,” Med. Image Anal. 14(5), 687–694 (2010).
[Crossref] [PubMed]

Borgert, J.

D. Schäfer, J. Borgert, V. Rasche, and M. Grass, “Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography,” IEEE Trans. Med. Imaging 25(7), 898–906 (2006).
[Crossref] [PubMed]

Botti, L.

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman, “An image-based modeling framework for patient-specific computational hemodynamics,” Med. Biol. Eng. Comput. 46(11), 1097–1112 (2008).
[Crossref] [PubMed]

Cao, G.

G. Cao, B. Liu, H. Gong, H. Yu, and G. Wang, “A Stationary-Sources and Rotating-Detectors Computed Tomography Architecture for Higher Temporal Resolution and Lower Radiation Dose,” IEEE Access 2, 1263–1271 (2014).
[Crossref]

Carroll, J. D.

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

E. Hansis, J. D. Carroll, D. Schäfer, O. Dössel, and M. Grass, “High-quality 3-D coronary artery imaging on an interventional C-arm x-ray system,” Med. Phys. 37(4), 1601–1609 (2010).
[Crossref] [PubMed]

Chen, M.

M. Chen, W. Lu, Q. Chen, K. J. Ruchala, and G. H. Olivera, “A simple fixed-point approach to invert a deformation field,” Med. Phys. 35(1), 81–88 (2008).
[Crossref] [PubMed]

Chen, Q.

M. Chen, W. Lu, Q. Chen, K. J. Ruchala, and G. H. Olivera, “A simple fixed-point approach to invert a deformation field,” Med. Phys. 35(1), 81–88 (2008).
[Crossref] [PubMed]

Çimen, S.

S. Çimen, A. Gooya, M. Grass, and A. F. Frangi, “Reconstruction of Coronary Arteries from X-ray Angiography: A Review,” Med. Image Anal. 32, 46–68 (2016).
[Crossref] [PubMed]

Davis, L. C.

De Buck, S.

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

Ding, M.

F. Yang, M. Ding, X. Zhang, W. Hou, and C. Zhong, “Non-rigid multi-modal medical image registration by combining L-BFGS-B with cat swarm optimization,” Inf. Sci. 316, 440–456 (2015).
[Crossref]

Dong, F.

Dössel, O.

E. Hansis, J. D. Carroll, D. Schäfer, O. Dössel, and M. Grass, “High-quality 3-D coronary artery imaging on an interventional C-arm x-ray system,” Med. Phys. 37(4), 1601–1609 (2010).
[Crossref] [PubMed]

E. Hansis, H. Schomberg, K. Erhard, O. Dössel, and M. Grass, “Four-dimensional cardiac reconstruction from rotational x-ray sequences: first results for 4D coronary angiography,” Proc. SPIE 7258, 72580B (2009).

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27(11), 1548–1555 (2008).
[Crossref] [PubMed]

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Projection-based motion compensation for gated coronary artery reconstruction from rotational x-ray angiograms,” Phys. Med. Biol. 53(14), 3807–3820 (2008).
[Crossref] [PubMed]

Ene-Iordache, B.

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman, “An image-based modeling framework for patient-specific computational hemodynamics,” Med. Biol. Eng. Comput. 46(11), 1097–1112 (2008).
[Crossref] [PubMed]

Erhard, K.

E. Hansis, H. Schomberg, K. Erhard, O. Dössel, and M. Grass, “Four-dimensional cardiac reconstruction from rotational x-ray sequences: first results for 4D coronary angiography,” Proc. SPIE 7258, 72580B (2009).

Fahrig, R.

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

Feldkamp, L. A.

Frangi, A. F.

S. Çimen, A. Gooya, M. Grass, and A. F. Frangi, “Reconstruction of Coronary Arteries from X-ray Angiography: A Review,” Med. Image Anal. 32, 46–68 (2016).
[Crossref] [PubMed]

Fujimoto, J. G.

Garcia, J. A.

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

Gong, H.

