Abstract

As a consequence of the random nature of photon emissions and detections, the data collected by a positron emission tomography (PET) imaging system can be shown to be Poisson distributed. Meanwhile, there have been considerable efforts within the tracer kinetic modeling communities aimed at establishing the relationship between the PET data and physiological parameters that affect the uptake and metabolism of the tracer. Both statistical and physiological models are important to PET reconstruction. The majority of previous efforts are based on simplified, nonphysical mathematical expression, such as Poisson modeling of the measured data, which is, on the whole, completed without consideration of the underlying physiology. In this paper, we proposed a graphics processing unit (GPU)-accelerated reconstruction strategy that can take both statistical model and physiological model into consideration with the aid of state-space evolution equations. The proposed strategy formulates the organ activity distribution through tracer kinetics models and the photon-counting measurements through observation equations, thus making it possible to unify these two constraints into a general framework. In order to accelerate reconstruction, GPU-based parallel computing is introduced. Experiments of Zubal-thorax-phantom data, Monte Carlo simulated phantom data, and real phantom data show the power of the method. Furthermore, thanks to the computing power of the GPU, the reconstruction time is practical for clinical application.

© 2012 Optical Society of America

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References

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  1. J. Ollinger and J. Fessler, “Positron-emission tomography,” IEEE Signal Process. Mag. 14 (1), 43–55 (1997).
    [CrossRef]
  2. P. P. Mondal, K. Rajan, and I. Ahmad, “Filter for biomedical imaging and image processing,” J. Opt. Soc. Am. A 23, 1678–1686 (2006).
    [CrossRef]
  3. P. P. Mondal and K. Rajan, “Fuzzy-rule-based image reconstruction for positron emission tomography,” J. Opt. Soc. Am. A 22, 1763–1771 (2005).
    [CrossRef]
  4. L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. 1, 113–122 (1982).
    [CrossRef]
  5. J. Nuyts, C. Michel, and P. Dupont, “Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations,” IEEE Trans. Med. Imag. 20, 365–375 (2001).
    [CrossRef]
  6. H. Wieczorek, “The image quality of FBP and MLEM reconstruction,” Phys. Med. Biol. 55, 3161–3176 (2010).
    [CrossRef]
  7. G. Wang and J. Qi, “Analysis of penalized likelihood image reconstruction for dynamic PET quantification,” IEEE Trans. Med. Imag. 28, 608–620 (2009).
    [CrossRef]
  8. C. Comtat, P. Kinahan, M. Defrise, C. Michel, and D. Townsend, “Fast reconstruction of 3D PET data with accurate statistical modeling,” IEEE Trans. Nucl. Sci. 45, 1083–1089 (1998).
    [CrossRef]
  9. R. Leahy and J. Qi “Statistical approaches in quantitative positron emission tomography,” Stat. Comput. 10, 147–165 (2000).
    [CrossRef]
  10. R. M. Lewitt and S. Matej, “Overview of methods for image reconstruction from projections in emission computed tomography,” Proc. IEEE 91, 1588–1611 (2003).
    [CrossRef]
  11. R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
    [CrossRef]
  12. E. Carson and C. Cobelli, Modelling Methodology for Physiology and Medicine (Academic, 2001).
  13. F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
    [CrossRef]
  14. S. Tong, A. M. Alessio, P. E. Kinahan, H. Liu, and P. Shi, “A robust state-space kinetics-guided framework for dynamic PET image reconstruction,” Phys. Med. Biol. 56, 2481–2498 (2011).
    [CrossRef]
  15. S. Tong and P. Shi, “Tracer kinetics guided dynamic PET reconstruction,” Information Process in Medical Imaging (2007), pp. 421–433.
  16. M. Phelps, PET: Molecular Imaging and Its Biological Applications (Springer, 2004).
  17. R. Gunn, S. Gunn, F. Turkheimer, J. Aston, and V. Cunningham, “Tracer kinetic modeling via basis pursuit,” in Brain Imaging Using PET, M. Senda, ed. (Academic, 2002), pp. 115–121.
  18. A. Doucet, “On sequential simulation-based methods for Bayesian filtering,” Tech. rep. CUED/F-INFENG/TR. 310 (Cambridge University Department of Engineering, 1998).
  19. F. Kemp, “An introduction to sequential Monte Carlo methods,” J. Roy. Stat. Soc. 52, 694–695 (2003).
    [CrossRef]
  20. M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50, 174–188 (2002).
    [CrossRef]
  21. A. F. M. Smith and A. E. Gelfand“ Bayesian statistics without tears: a sampling–resampling perspective,” Amer. Stat. 46, 84–88 (1992).
    [CrossRef]
  22. V.V. Selivanov, Y. Picard, J. Cadorette, S. Rodrigue, and R. Lecomte, “Detector response models for statistical iterative image reconstruction in high resolution PET,” IEEE Trans. Nucl. Sci. 47, 1168–1175 (2000).
    [CrossRef]
  23. K.R. Muzic and S. Cornelius, “COMKAT: compartment model kinetic analysis tool,” J. Nucl. Med. 42, 636–645 (2001).

