Abstract

In order to improve the spatial resolution of time-domain (TD) fluorescence molecular lifetime tomography (FMLT), an accelerated nonlinear orthogonal matching pursuit (ANOMP) algorithm is proposed. As a kind of nonlinear greedy sparsity-constrained methods, ANOMP can find an approximate solution of L0 minimization problem. ANOMP consists of two parts, i.e., the outer iterations and the inner iterations. Each outer iteration selects multiple elements to expand the support set of the inverse lifetime based on the gradients of a mismatch error. The inner iterations obtain an intermediate estimate based on the support set estimated in the outer iterations. The stopping criterion for the outer iterations is based on the stability of the maximum reconstructed values and is robust for problems with targets at different edge-to-edge distances (EEDs). Phantom experiments with two fluorophores at different EEDs and in vivo mouse experiments demonstrate that ANOMP can provide high quantification accuracy, even if the EED is relatively small, and high resolution.

© 2016 Optical Society of America

Full Article  |  PDF Article
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  1. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
    [Crossref] [PubMed]
  2. J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
    [Crossref] [PubMed]
  3. M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21(2), 158–160 (1996).
    [Crossref] [PubMed]
  4. J. McGinty, D. W. Stuckey, V. Y. Soloviev, R. Laine, M. Wylezinska-Arridge, D. J. Wells, S. R. Arridge, P. M. French, J. V. Hajnal, and A. Sardini, “In vivo fluorescence lifetime tomography of a FRET probe expressed in mouse,” Biomed. Opt. Express 2(7), 1907–1917 (2011).
    [Crossref] [PubMed]
  5. S. S. Hou, W. L. Rice, B. J. Bacskai, and A. T. N. Kumar, “Tomographic lifetime imaging using combined early- and late-arriving photons,” Opt. Lett. 39(5), 1165–1168 (2014).
    [Crossref] [PubMed]
  6. W. L. Rice, S. Hou, and A. T. N. Kumar, “Resolution below the point spread function for diffuse optical imaging using fluorescence lifetime multiplexing,” Opt. Lett. 38(12), 2038–2040 (2013).
    [Crossref] [PubMed]
  7. R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
    [Crossref] [PubMed]
  8. L. Zhang, F. Gao, H. He, and H. Zhao, “Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors,” Opt. Express 16(10), 7214–7223 (2008).
    [Crossref] [PubMed]
  9. C. Cai, L. Zhang, J. Zhang, J. Bai, and J. Luo, “Direct reconstruction method for time-domain fluorescence molecular lifetime tomography,” Opt. Lett. 40(17), 4038–4041 (2015).
    [Crossref] [PubMed]
  10. P. Mohajerani, A. A. Eftekhar, J. Huang, and A. Adibi, “Optimal sparse solution for fluorescent diffuse optical tomography: theory and phantom experimental results,” Appl. Opt. 46(10), 1679–1685 (2007).
    [Crossref] [PubMed]
  11. J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
    [Crossref] [PubMed]
  12. J. Yu, F. Liu, J. Wu, L. Jiao, and X. He, “Fast source reconstruction for bioluminescence tomography based on sparse regularization,” IEEE Trans. Biomed. Eng. 57(10), 2583–2586 (2010).
    [Crossref] [PubMed]
  13. A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. 23(6), 2609–2624 (2014).
    [Crossref] [PubMed]
  14. J. Tropp and S. J. Wright, “Computational methods for sparse solution of linear inverse problems,” Proc. IEEE 98(6), 948–958 (2010).
    [Crossref]
  15. S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
    [Crossref]
  16. M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
    [Crossref]
  17. S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41(12), 3397–3415 (1993).
    [Crossref]
  18. J. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
    [Crossref]
  19. T. T. Do, L. Gan, N. Nguyen, and T. D. Tran, “Sparsity adaptive matching pursuit algorithm for practical compressed sensing,” In 2008 42nd Asilomar Conference on Signals, Systems and Computers (IEEE, 2008), pp. 581–587.
    [Crossref]
  20. D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009).
    [Crossref]
  21. J. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
    [Crossref]
  22. M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
    [Crossref]
  23. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