G. Cao, B. Liu, H. Gong, H. Yu, and G. Wang, “A Stationary-Sources and Rotating-Detectors Computed Tomography Architecture for Higher Temporal Resolution and Lower Radiation Dose,” IEEE Access 2, 1263–1271 (2014).
[Crossref]

Gooya, A.

S. Çimen, A. Gooya, M. Grass, and A. F. Frangi, “Reconstruction of Coronary Arteries from X-ray Angiography: A Review,” Med. Image Anal. 32, 46–68 (2016).
[Crossref] [PubMed]

Grass, M.

S. Çimen, A. Gooya, M. Grass, and A. F. Frangi, “Reconstruction of Coronary Arteries from X-ray Angiography: A Review,” Med. Image Anal. 32, 46–68 (2016).
[Crossref] [PubMed]

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

E. Hansis, J. D. Carroll, D. Schäfer, O. Dössel, and M. Grass, “High-quality 3-D coronary artery imaging on an interventional C-arm x-ray system,” Med. Phys. 37(4), 1601–1609 (2010).
[Crossref] [PubMed]

G. Schoonenberg, A. Neubauer, and M. Grass, “Three-Dimensional Coronary Visualization, Part 2: 3D Reconstruction,” Cardiol. Clin. 27(3), 453–465 (2009).
[Crossref] [PubMed]

E. Hansis, H. Schomberg, K. Erhard, O. Dössel, and M. Grass, “Four-dimensional cardiac reconstruction from rotational x-ray sequences: first results for 4D coronary angiography,” Proc. SPIE 7258, 72580B (2009).

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27(11), 1548–1555 (2008).
[Crossref] [PubMed]

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Projection-based motion compensation for gated coronary artery reconstruction from rotational x-ray angiograms,” Phys. Med. Biol. 53(14), 3807–3820 (2008).
[Crossref] [PubMed]

D. Schäfer, J. Borgert, V. Rasche, and M. Grass, “Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography,” IEEE Trans. Med. Imaging 25(7), 898–906 (2006).
[Crossref] [PubMed]

Grimes, J.

W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
[Crossref] [PubMed]

Guo, H.

Hansis, E.

E. Hansis, J. D. Carroll, D. Schäfer, O. Dössel, and M. Grass, “High-quality 3-D coronary artery imaging on an interventional C-arm x-ray system,” Med. Phys. 37(4), 1601–1609 (2010).
[Crossref] [PubMed]

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

E. Hansis, H. Schomberg, K. Erhard, O. Dössel, and M. Grass, “Four-dimensional cardiac reconstruction from rotational x-ray sequences: first results for 4D coronary angiography,” Proc. SPIE 7258, 72580B (2009).

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27(11), 1548–1555 (2008).
[Crossref] [PubMed]

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Projection-based motion compensation for gated coronary artery reconstruction from rotational x-ray angiograms,” Phys. Med. Biol. 53(14), 3807–3820 (2008).
[Crossref] [PubMed]

Hawkes, D. J.

D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18(8), 712–721 (1999).
[Crossref] [PubMed]

Hayes, C.

D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18(8), 712–721 (1999).
[Crossref] [PubMed]

He, X.

Hill, D. L.

D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18(8), 712–721 (1999).
[Crossref] [PubMed]

Hornegger, J.

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

C. Schwemmer, C. Rohkohl, G. Lauritsch, K. Müller, and J. Hornegger, “Residual motion compensation in ECG-gated interventional cardiac vasculature reconstruction,” Phys. Med. Biol. 58(11), 3717–3737 (2013).
[Crossref] [PubMed]

M. F. Kraus, B. Potsaid, M. A. Mayer, R. Bock, B. Baumann, J. J. Liu, J. Hornegger, and J. G. Fujimoto, “Motion correction in optical coherence tomography volumes on a per A-scan basis using orthogonal scan patterns,” Biomed. Opt. Express 3(6), 1182–1199 (2012).
[Crossref] [PubMed]

C. Rohkohl, G. Lauritsch, L. Biller, M. Prümmer, J. Boese, and J. Hornegger, “Interventional 4D motion estimation and reconstruction of cardiac vasculature without motion periodicity assumption,” Med. Image Anal. 14(5), 687–694 (2010).
[Crossref] [PubMed]

Hou, W.