2011 (1)

S. Tong, A. M. Alessio, P. E. Kinahan, H. Liu, and P. Shi, “A robust state-space kinetics-guided framework for dynamic PET image reconstruction,” Phys. Med. Biol. 56, 2481–2498 (2011).
[CrossRef]

2010 (2)

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

H. Wieczorek, “The image quality of FBP and MLEM reconstruction,” Phys. Med. Biol. 55, 3161–3176 (2010).
[CrossRef]

2009 (1)

G. Wang and J. Qi, “Analysis of penalized likelihood image reconstruction for dynamic PET quantification,” IEEE Trans. Med. Imag. 28, 608–620 (2009).
[CrossRef]

2008 (1)

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

2006 (1)

2005 (1)

2003 (2)

R. M. Lewitt and S. Matej, “Overview of methods for image reconstruction from projections in emission computed tomography,” Proc. IEEE 91, 1588–1611 (2003).
[CrossRef]

F. Kemp, “An introduction to sequential Monte Carlo methods,” J. Roy. Stat. Soc. 52, 694–695 (2003).
[CrossRef]

2002 (1)

M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50, 174–188 (2002).
[CrossRef]

2001 (2)

K.R. Muzic and S. Cornelius, “COMKAT: compartment model kinetic analysis tool,” J. Nucl. Med. 42, 636–645 (2001).

J. Nuyts, C. Michel, and P. Dupont, “Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations,” IEEE Trans. Med. Imag. 20, 365–375 (2001).
[CrossRef]

2000 (2)

R. Leahy and J. Qi “Statistical approaches in quantitative positron emission tomography,” Stat. Comput. 10, 147–165 (2000).
[CrossRef]

V.V. Selivanov, Y. Picard, J. Cadorette, S. Rodrigue, and R. Lecomte, “Detector response models for statistical iterative image reconstruction in high resolution PET,” IEEE Trans. Nucl. Sci. 47, 1168–1175 (2000).
[CrossRef]

1998 (1)

C. Comtat, P. Kinahan, M. Defrise, C. Michel, and D. Townsend, “Fast reconstruction of 3D PET data with accurate statistical modeling,” IEEE Trans. Nucl. Sci. 45, 1083–1089 (1998).
[CrossRef]

1997 (1)

J. Ollinger and J. Fessler, “Positron-emission tomography,” IEEE Signal Process. Mag. 14 (1), 43–55 (1997).
[CrossRef]

1992 (1)

A. F. M. Smith and A. E. Gelfand“ Bayesian statistics without tears: a sampling–resampling perspective,” Amer. Stat. 46, 84–88 (1992).
[CrossRef]

1982 (1)

L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. 1, 113–122 (1982).
[CrossRef]

Ahmad, I.

Alessio, A. M.

S. Tong, A. M. Alessio, P. E. Kinahan, H. Liu, and P. Shi, “A robust state-space kinetics-guided framework for dynamic PET image reconstruction,” Phys. Med. Biol. 56, 2481–2498 (2011).
[CrossRef]

Arulampalam, M.

M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50, 174–188 (2002).
[CrossRef]

Aston, J.

R. Gunn, S. Gunn, F. Turkheimer, J. Aston, and V. Cunningham, “Tracer kinetic modeling via basis pursuit,” in Brain Imaging Using PET, M. Senda, ed. (Academic, 2002), pp. 115–121.

Boisgard, R.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Cadorette, J.