    [Crossref]
  24. G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
    [Crossref] [PubMed]
  25. R. Tur, Y. C. Eldar, and Z. Friedman, “Innovation rate sampling of pulse streams with application to ultrasound imaging,” IEEE Trans. Signal Process. 59(4), 1827–1842 (2011).
    [Crossref]
  26. J. Liu, Q. He, and J. Luo, “Compressed sensing for high frame rate, high resolution and high contrast ultrasound imaging,” In 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) (IEEE, 2015), pp. 1552–1555.
  27. J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28(4), 585–594 (2009).
    [Crossref] [PubMed]
  28. F. Bunea, “Honest variable selection in linear and logistic regression models via l1 and l 1 + l 2 penalization,” Electron. J. Stat. 2(0), 1153–1194 (2008).
    [Crossref]
  29. S. M. Kakade, O. Shamir, K. Sridharan, and A. Tewari, “Learning exponential families in high-dimensions: Strong convexity and sparsity,” arXiv preprint arXiv: 0911.0054 (2009).
  30. S. Negahban, B. Yu, M. J. Wainwright, and P. K. Ravikumar, “A unified framework for high-dimensional analysis of M -estimators with decomposable regularizers,” In Proceeding of Advances in Neural Information Processing Systems, Y. Bengio, D. Schuurmans, J. D. Lafferty, C. K. I. Williams and A. Culotta, ed. (MIT, 2009), pp. 1348–1356.
  31. A. Agarwal, S. Negahban, and M. J. Wainwright, “Fast global convergence rates of gradient methods for high-dimensional statistical recovery,” In Proceeding of Advances in Neural Information Processing Systems, J. D. Lafferty, C. K. I. Williams, J. Shawe-Taylor, R. S. Zemel and A. Culotta, ed. (MIT, 2010), pp. 37–45.
  32. T. Blumensath and M. E. Davies, “Gradient pursuit for non-linear sparse signal modelling,” In 2008 16th European Signal Processing Conference (IEEE, 2008), pp. 1–5.
  33. F. Dupé, “Greed is Fine: on Finding Sparse Zeros of Hilbert Operators,” in Proceedings of the 31st International Conference on Machine Learning, E. P. Xing and T. Jebara, ed. (Microtome Publ, 2015), Vol. 37.
  34. T. Blumensath, “Compressed sensing with nonlinear observations and related nonlinear optimization problems,” IEEE Trans. Inf. Theory 59(6), 3466–3474 (2013).
    [Crossref]
  35. X. Yuan, P. Li, and T. Zhang, “Gradient hard thresholding pursuit for sparsity-constrained optimization,” arXiv preprint arXiv:1311.5750 (2013).
  36. S. Bahmani, B. Raj, and P. T. Boufounos, “Greedy sparsity-constrained optimization,” J. Mach. Learn. Res. 14(1), 807–841 (2013).
  37. A. J. Dobson and A. Barnett, An Introduction to Generalized Linear Models (CRC press, 2008).
  38. S. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu, “A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers,” Manuscript, University of California, Berkeley, Dept. of Statistics and EECS (2011).
  39. B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50(28), 5397–5407 (2011).
    [Crossref] [PubMed]
  40. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2), 299–309 (1993).
    [Crossref] [PubMed]
  41. F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express 16(17), 13104–13121 (2008).
    [Crossref] [PubMed]
  42. D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Comparison of regularization methods in fluorescence molecular tomography, in Photonics (Multidisciplinary Digital Publishing Institute, 2014), pp. 95–109.
  43. J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30(5), 1143–1153 (2011).
    [Crossref] [PubMed]
  44. H. Lee, M. Y. Berezin, M. Henary, L. Strekowski, and S. Achilefu, “Fluorescence lifetime properties of near-infrared cyanine dyes in relation to their structures,” J. Photochem. Photobiol. Chem. 200(2-3), 438–444 (2008).
    [Crossref] [PubMed]
  45. C. A. Mela, C. Patterson, W. K. Thompson, F. Papay, and Y. Liu, “Stereoscopic Integrated Imaging Goggles for Multimodal Intraoperative Image Guidance,” PLoS One 10(11), e0141956 (2015).
    [Crossref] [PubMed]
  46. G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225–4241 (2005).
    [Crossref] [PubMed]
  47. J. Shi, F. Liu, H. Pu, S. Zuo, J. Luo, and J. Bai, “An adaptive support driven reweighted L1-regularization algorithm for fluorescence molecular tomography,” Biomed. Opt. Express 5(11), 4039–4052 (2014).
    [Crossref] [PubMed]