F. Yang, M. Ding, X. Zhang, W. Hou, and C. Zhong, “Non-rigid multi-modal medical image registration by combining L-BFGS-B with cat swarm optimization,” Inf. Sci. 316, 440–456 (2015).
[Crossref]

Hou, Y.

Hu, J.

M. Li, H. Kudo, J. Hu, and R. H. Johnson, “Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data,” IEEE Trans. Nucl. Sci. 51(3), 659–666 (2004).
[Crossref]

Jacobs, M. A.

T. Rohlfing, C. R. Maurer, D. A. Bluemke, and M. A. Jacobs, “Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint,” IEEE Trans. Med. Imaging 22(6), 730–741 (2003).
[Crossref] [PubMed]

Johnson, R. H.

M. Li, H. Kudo, J. Hu, and R. H. Johnson, “Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data,” IEEE Trans. Nucl. Sci. 51(3), 659–666 (2004).
[Crossref]

Keil, A.

A. Keil, J. Vogel, G. Lauritsch, and N. Navab, “Dynamic cone beam reconstruction using a new level set formulation,” Med Image Comput Comput Assist Interv 12(2), 389–397 (2009).
[PubMed]

Kim, M. S.

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

Klein, A. J.

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

Klein, S.

M. Staring and S. Klein, “Itk:Transforms supporting spatial derivatives,” Insight J. (2010).

Kraus, M. F.

Kress, J. W.

Kudo, H.

M. Li, H. Kudo, J. Hu, and R. H. Johnson, “Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data,” IEEE Trans. Nucl. Sci. 51(3), 659–666 (2004).
[Crossref]

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47(15), 2599–2609 (2002).
[Crossref] [PubMed]

Lauritsch, G.

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

C. Schwemmer, C. Rohkohl, G. Lauritsch, K. Müller, and J. Hornegger, “Residual motion compensation in ECG-gated interventional cardiac vasculature reconstruction,” Phys. Med. Biol. 58(11), 3717–3737 (2013).
[Crossref] [PubMed]

C. Rohkohl, G. Lauritsch, L. Biller, M. Prümmer, J. Boese, and J. Hornegger, “Interventional 4D motion estimation and reconstruction of cardiac vasculature without motion periodicity assumption,” Med. Image Anal. 14(5), 687–694 (2010).
[Crossref] [PubMed]

A. Keil, J. Vogel, G. Lauritsch, and N. Navab, “Dynamic cone beam reconstruction using a new level set formulation,” Med Image Comput Comput Assist Interv 12(2), 389–397 (2009).
[PubMed]

Leach, M. O.

D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18(8), 712–721 (1999).
[Crossref] [PubMed]

Li, M.

M. Li, H. Kudo, J. Hu, and R. H. Johnson, “Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data,” IEEE Trans. Nucl. Sci. 51(3), 659–666 (2004).
[Crossref]

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47(15), 2599–2609 (2002).
[Crossref] [PubMed]

Liu, B.

B. Liu, F. Zhou, and X. Bai, “Improved C-arm cardiac cone beam CT based on alternate reconstruction and segmentation,” Biomed. Signal Process. Control 13, 113–122 (2014).
[Crossref]

G. Cao, B. Liu, H. Gong, H. Yu, and G. Wang, “A Stationary-Sources and Rotating-Detectors Computed Tomography Architecture for Higher Temporal Resolution and Lower Radiation Dose,” IEEE Access 2, 1263–1271 (2014).
[Crossref]

Liu, D. C.

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45(1-3), 503–528 (1989).
[Crossref]

Liu, J. J.

Lu, W.