V.V. Selivanov, Y. Picard, J. Cadorette, S. Rodrigue, and R. Lecomte, “Detector response models for statistical iterative image reconstruction in high resolution PET,” IEEE Trans. Nucl. Sci. 47, 1168–1175 (2000).
[CrossRef]

Carson, E.

E. Carson and C. Cobelli, Modelling Methodology for Physiology and Medicine (Academic, 2001).

Cathier, P.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Clapp, T.

M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50, 174–188 (2002).
[CrossRef]

Cobelli, C.

E. Carson and C. Cobelli, Modelling Methodology for Physiology and Medicine (Academic, 2001).

Comtat, C.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

C. Comtat, P. Kinahan, M. Defrise, C. Michel, and D. Townsend, “Fast reconstruction of 3D PET data with accurate statistical modeling,” IEEE Trans. Nucl. Sci. 45, 1083–1089 (1998).
[CrossRef]

Cornelius, S.

K.R. Muzic and S. Cornelius, “COMKAT: compartment model kinetic analysis tool,” J. Nucl. Med. 42, 636–645 (2001).

Cunningham, V.

R. Gunn, S. Gunn, F. Turkheimer, J. Aston, and V. Cunningham, “Tracer kinetic modeling via basis pursuit,” in Brain Imaging Using PET, M. Senda, ed. (Academic, 2002), pp. 115–121.

Defrise, M.

C. Comtat, P. Kinahan, M. Defrise, C. Michel, and D. Townsend, “Fast reconstruction of 3D PET data with accurate statistical modeling,” IEEE Trans. Nucl. Sci. 45, 1083–1089 (1998).
[CrossRef]

Dolle, F.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Doucet, A.

A. Doucet, “On sequential simulation-based methods for Bayesian filtering,” Tech. rep. CUED/F-INFENG/TR. 310 (Cambridge University Department of Engineering, 1998).

Duchesnay, E.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Dupont, P.

J. Nuyts, C. Michel, and P. Dupont, “Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations,” IEEE Trans. Med. Imag. 20, 365–375 (2001).
[CrossRef]

Fessler, J.

J. Ollinger and J. Fessler, “Positron-emission tomography,” IEEE Signal Process. Mag. 14 (1), 43–55 (1997).
[CrossRef]

Frouin, V.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Gelfand, A. E.

A. F. M. Smith and A. E. Gelfand“ Bayesian statistics without tears: a sampling–resampling perspective,” Amer. Stat. 46, 84–88 (1992).
[CrossRef]

Gordon, N.

M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50, 174–188 (2002).
[CrossRef]

Gunn, R.

R. Gunn, S. Gunn, F. Turkheimer, J. Aston, and V. Cunningham, “Tracer kinetic modeling via basis pursuit,” in Brain Imaging Using PET, M. Senda, ed. (Academic, 2002), pp. 115–121.

Gunn, S.

R. Gunn, S. Gunn, F. Turkheimer, J. Aston, and V. Cunningham, “Tracer kinetic modeling via basis pursuit,” in Brain Imaging Using PET, M. Senda, ed. (Academic, 2002), pp. 115–121.

Kemp, F.

F. Kemp, “An introduction to sequential Monte Carlo methods,” J. Roy. Stat. Soc. 52, 694–695 (2003).
[CrossRef]

Kinahan, P.

C. Comtat, P. Kinahan, M. Defrise, C. Michel, and D. Townsend, “Fast reconstruction of 3D PET data with accurate statistical modeling,” IEEE Trans. Nucl. Sci. 45, 1083–1089 (1998).
[CrossRef]

Kinahan, P. E.

S. Tong, A. M. Alessio, P. E. Kinahan, H. Liu, and P. Shi, “A robust state-space kinetics-guided framework for dynamic PET image reconstruction,” Phys. Med. Biol. 56, 2481–2498 (2011).
[CrossRef]

Kirrane, J.

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

Krohn, K.

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

Leahy, R.

R. Leahy and J. Qi “Statistical approaches in quantitative positron emission tomography,” Stat. Comput. 10, 147–165 (2000).
[CrossRef]

Lecomte, R.

V.V. Selivanov, Y. Picard, J. Cadorette, S. Rodrigue, and R. Lecomte, “Detector response models for statistical iterative image reconstruction in high resolution PET,” IEEE Trans. Nucl. Sci. 47, 1168–1175 (2000).
[CrossRef]

Lewitt, R. M.