2015 (2)

C. Cai, L. Zhang, J. Zhang, J. Bai, and J. Luo, “Direct reconstruction method for time-domain fluorescence molecular lifetime tomography,” Opt. Lett. 40(17), 4038–4041 (2015).
[Crossref] [PubMed]

C. A. Mela, C. Patterson, W. K. Thompson, F. Papay, and Y. Liu, “Stereoscopic Integrated Imaging Goggles for Multimodal Intraoperative Image Guidance,” PLoS One 10(11), e0141956 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (4)

2011 (4)

B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50(28), 5397–5407 (2011).
[Crossref] [PubMed]

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

R. Tur, Y. C. Eldar, and Z. Friedman, “Innovation rate sampling of pulse streams with application to ultrasound imaging,” IEEE Trans. Signal Process. 59(4), 1827–1842 (2011).
[Crossref]

J. McGinty, D. W. Stuckey, V. Y. Soloviev, R. Laine, M. Wylezinska-Arridge, D. J. Wells, S. R. Arridge, P. M. French, J. V. Hajnal, and A. Sardini, “In vivo fluorescence lifetime tomography of a FRET probe expressed in mouse,” Biomed. Opt. Express 2(7), 1907–1917 (2011).
[Crossref] [PubMed]

2010 (2)

J. Yu, F. Liu, J. Wu, L. Jiao, and X. He, “Fast source reconstruction for bioluminescence tomography based on sparse regularization,” IEEE Trans. Biomed. Eng. 57(10), 2583–2586 (2010).
[Crossref] [PubMed]

J. Tropp and S. J. Wright, “Computational methods for sparse solution of linear inverse problems,” Proc. IEEE 98(6), 948–958 (2010).
[Crossref]

2009 (3)

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
[Crossref] [PubMed]

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28(4), 585–594 (2009).
[Crossref] [PubMed]

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009).
[Crossref]

2008 (7)

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[Crossref]

F. Bunea, “Honest variable selection in linear and logistic regression models via l1 and l 1 + l 2 penalization,” Electron. J. Stat. 2(0), 1153–1194 (2008).
[Crossref]

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

H. Lee, M. Y. Berezin, M. Henary, L. Strekowski, and S. Achilefu, “Fluorescence lifetime properties of near-infrared cyanine dyes in relation to their structures,” J. Photochem. Photobiol. Chem. 200(2-3), 438–444 (2008).
[Crossref] [PubMed]

L. Zhang, F. Gao, H. He, and H. Zhao, “Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors,” Opt. Express 16(10), 7214–7223 (2008).
[Crossref] [PubMed]

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[Crossref] [PubMed]

F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express 16(17), 13104–13121 (2008).
[Crossref] [PubMed]

2007 (3)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

P. Mohajerani, A. A. Eftekhar, J. Huang, and A. Adibi, “Optimal sparse solution for fluorescent diffuse optical tomography: theory and phantom experimental results,” Appl. Opt. 46(10), 1679–1685 (2007).
[Crossref] [PubMed]

J. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

2006 (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

2005 (2)

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225–4241 (2005).
[Crossref] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[Crossref] [PubMed]

2004 (1)

J. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

1998 (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[Crossref]

1996 (1)

1993 (2)

S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41(12), 3397–3415 (1993).
[Crossref]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2), 299–309 (1993).
[Crossref] [PubMed]

Achilefu, S.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
[Crossref] [PubMed]

H. Lee, M. Y. Berezin, M. Henary, L. Strekowski, and S. Achilefu, “Fluorescence lifetime properties of near-infrared cyanine dyes in relation to their structures,” J. Photochem. Photobiol. Chem. 200(2-3), 438–444 (2008).
[Crossref] [PubMed]

Adibi, A.

Akers, W.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
[Crossref] [PubMed]

Alexandrakis, G.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225–4241 (2005).
[Crossref] [PubMed]

Arridge, S. R.

Bacskai, B. J.

Bahmani, S.

S. Bahmani, B. Raj, and P. T. Boufounos, “Greedy sparsity-constrained optimization,” J. Mach. Learn. Res. 14(1), 807–841 (2013).

Bai, J.

Baritaux, J. C.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

Berezin, M. Y.