M. Chen, W. Lu, Q. Chen, K. J. Ruchala, and G. H. Olivera, “A simple fixed-point approach to invert a deformation field,” Med. Phys. 35(1), 81–88 (2008).
[Crossref] [PubMed]

Maier, A. K.

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

Maurer, C. R.

T. Rohlfing, C. R. Maurer, D. A. Bluemke, and M. A. Jacobs, “Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint,” IEEE Trans. Med. Imaging 22(6), 730–741 (2003).
[Crossref] [PubMed]

Mayer, M. A.

McVeigh, E. R.

G. Shechter, J. R. Resar, and E. R. McVeigh, “Displacement and velocity of the coronary arteries: cardiac and respiratory motion,” IEEE Trans. Med. Imaging 25(3), 369–375 (2006).
[Crossref] [PubMed]

Mendonca, S.

W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
[Crossref] [PubMed]

Messenger, J. C.

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

Moré, J. J.

J. J. Moré and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,” ACM Trans. Math. Softw. 20(3), 286–307 (1994).
[Crossref]

Müller, K.

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

C. Schwemmer, C. Rohkohl, G. Lauritsch, K. Müller, and J. Hornegger, “Residual motion compensation in ECG-gated interventional cardiac vasculature reconstruction,” Phys. Med. Biol. 58(11), 3717–3737 (2013).
[Crossref] [PubMed]

Navab, N.

A. Keil, J. Vogel, G. Lauritsch, and N. Navab, “Dynamic cone beam reconstruction using a new level set formulation,” Med Image Comput Comput Assist Interv 12(2), 389–397 (2009).
[PubMed]

Neubauer, A.

G. Schoonenberg, A. Neubauer, and M. Grass, “Three-Dimensional Coronary Visualization, Part 2: 3D Reconstruction,” Cardiol. Clin. 27(3), 453–465 (2009).
[Crossref] [PubMed]

Neubauer, A. M.

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

Nocedal, J.

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45(1-3), 503–528 (1989).
[Crossref]

Olivera, G. H.

M. Chen, W. Lu, Q. Chen, K. J. Ruchala, and G. H. Olivera, “A simple fixed-point approach to invert a deformation field,” Med. Phys. 35(1), 81–88 (2008).
[Crossref] [PubMed]

Pengpan, T.

T. Pengpan, W. Qiu, N. D. Smith, and M. Soleimani, “Cone Beam CT using motion-compensated algebraic reconstruction methods with limited data,” Comput. Methods Programs Biomed. 105(3), 246–256 (2012).
[Crossref] [PubMed]

Piccinelli, M.

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman, “An image-based modeling framework for patient-specific computational hemodynamics,” Med. Biol. Eng. Comput. 46(11), 1097–1112 (2008).
[Crossref] [PubMed]

Potsaid, B.

Prümmer, M.

C. Rohkohl, G. Lauritsch, L. Biller, M. Prümmer, J. Boese, and J. Hornegger, “Interventional 4D motion estimation and reconstruction of cardiac vasculature without motion periodicity assumption,” Med. Image Anal. 14(5), 687–694 (2010).
[Crossref] [PubMed]

Qiu, W.

T. Pengpan, W. Qiu, N. D. Smith, and M. Soleimani, “Cone Beam CT using motion-compensated algebraic reconstruction methods with limited data,” Comput. Methods Programs Biomed. 105(3), 246–256 (2012).
[Crossref] [PubMed]

Rasche, V.

D. Schäfer, J. Borgert, V. Rasche, and M. Grass, “Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography,” IEEE Trans. Med. Imaging 25(7), 898–906 (2006).
[Crossref] [PubMed]

Remuzzi, A.

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman, “An image-based modeling framework for patient-specific computational hemodynamics,” Med. Biol. Eng. Comput. 46(11), 1097–1112 (2008).
[Crossref] [PubMed]

Resar, J. R.

G. Shechter, J. R. Resar, and E. R. McVeigh, “Displacement and velocity of the coronary arteries: cardiac and respiratory motion,” IEEE Trans. Med. Imaging 25(3), 369–375 (2006).
[Crossref] [PubMed]

Rohkohl, C.