R. M. Lewitt and S. Matej, “Overview of methods for image reconstruction from projections in emission computed tomography,” Proc. IEEE 91, 1588–1611 (2003).
[CrossRef]

Liu, H.

S. Tong, A. M. Alessio, P. E. Kinahan, H. Liu, and P. Shi, “A robust state-space kinetics-guided framework for dynamic PET image reconstruction,” Phys. Med. Biol. 56, 2481–2498 (2011).
[CrossRef]

Mankoff, D.

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

Maroy, R.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Maskell, S.

M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50, 174–188 (2002).
[CrossRef]

Matej, S.

R. M. Lewitt and S. Matej, “Overview of methods for image reconstruction from projections in emission computed tomography,” Proc. IEEE 91, 1588–1611 (2003).
[CrossRef]

Michel, C.

J. Nuyts, C. Michel, and P. Dupont, “Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations,” IEEE Trans. Med. Imag. 20, 365–375 (2001).
[CrossRef]

C. Comtat, P. Kinahan, M. Defrise, C. Michel, and D. Townsend, “Fast reconstruction of 3D PET data with accurate statistical modeling,” IEEE Trans. Nucl. Sci. 45, 1083–1089 (1998).
[CrossRef]

Mondal, P. P.

Muzi, M.

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

Muzic, K.R.

K.R. Muzic and S. Cornelius, “COMKAT: compartment model kinetic analysis tool,” J. Nucl. Med. 42, 636–645 (2001).

Nielsen, P.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Nuyts, J.

J. Nuyts, C. Michel, and P. Dupont, “Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations,” IEEE Trans. Med. Imag. 20, 365–375 (2001).
[CrossRef]

O’Sullivan, F.

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

O’Sullivan, J.

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

Ollinger, J.

J. Ollinger and J. Fessler, “Positron-emission tomography,” IEEE Signal Process. Mag. 14 (1), 43–55 (1997).
[CrossRef]

Phelps, M.

M. Phelps, PET: Molecular Imaging and Its Biological Applications (Springer, 2004).

Picard, Y.

V.V. Selivanov, Y. Picard, J. Cadorette, S. Rodrigue, and R. Lecomte, “Detector response models for statistical iterative image reconstruction in high resolution PET,” IEEE Trans. Nucl. Sci. 47, 1168–1175 (2000).
[CrossRef]

Qi, J.

G. Wang and J. Qi, “Analysis of penalized likelihood image reconstruction for dynamic PET quantification,” IEEE Trans. Med. Imag. 28, 608–620 (2009).
[CrossRef]

R. Leahy and J. Qi “Statistical approaches in quantitative positron emission tomography,” Stat. Comput. 10, 147–165 (2000).
[CrossRef]

Rajan, K.

Rodrigue, S.

V.V. Selivanov, Y. Picard, J. Cadorette, S. Rodrigue, and R. Lecomte, “Detector response models for statistical iterative image reconstruction in high resolution PET,” IEEE Trans. Nucl. Sci. 47, 1168–1175 (2000).
[CrossRef]

Selivanov, V.V.

V.V. Selivanov, Y. Picard, J. Cadorette, S. Rodrigue, and R. Lecomte, “Detector response models for statistical iterative image reconstruction in high resolution PET,” IEEE Trans. Nucl. Sci. 47, 1168–1175 (2000).
[CrossRef]

Shepp, L. A.

L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. 1, 113–122 (1982).
[CrossRef]

Shi, P.

S. Tong, A. M. Alessio, P. E. Kinahan, H. Liu, and P. Shi, “A robust state-space kinetics-guided framework for dynamic PET image reconstruction,” Phys. Med. Biol. 56, 2481–2498 (2011).
[CrossRef]

S. Tong and P. Shi, “Tracer kinetics guided dynamic PET reconstruction,” Information Process in Medical Imaging (2007), pp. 421–433.

Smith, A. F. M.

A. F. M. Smith and A. E. Gelfand“ Bayesian statistics without tears: a sampling–resampling perspective,” Amer. Stat. 46, 84–88 (1992).
[CrossRef]

Spence, A.

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

Tavitian, B.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Tong, S.

