Fast Gated PET Direct Motion Estimation Using Ordered Subsets

Alexandre Bousse, Brian F. Hutton, Kris Thielemans

DOI:10.12059/Fully3D.2017-11-3202020

Published in:Fully3D 2017 Proceedings

Pages:150-153

Keywords:
motion-compensated PET reconstruction, ordered subsets, maximum-likelihood, direct motion estimation
Direct motion compensation in gated PET can be achieved with maximum-likelihood (ML) joint activity reconstruction/motion estimation (JRM). Whereas the motion-compensated (MC) activity image can be efficiently updated with ordered subsets (OS) expectation maximisation (EM), the motion optimisation suffers from high computational cost due to the utilisation of line-search algorithms, which require to perform projections/backprojections each time the likelihood and its gradient are evaluated. The idea of this work is to use OS to speed-up the estimation of the motion parameters, by maximising each sub-likelihood sequentially. We show that the utilisation of OS significantly reduces the overall joint-estimation computational cost with negligible effect on the final solution.
Alexandre Bousse
University College London, United Kingdom
Brian F. Hutton
University College London, United Kingdom
Kris Thielemans
University College London, United Kingdom
  1. M. W. Jacobson and J. A. Fessler, “Joint estimation of image and deformation parameters in motion-corrected PET,” in IEEE Nucl. Sci. Symp. Conf. Rec., 2003, pp. 3290–3294. 
  2. M. W. Jacobson, “Approaches to motion-corrected PET image reconstruction from respiratory gated projection data,” PhD thesis, The University of Michigan, Ann Arbor, USA, 2006. 
  3. M. Blume, A. Martinez-M¨uller, A. Keil, N. Navab, and M. Rafecas, “Joint reconstruction of image and motion in gated positron emission tomography,” IEEE Trans. Med. Imag., vol. 29, no. 11, pp. 1892–1906, 2010. 
  4. G. Wang and J. Qi, “A monotonic image-space algorithm for joint PET image reconstruction and motion estimation,” in IEEE Nucl. Sci. Symp. Med. Imag. Conf. Rec., 2015. 
  5. A. Bousse, O. Bertolli, D. Atkinson, S. Arridge, S. Ourselin, B. F. Hutton, and K. Thielemans, “Maximum-likelihood joint image reconstruction/motion estimation in attenuationcorrected respiratory gated PET/CT using a single attenuation map,” IEEE Trans. Med. Imag., vol. 35, no. 1, pp. 217–228, 2016. 
  6. M. Dawood, T. K¨osters, M. Fieseler, F. B¨uther, X. Jiang, F. W¨ubbeling, and K. P. Sch¨afers, “Motion correction in respiratory gated cardiac PET/CT using multi-scale optical flow,” Med. Image Comput. Comput. Assist Interv., vol. 11, no. 2, pp. 155–162, 2008. 
  7. F. Qiao, T. Pan, J. W. Clark, and O. R. Mawlawi, “A motionincorporated reconstruction method for gated PET studies,” Phys. Med. Biol., vol. 51, pp. 3769–3783, 2006. 
  8. R. Manber, K. Thielemans, B. F. Hutton, A. Barnes, S. Ourselin, S. Arridge, C. O’Meara, S. Wan, and D. Atkinson, “Practical PET respiratory motion correction in clinical PET/MR,” J. Nucl. Med., vol. 56, no. 6, pp. 1–6, 2015.
  9. L. A. Shepp and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag., vol. 1, no. 2, pp. 113–122, 1982. 
  10. K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comput. Assist. Tomogr., vol. 8, no. 2, pp. 306–316, 1984. 
  11. H. M. Hudson and R. S. Larkin, “A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography.,” IEEE Trans. Med. Imag., vol. 13, no. 4, pp. 601–609, 1994. 
  12. Y. Otani, I. Fukuda, N. Tsukamoto, Y. Kumazaki, H. Sekine, E. Imabayashi, O. Kawaguchi, T. Nose, T. Teshima, and T. Dokiya, “A comparison of the respiratory signals acquired by different respiratory monitoring systems used in respiratory gated radiotherapy,” Med. Phys., vol. 37, no. 2, pp. 6178– 6186, 2010. 
  13. K. Thielemans, S. Rathore, F. Engbrant, and P. Razifar, “Device-less gating for PET/CT using PCA,” in IEEE Nucl. Sci. Symp. Med. Imag. Conf. Rec., 2011, pp. 3904–3910. 
  14. J. Xu and B. M. W. Tsui, “Improved intrinsic motion detection using time-of-flight PET,” IEEE Trans. Med. Imag., vol. 34, no. 10, pp. 2131–2145, 2015. 
  15. J. Jiao, A. Bousse, K. Thielemans, N. Burgos, P. Weston, P. Markiewicz, J. Schott, D. Atkinson, S. Arridge, B. F. Hutton, and S. Ourselin, “Direct parametric reconstruction with joint motion estimation/correction for dynamic brain PET data,” IEEE Trans. Med. Imag., vol. 36, no. 1, pp. 203–213, 2017. 
  16. R. H. Byrd, P. Lu, and J. Nocedal, “A limited memory algorithm for bound constrained optimization,” SIAM J. Sci. Stat. Comp., vol. 16, no. 5, pp. 1190–1208, 1995. 
  17. A. Bousse, O. Bertolli, D. Atkinson, S. Arridge, S. Ourselin, B. F. Hutton, and K. Thielemans, “Maximum-likelihood joint image reconstruction and motion estimation with misaligned attenuation in TOF-PET/CT,” Phys. Med. Biol., vol. 61, no. 3, pp. L11–19, 2016.