C. Schwemmer, C. Rohkohl, G. Lauritsch, K. Müller, and J. Hornegger, “Residual motion compensation in ECG-gated interventional cardiac vasculature reconstruction,” Phys. Med. Biol. 58(11), 3717–3737 (2013).
[Crossref] [PubMed]

C. Rohkohl, G. Lauritsch, L. Biller, M. Prümmer, J. Boese, and J. Hornegger, “Interventional 4D motion estimation and reconstruction of cardiac vasculature without motion periodicity assumption,” Med. Image Anal. 14(5), 687–694 (2010).
[Crossref] [PubMed]

Rohlfing, T.

T. Rohlfing, C. R. Maurer, D. A. Bluemke, and M. A. Jacobs, “Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint,” IEEE Trans. Med. Imaging 22(6), 730–741 (2003).
[Crossref] [PubMed]

Ruchala, K. J.

M. Chen, W. Lu, Q. Chen, K. J. Ruchala, and G. H. Olivera, “A simple fixed-point approach to invert a deformation field,” Med. Phys. 35(1), 81–88 (2008).
[Crossref] [PubMed]

Rueckert, D.

D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18(8), 712–721 (1999).
[Crossref] [PubMed]

Schäfer, D.

E. Hansis, J. D. Carroll, D. Schäfer, O. Dössel, and M. Grass, “High-quality 3-D coronary artery imaging on an interventional C-arm x-ray system,” Med. Phys. 37(4), 1601–1609 (2010).
[Crossref] [PubMed]

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27(11), 1548–1555 (2008).
[Crossref] [PubMed]

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Projection-based motion compensation for gated coronary artery reconstruction from rotational x-ray angiograms,” Phys. Med. Biol. 53(14), 3807–3820 (2008).
[Crossref] [PubMed]

D. Schäfer, J. Borgert, V. Rasche, and M. Grass, “Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography,” IEEE Trans. Med. Imaging 25(7), 898–906 (2006).
[Crossref] [PubMed]

Schomberg, H.

E. Hansis, H. Schomberg, K. Erhard, O. Dössel, and M. Grass, “Four-dimensional cardiac reconstruction from rotational x-ray sequences: first results for 4D coronary angiography,” Proc. SPIE 7258, 72580B (2009).

Schoonenberg, G.

G. Schoonenberg, A. Neubauer, and M. Grass, “Three-Dimensional Coronary Visualization, Part 2: 3D Reconstruction,” Cardiol. Clin. 27(3), 453–465 (2009).
[Crossref] [PubMed]

Schoonenberg, G. A.

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

Schwemmer, C.

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

C. Schwemmer, C. Rohkohl, G. Lauritsch, K. Müller, and J. Hornegger, “Residual motion compensation in ECG-gated interventional cardiac vasculature reconstruction,” Phys. Med. Biol. 58(11), 3717–3737 (2013).
[Crossref] [PubMed]

Segars, W. P.

W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
[Crossref] [PubMed]

Shechter, G.

G. Shechter, J. R. Resar, and E. R. McVeigh, “Displacement and velocity of the coronary arteries: cardiac and respiratory motion,” IEEE Trans. Med. Imaging 25(3), 369–375 (2006).
[Crossref] [PubMed]

Smith, N. D.

T. Pengpan, W. Qiu, N. D. Smith, and M. Soleimani, “Cone Beam CT using motion-compensated algebraic reconstruction methods with limited data,” Comput. Methods Programs Biomed. 105(3), 246–256 (2012).
[Crossref] [PubMed]

Soleimani, M.

T. Pengpan, W. Qiu, N. D. Smith, and M. Soleimani, “Cone Beam CT using motion-compensated algebraic reconstruction methods with limited data,” Comput. Methods Programs Biomed. 105(3), 246–256 (2012).
[Crossref] [PubMed]

Sonoda, L. I.