S. Tong, A. M. Alessio, P. E. Kinahan, H. Liu, and P. Shi, “A robust state-space kinetics-guided framework for dynamic PET image reconstruction,” Phys. Med. Biol. 56, 2481–2498 (2011).
[CrossRef]

S. Tong and P. Shi, “Tracer kinetics guided dynamic PET reconstruction,” Information Process in Medical Imaging (2007), pp. 421–433.

Townsend, D.

C. Comtat, P. Kinahan, M. Defrise, C. Michel, and D. Townsend, “Fast reconstruction of 3D PET data with accurate statistical modeling,” IEEE Trans. Nucl. Sci. 45, 1083–1089 (1998).
[CrossRef]

Trebossen, R.

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

Turkheimer, F.

R. Gunn, S. Gunn, F. Turkheimer, J. Aston, and V. Cunningham, “Tracer kinetic modeling via basis pursuit,” in Brain Imaging Using PET, M. Senda, ed. (Academic, 2002), pp. 115–121.

Vardi, Y.

L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. 1, 113–122 (1982).
[CrossRef]

Wang, G.

G. Wang and J. Qi, “Analysis of penalized likelihood image reconstruction for dynamic PET quantification,” IEEE Trans. Med. Imag. 28, 608–620 (2009).
[CrossRef]

Wieczorek, H.

H. Wieczorek, “The image quality of FBP and MLEM reconstruction,” Phys. Med. Biol. 55, 3161–3176 (2010).
[CrossRef]

Amer. Stat. (1)

A. F. M. Smith and A. E. Gelfand“ Bayesian statistics without tears: a sampling–resampling perspective,” Amer. Stat. 46, 84–88 (1992).
[CrossRef]

IEEE Signal Process. Mag. (1)

J. Ollinger and J. Fessler, “Positron-emission tomography,” IEEE Signal Process. Mag. 14 (1), 43–55 (1997).
[CrossRef]

IEEE Trans. Med. Imag. (5)

R. Maroy, R. Boisgard, C. Comtat, V. Frouin, P. Cathier, E. Duchesnay, F. Dolle, P. Nielsen, R. Trebossen, and B. Tavitian, “Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics,” IEEE Trans. Med. Imag. 27, 342–354 (2008).
[CrossRef]

L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. 1, 113–122 (1982).
[CrossRef]

J. Nuyts, C. Michel, and P. Dupont, “Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations,” IEEE Trans. Med. Imag. 20, 365–375 (2001).
[CrossRef]

G. Wang and J. Qi, “Analysis of penalized likelihood image reconstruction for dynamic PET quantification,” IEEE Trans. Med. Imag. 28, 608–620 (2009).
[CrossRef]

F. O’Sullivan, J. Kirrane, M. Muzi, J. O’Sullivan, A. Spence, D. Mankoff, and K. Krohn, “Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function,” IEEE Trans. Med. Imag. 29, 610–624 (2010).
[CrossRef]

IEEE Trans. Nucl. Sci. (2)

C. Comtat, P. Kinahan, M. Defrise, C. Michel, and D. Townsend, “Fast reconstruction of 3D PET data with accurate statistical modeling,” IEEE Trans. Nucl. Sci. 45, 1083–1089 (1998).
[CrossRef]

V.V. Selivanov, Y. Picard, J. Cadorette, S. Rodrigue, and R. Lecomte, “Detector response models for statistical iterative image reconstruction in high resolution PET,” IEEE Trans. Nucl. Sci. 47, 1168–1175 (2000).
[CrossRef]

IEEE Trans. Signal Process. (1)

M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50, 174–188 (2002).
[CrossRef]

J. Nucl. Med. (1)

K.R. Muzic and S. Cornelius, “COMKAT: compartment model kinetic analysis tool,” J. Nucl. Med. 42, 636–645 (2001).