H. Lee, M. Y. Berezin, M. Henary, L. Strekowski, and S. Achilefu, “Fluorescence lifetime properties of near-infrared cyanine dyes in relation to their structures,” J. Photochem. Photobiol. Chem. 200(2-3), 438–444 (2008).
[Crossref] [PubMed]

Blumensath, T.

T. Blumensath, “Compressed sensing with nonlinear observations and related nonlinear optimization problems,” IEEE Trans. Inf. Theory 59(6), 3466–3474 (2013).
[Crossref]

Boas, D. A.

Boufounos, P. T.

S. Bahmani, B. Raj, and P. T. Boufounos, “Greedy sparsity-constrained optimization,” J. Mach. Learn. Res. 14(1), 807–841 (2013).

Bucher, M.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

Bunea, F.

F. Bunea, “Honest variable selection in linear and logistic regression models via l1 and l 1 + l 2 penalization,” Electron. J. Stat. 2(0), 1153–1194 (2008).
[Crossref]

Cai, C.

Cao, X.

Chance, B.

Chatziioannou, A. F.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225–4241 (2005).
[Crossref] [PubMed]

Chen, G. H.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Chen, S. S.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[Crossref]

Culver, J. P.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
[Crossref] [PubMed]

Delpy, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2), 299–309 (1993).
[Crossref] [PubMed]

Dinkelborg, L. M.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[Crossref] [PubMed]

Donoho, D. L.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[Crossref]

Eftekhar, A. A.

Eldar, Y. C.

R. Tur, Y. C. Eldar, and Z. Friedman, “Innovation rate sampling of pulse streams with application to ultrasound imaging,” IEEE Trans. Signal Process. 59(4), 1827–1842 (2011).
[Crossref]

Figueiredo, M. A.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

French, P. M.

Friedman, Z.

R. Tur, Y. C. Eldar, and Z. Friedman, “Innovation rate sampling of pulse streams with application to ultrasound imaging,” IEEE Trans. Signal Process. 59(4), 1827–1842 (2011).
[Crossref]

Gambhir, S. S.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[Crossref] [PubMed]

Gao, F.

Gilbert, A. C.

J. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

Hajnal, J. V.

Hassler, K.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

He, H.

He, X.

J. Yu, F. Liu, J. Wu, L. Jiao, and X. He, “Fast source reconstruction for bioluminescence tomography based on sparse regularization,” IEEE Trans. Biomed. Eng. 57(10), 2583–2586 (2010).
[Crossref] [PubMed]

Henary, M.

H. Lee, M. Y. Berezin, M. Henary, L. Strekowski, and S. Achilefu, “Fluorescence lifetime properties of near-infrared cyanine dyes in relation to their structures,” J. Photochem. Photobiol. Chem. 200(2-3), 438–444 (2008).
[Crossref] [PubMed]

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2), 299–309 (1993).
[Crossref] [PubMed]

Hou, S.

Hou, S. S.

Huang, J.

Jiao, L.

J. Yu, F. Liu, J. Wu, L. Jiao, and X. He, “Fast source reconstruction for bioluminescence tomography based on sparse regularization,” IEEE Trans. Biomed. Eng. 57(10), 2583–2586 (2010).
[Crossref] [PubMed]

Jin, A.

A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. 23(6), 2609–2624 (2014).
[Crossref] [PubMed]

Kumar, A. T. N.

Laine, R.

Lee, H.

H. Lee, M. Y. Berezin, M. Henary, L. Strekowski, and S. Achilefu, “Fluorescence lifetime properties of near-infrared cyanine dyes in relation to their structures,” J. Photochem. Photobiol. Chem. 200(2-3), 438–444 (2008).
[Crossref] [PubMed]

Leng, S.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Lesage, F.

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28(4), 585–594 (2009).
[Crossref] [PubMed]

Li, X. D.

Liu, F.

Liu, X.

Liu, Y.

C. A. Mela, C. Patterson, W. K. Thompson, F. Papay, and Y. Liu, “Stereoscopic Integrated Imaging Goggles for Multimodal Intraoperative Image Guidance,” PLoS One 10(11), e0141956 (2015).
[Crossref] [PubMed]

Luo, J.

Lustig, M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[Crossref]

Mallat, S. G.

S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41(12), 3397–3415 (1993).
[Crossref]

Marjono, A.

McGinty, J.

Mela, C. A.