D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18(8), 712–721 (1999).
[Crossref] [PubMed]

Staring, M.

M. Staring and S. Klein, “Itk:Transforms supporting spatial derivatives,” Insight J. (2010).

Steinman, D. A.

L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman, “An image-based modeling framework for patient-specific computational hemodynamics,” Med. Biol. Eng. Comput. 46(11), 1097–1112 (2008).
[Crossref] [PubMed]

Sturgeon, G.

W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
[Crossref] [PubMed]

Thuente, D. J.

J. J. Moré and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,” ACM Trans. Math. Softw. 20(3), 286–307 (1994).
[Crossref]

Tsui, B. M.

W. P. Segars, G. Sturgeon, S. Mendonca, J. Grimes, and B. M. Tsui, “4D XCAT phantom for multimodality imaging research,” Med. Phys. 37(9), 4902–4915 (2010).
[Crossref] [PubMed]

Vogel, J.

A. Keil, J. Vogel, G. Lauritsch, and N. Navab, “Dynamic cone beam reconstruction using a new level set formulation,” Med Image Comput Comput Assist Interv 12(2), 389–397 (2009).
[PubMed]

Wang, G.

G. Cao, B. Liu, H. Gong, H. Yu, and G. Wang, “A Stationary-Sources and Rotating-Detectors Computed Tomography Architecture for Higher Temporal Resolution and Lower Radiation Dose,” IEEE Access 2, 1263–1271 (2014).
[Crossref]

Wielandts, J. Y.

K. Müller, A. K. Maier, C. Schwemmer, G. Lauritsch, S. De Buck, J. Y. Wielandts, J. Hornegger, and R. Fahrig, “Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT,” Phys. Med. Biol. 59(12), 3121–3138 (2014).
[Crossref] [PubMed]

Yang, F.

F. Yang, M. Ding, X. Zhang, W. Hou, and C. Zhong, “Non-rigid multi-modal medical image registration by combining L-BFGS-B with cat swarm optimization,” Inf. Sci. 316, 440–456 (2015).
[Crossref]

Yang, H.

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47(15), 2599–2609 (2002).
[Crossref] [PubMed]

Yu, H.

G. Cao, B. Liu, H. Gong, H. Yu, and G. Wang, “A Stationary-Sources and Rotating-Detectors Computed Tomography Architecture for Higher Temporal Resolution and Lower Radiation Dose,” IEEE Access 2, 1263–1271 (2014).
[Crossref]

Yu, J.

Zhang, S.

Zhang, X.

F. Yang, M. Ding, X. Zhang, W. Hou, and C. Zhong, “Non-rigid multi-modal medical image registration by combining L-BFGS-B with cat swarm optimization,” Inf. Sci. 316, 440–456 (2015).
[Crossref]

Zhong, C.

F. Yang, M. Ding, X. Zhang, W. Hou, and C. Zhong, “Non-rigid multi-modal medical image registration by combining L-BFGS-B with cat swarm optimization,” Inf. Sci. 316, 440–456 (2015).
[Crossref]

Zhou, F.

B. Liu, F. Zhou, and X. Bai, “Improved C-arm cardiac cone beam CT based on alternate reconstruction and segmentation,” Biomed. Signal Process. Control 13, 113–122 (2014).
[Crossref]

ACM Trans. Math. Softw. (1)

J. J. Moré and D. J. Thuente, “Line search algorithms with guaranteed sufficient decrease,” ACM Trans. Math. Softw. 20(3), 286–307 (1994).
[Crossref]

Biomed. Opt. Express (2)

Biomed. Signal Process. Control (1)

B. Liu, F. Zhou, and X. Bai, “Improved C-arm cardiac cone beam CT based on alternate reconstruction and segmentation,” Biomed. Signal Process. Control 13, 113–122 (2014).
[Crossref]

Cardiol. Clin. (1)