J. Opt. Soc. Am. A (2)

J. Roy. Stat. Soc. (1)

F. Kemp, “An introduction to sequential Monte Carlo methods,” J. Roy. Stat. Soc. 52, 694–695 (2003).
[CrossRef]

Phys. Med. Biol. (2)

H. Wieczorek, “The image quality of FBP and MLEM reconstruction,” Phys. Med. Biol. 55, 3161–3176 (2010).
[CrossRef]

S. Tong, A. M. Alessio, P. E. Kinahan, H. Liu, and P. Shi, “A robust state-space kinetics-guided framework for dynamic PET image reconstruction,” Phys. Med. Biol. 56, 2481–2498 (2011).
[CrossRef]

Proc. IEEE (1)

R. M. Lewitt and S. Matej, “Overview of methods for image reconstruction from projections in emission computed tomography,” Proc. IEEE 91, 1588–1611 (2003).
[CrossRef]

Stat. Comput. (1)

R. Leahy and J. Qi “Statistical approaches in quantitative positron emission tomography,” Stat. Comput. 10, 147–165 (2000).
[CrossRef]

Other (5)

S. Tong and P. Shi, “Tracer kinetics guided dynamic PET reconstruction,” Information Process in Medical Imaging (2007), pp. 421–433.

M. Phelps, PET: Molecular Imaging and Its Biological Applications (Springer, 2004).

R. Gunn, S. Gunn, F. Turkheimer, J. Aston, and V. Cunningham, “Tracer kinetic modeling via basis pursuit,” in Brain Imaging Using PET, M. Senda, ed. (Academic, 2002), pp. 115–121.

A. Doucet, “On sequential simulation-based methods for Bayesian filtering,” Tech. rep. CUED/F-INFENG/TR. 310 (Cambridge University Department of Engineering, 1998).

E. Carson and C. Cobelli, Modelling Methodology for Physiology and Medicine (Academic, 2001).

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Figures (6)

Fig. 1.
Fig. 1.

PET projection diagram. PET data are the projection of certain angles.

Fig. 2.
Fig. 2.

Digital phantom generated from Zubal thorax. Three areas that are important for detail identification are marked by red circles.

Fig. 3.
Fig. 3.

Reconstructed images with the PF (left) and ML-EM (right) methods. Top row, 10% noises in measured data; bottom row, 30% noises in measured data. Just as in Fig. 2, three areas of every image are marked by red circles.

Fig. 4.
Fig. 4.

Monte Carlo simulation result with the (a) PF and (b) ML-EM methods. Three important areas in each image are marked to show the advantage of the PF method.

Fig. 5.
Fig. 5.

Cylinder phantom with six spheres and transaxial view: (a) cylinder phantom, (b) transaxial view. Six spheres filled with FDG are set in a big container. The initial activity of the FDG is 107.92Bq/ml.

Fig. 6.
Fig. 6.

Six-sphere phantom’s result reconstructed by the (a) PF and (b) ML-EM methods. Although more artifacts are around those spheres, the distribution within each sphere is more uniform in the PF result. This is also demonstrated by the variance of the two results.

Tables (4)

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Table 1. Bias and Variance of the PF and ML-EM Methodsa

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Table 2. Variance of Real Data Reconstruction by the PF and ML-EM Methodsa

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Table 3. Computation Time of Both GPU Computing and Serial Computinga

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Table 4. Bias and Variance of GPU Computing and Serial Computinga

Equations (17)

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y=Gx+ν,
x˙(k)=Ax(k)+BU(k),
x˙(k)=k2x(k)+(k1+k2Va)Ca(k)+VadCa(k)dk,
x.(k)=0.
y(k)=Gx(k)+ν(k),
x(k+1)=Ax(k)+z(k),
x(k+1)=x(k).
p(x(k)|y(k))=p(y(k)|y(k1),x(k))p(x(k)|y(k1))p(y(k)|y(k1)).
p(x(k)|y(k))=p(y(k)|x(k))p(x(k)|y(k1))p(y(k)|y(k1)).
p(x(k)|y(k))1Ni=1Np(x(k)|x(i)(k1))w(i)(k1),
w(i)(k)=w(i)(k1)p(y(k)|x(i)(k))p(x(i)(k)|x(i)(k1))q(x(i)(k)|x(i)(k1),y(k)).
p(x(i)(k)|x(i)(k1))=q(x(i)k)|x(i)(1),y(k)).
w(i)=w(i)p(y|x(i)).
ν=yGx(i).
w(i)=w(i)p(y=y*|x=x(i))w(i)fv(y*Gx(i)),
y*=iyp(xj|yi),
p(xj|yi)=p(yi|xj)p(xj)jp(yi|xj)p(xj),

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