C. A. Mela, C. Patterson, W. K. Thompson, F. Papay, and Y. Liu, “Stereoscopic Integrated Imaging Goggles for Multimodal Intraoperative Image Guidance,” PLoS One 10(11), e0141956 (2015).
[Crossref] [PubMed]

Mohajerani, P.

Needell, D.

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009).
[Crossref]

Nothdurft, R. E.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
[Crossref] [PubMed]

Nowak, R. D.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Ntziachristos, V.

A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. 23(6), 2609–2624 (2014).
[Crossref] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[Crossref] [PubMed]

O’Leary, M. A.

Papay, F.

C. A. Mela, C. Patterson, W. K. Thompson, F. Papay, and Y. Liu, “Stereoscopic Integrated Imaging Goggles for Multimodal Intraoperative Image Guidance,” PLoS One 10(11), e0141956 (2015).
[Crossref] [PubMed]

Patterson, C.

C. A. Mela, C. Patterson, W. K. Thompson, F. Papay, and Y. Liu, “Stereoscopic Integrated Imaging Goggles for Multimodal Intraoperative Image Guidance,” PLoS One 10(11), e0141956 (2015).
[Crossref] [PubMed]

Patwardhan, S. V.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
[Crossref] [PubMed]

Pauly, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[Crossref]

Provost, J.

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28(4), 585–594 (2009).
[Crossref] [PubMed]

Pu, H.

Raj, B.

S. Bahmani, B. Raj, and P. T. Boufounos, “Greedy sparsity-constrained optimization,” J. Mach. Learn. Res. 14(1), 807–841 (2013).

Rannou, F. R.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225–4241 (2005).
[Crossref] [PubMed]

Rice, W. L.

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[Crossref] [PubMed]

Santos, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[Crossref]

Sanyal, S.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

Sardini, A.

Saunders, M. A.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[Crossref]

Schweiger, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2), 299–309 (1993).
[Crossref] [PubMed]

Shi, J.

Soloviev, V. Y.

Strekowski, L.

H. Lee, M. Y. Berezin, M. Henary, L. Strekowski, and S. Achilefu, “Fluorescence lifetime properties of near-infrared cyanine dyes in relation to their structures,” J. Photochem. Photobiol. Chem. 200(2-3), 438–444 (2008).
[Crossref] [PubMed]

Stuckey, D. W.

Tang, J.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Tanikawa, Y.

Thompson, W. K.

C. A. Mela, C. Patterson, W. K. Thompson, F. Papay, and Y. Liu, “Stereoscopic Integrated Imaging Goggles for Multimodal Intraoperative Image Guidance,” PLoS One 10(11), e0141956 (2015).
[Crossref] [PubMed]

Tropp, J.

J. Tropp and S. J. Wright, “Computational methods for sparse solution of linear inverse problems,” Proc. IEEE 98(6), 948–958 (2010).
[Crossref]

J. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

J. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

Tropp, J. A.

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009).
[Crossref]

Tur, R.

R. Tur, Y. C. Eldar, and Z. Friedman, “Innovation rate sampling of pulse streams with application to ultrasound imaging,” IEEE Trans. Signal Process. 59(4), 1827–1842 (2011).
[Crossref]

Unser, M.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

van Bruggen, N.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[Crossref] [PubMed]

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[Crossref] [PubMed]

Wang, X.

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[Crossref] [PubMed]

Wells, D. J.

Willmann, J. K.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[Crossref] [PubMed]

Wright, S. J.

J. Tropp and S. J. Wright, “Computational methods for sparse solution of linear inverse problems,” Proc. IEEE 98(6), 948–958 (2010).
[Crossref]

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Wu, J.

J. Yu, F. Liu, J. Wu, L. Jiao, and X. He, “Fast source reconstruction for bioluminescence tomography based on sparse regularization,” IEEE Trans. Biomed. Eng. 57(10), 2583–2586 (2010).
[Crossref] [PubMed]

Wylezinska-Arridge, M.

Yamada, Y.

Yazici, B.

A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. 23(6), 2609–2624 (2014).
[Crossref] [PubMed]

Ye, Y.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
[Crossref] [PubMed]

Yodh, A. G.

Yu, J.

J. Yu, F. Liu, J. Wu, L. Jiao, and X. He, “Fast source reconstruction for bioluminescence tomography based on sparse regularization,” IEEE Trans. Biomed. Eng. 57(10), 2583–2586 (2010).
[Crossref] [PubMed]

Zhang, B.