G. Schoonenberg, A. Neubauer, and M. Grass, “Three-Dimensional Coronary Visualization, Part 2: 3D Reconstruction,” Cardiol. Clin. 27(3), 453–465 (2009).
[Crossref] [PubMed]

Circ. Cardiovasc. Interv. (1)

A. M. Neubauer, J. A. Garcia, J. C. Messenger, E. Hansis, M. S. Kim, A. J. Klein, G. A. Schoonenberg, M. Grass, and J. D. Carroll, “Clinical feasibility of a fully automated 3D reconstruction of rotational coronary X-ray angiograms,” Circ. Cardiovasc. Interv. 3(1), 71–79 (2010).
[Crossref] [PubMed]

Comput. Methods Programs Biomed. (1)

T. Pengpan, W. Qiu, N. D. Smith, and M. Soleimani, “Cone Beam CT using motion-compensated algebraic reconstruction methods with limited data,” Comput. Methods Programs Biomed. 105(3), 246–256 (2012).
[Crossref] [PubMed]

IEEE Access (1)

G. Cao, B. Liu, H. Gong, H. Yu, and G. Wang, “A Stationary-Sources and Rotating-Detectors Computed Tomography Architecture for Higher Temporal Resolution and Lower Radiation Dose,” IEEE Access 2, 1263–1271 (2014).
[Crossref]

IEEE Trans. Med. Imaging (5)

E. Hansis, D. Schäfer, O. Dössel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27(11), 1548–1555 (2008).
[Crossref] [PubMed]

D. Schäfer, J. Borgert, V. Rasche, and M. Grass, “Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography,” IEEE Trans. Med. Imaging 25(7), 898–906 (2006).
[Crossref] [PubMed]

G. Shechter, J. R. Resar, and E. R. McVeigh, “Displacement and velocity of the coronary arteries: cardiac and respiratory motion,” IEEE Trans. Med. Imaging 25(3), 369–375 (2006).
[Crossref] [PubMed]

D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18(8), 712–721 (1999).
[Crossref] [PubMed]

T. Rohlfing, C. R. Maurer, D. A. Bluemke, and M. A. Jacobs, “Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint,” IEEE Trans. Med. Imaging 22(6), 730–741 (2003).
[Crossref] [PubMed]

IEEE Trans. Nucl. Sci. (1)

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Med Image Comput Comput Assist Interv (1)

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Other (6)

H. Wu, C. Rohkohl, and J. Hornegger, “Total Variation Regularization Method for 3D Rotational Coronary Angiography,” in Bildverarbeitung für die Medizin 2011, H. Handels, J. Ehrhardt, T. M. Deserno, H.-P. Meinzer, and T. Tolxdorff, eds. (Springer Berlin Heidelberg, 2011), pp. 434–438.

H. Yining, X. Lizhe, J. C. Nunes, J. J. Bellanger, M. Bedossa, and C. Toumoulin, “ECG gated tomographic reconstruction for 3-D rotational coronary angiography,” in Engineering in Medicine and Biology Society (EMBC),2010Annual International Conference of the IEEE, 2010), 3614–3617.
[Crossref]

C. Rohkohl, G. Lauritsch, A. Nottling, M. Prummer, and J. Hornegger, “C-arm CT: Reconstruction of dynamic high contrast objects applied to the coronary sinus,” in Nuclear Science Symposium Conference Record,2008. NSS '08. IEEE, 2008), 5113–5120.
[Crossref]

C. Schwemmer, G. Lauritsch, A. Kleinfeld, C. Rohkohl, K. Müller, and J. Hornegger, “Clinical Data Evaluation of C-arm-based Motion Compensated Coronary Artery Reconstruction,” in The third international conference on image formation in X-ray computed tomography(2014), pp. 60–63.

C. Rohkohl, G. Lauritsch, L. Biller, and J. Hornegger, “ECG-Gated Interventional Cardiac Reconstruction for Non-periodic Motion,” in Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010 (Springer Berlin / Heidelberg, 2010), pp. 151–158.

M. Staring and S. Klein, “Itk:Transforms supporting spatial derivatives,” Insight J. (2010).

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Figures (11)

Fig. 1
Fig. 1

The flowchart of the proposed method.

Fig. 2
Fig. 2

The main steps of the reconstruction iteration with motion compensation.

Fig. 3
Fig. 3

(a) 3D vessel morphology at different cardiac phases: 0% (white), 40% (red), 70% (green), and 90% (blue); (b) the vessel centerlines used for quantitative evaluation.

Fig. 4
Fig. 4

The cardiac phase of the simulated angiograms and the chosen angiograms using NN gating (red circled) and FW gating (green circled, window width = 10%) for cardiac phase 90%.

Fig. 5
Fig. 5

The volume rendering of the initial and motion-compensated reconstructions of the proposed method (using NN gating) under different magnitudes of residual motion: (a) no residual motion; (b) 1 × ; (c) 2 × ; (d) 3 × . The top row of (b-d) show the initial reconstructions; the bottom row of (b-d) show the motion-compensated reconstructions.

Fig. 6
Fig. 6

The registration iteration information for angiograms with different magnitude of residual motion. (a) 1 × ; (b) 3 × . The iterations in different registration resolution is represented using different markers.

Fig. 7
Fig. 7

Chessboard display of the angiogram and reprojection of the initial reconstruction for the data with 3 × motion before the registration (the first row) and after the registration (the second row).

Fig. 8
Fig. 8

Quantitative metrics for different reconstructions. Initial: the initial reconstruction; MCnn and MCfw: the motion-compensated reconstruction of the proposed method using NN gating and using a finite gating width of 10% respectively.

Fig. 9
Fig. 9

(a): one original angiograms; (b): the corresponding reprojection of the initial reconstruction; (c) and (d): the reprojection of the registration results with ( β 1 = 1 β 2 = 0.1) and without imposing constraints; (e) and (f): the obtained motion fields near the vessel surface with and without imposing constraints

Fig. 10
Fig. 10

Quantitative metrics for different reconstructions. Initialproposed and MCproposed: the initial and the motion-compensated reconstruction of the proposed method respectively; Initial2D&FDK: the initial reconstruction of the MC2D&FDK method; MC2D&FDK-FirstIter and MC2D&FDK-SecondIter: the results of MC2D&FDK after first and second iteration of motion compensation respectively

Fig. 11
Fig. 11

The volume rendering of the gated and motion-compensated reconstruction of the MC2D&FDK method under different magnitude of residual motion: (a) no residual motion; (b) 1 × ; (c) 2 × ; (d) 3 × . The top row of (b-d) shows the initial reconstructions; the middle row of (b-d) shows the results after first iteration of motion-compensation; the bottom row of (b-d) shows the results after second iteration

Tables (3)

Tables Icon

Table 1 Comparison of the metric values for reconstructions using different constraint weights. For comparison, the MMO and RRE for the initial reconstruction are also shown

Tables Icon

Table 2 Comparison of the metric values for different reconstruction. Ideal: reconstruction using data without residual motion; Initial: initial reconstruction; MC: motion-compensated reconstruction

Tables Icon

Table 3 Reconstruction time (minutes)

Equations (10)

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argmin X R N X 1 s.t.X0,AX=b
T(X,D)=X+ l=0 3 m=0 3 n=0 3 B l (u) B m (v) B n (w) d i+l,j+m,k+n
D * =arg max D M( A i , P i I(T(X,D)))
argmin D E(D)= E similarity (D)+ β 1 E smooth (D)+ β 2 E volume (D)
NC( A i , A i p )=NC( A i , P i I( X ' ))=NC( A i , P i I(T(X,D)))
NC d = T d I X' P i T NC A i p
ROI={x|dist(x,vessel)d}
χ k+1 = χ k +α V 1 A T W 1 ( b i A X k )
X k+1 =H( χ k+1 )
χ k+1 = χ k +αT( V 1 A T W ^ 1 ( b i AT( X k , D i )), D i 1 )

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