Zhang, J.

Zhang, L.

Zhang, Z.

S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41(12), 3397–3415 (1993).
[Crossref]

Zhao, H.

Zuo, S.

Appl. Comput. Harmon. Anal. (1)

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009).
[Crossref]

Appl. Opt. (2)

Biomed. Opt. Express (2)

Electron. J. Stat. (1)

F. Bunea, “Honest variable selection in linear and logistic regression models via l1 and l 1 + l 2 penalization,” Electron. J. Stat. 2(0), 1153–1194 (2008).
[Crossref]

IEEE J. Sel. Top. Signal Process. (1)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

IEEE Signal Process. Mag. (1)

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

J. Yu, F. Liu, J. Wu, L. Jiao, and X. He, “Fast source reconstruction for bioluminescence tomography based on sparse regularization,” IEEE Trans. Biomed. Eng. 57(10), 2583–2586 (2010).
[Crossref] [PubMed]

IEEE Trans. Image Process. (1)

A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. 23(6), 2609–2624 (2014).
[Crossref] [PubMed]

IEEE Trans. Inf. Theory (4)

J. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

J. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

T. Blumensath, “Compressed sensing with nonlinear observations and related nonlinear optimization problems,” IEEE Trans. Inf. Theory 59(6), 3466–3474 (2013).
[Crossref]

IEEE Trans. Med. Imaging (2)

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30(5), 1143–1153 (2011).
[Crossref] [PubMed]

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28(4), 585–594 (2009).
[Crossref] [PubMed]

IEEE Trans. Signal Process. (2)

R. Tur, Y. C. Eldar, and Z. Friedman, “Innovation rate sampling of pulse streams with application to ultrasound imaging,” IEEE Trans. Signal Process. 59(4), 1827–1842 (2011).
[Crossref]

S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process. 41(12), 3397–3415 (1993).
[Crossref]

J. Biomed. Opt. (1)

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14(2), 024004 (2009).
[Crossref] [PubMed]

J. Mach. Learn. Res. (1)

S. Bahmani, B. Raj, and P. T. Boufounos, “Greedy sparsity-constrained optimization,” J. Mach. Learn. Res. 14(1), 807–841 (2013).

J. Opt. Soc. Am. A (1)

J. Photochem. Photobiol. Chem. (1)

H. Lee, M. Y. Berezin, M. Henary, L. Strekowski, and S. Achilefu, “Fluorescence lifetime properties of near-infrared cyanine dyes in relation to their structures,” J. Photochem. Photobiol. Chem. 200(2-3), 438–444 (2008).
[Crossref] [PubMed]

Med. Phys. (2)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2), 299–309 (1993).
[Crossref] [PubMed]

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Nat. Biotechnol. (1)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[Crossref] [PubMed]

Nat. Rev. Drug Discov. (1)

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Med. Biol. (1)

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225–4241 (2005).
[Crossref] [PubMed]

PLoS One (1)

C. A. Mela, C. Patterson, W. K. Thompson, F. Papay, and Y. Liu, “Stereoscopic Integrated Imaging Goggles for Multimodal Intraoperative Image Guidance,” PLoS One 10(11), e0141956 (2015).
[Crossref] [PubMed]

Proc. IEEE (1)

J. Tropp and S. J. Wright, “Computational methods for sparse solution of linear inverse problems,” Proc. IEEE 98(6), 948–958 (2010).
[Crossref]

SIAM J. Sci. Comput. (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20(1), 33–61 (1998).
[Crossref]

Other (11)

T. T. Do, L. Gan, N. Nguyen, and T. D. Tran, “Sparsity adaptive matching pursuit algorithm for practical compressed sensing,” In 2008 42nd Asilomar Conference on Signals, Systems and Computers (IEEE, 2008), pp. 581–587.
[Crossref]

J. Liu, Q. He, and J. Luo, “Compressed sensing for high frame rate, high resolution and high contrast ultrasound imaging,” In 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) (IEEE, 2015), pp. 1552–1555.

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Comparison of regularization methods in fluorescence molecular tomography, in Photonics (Multidisciplinary Digital Publishing Institute, 2014), pp. 95–109.

A. J. Dobson and A. Barnett, An Introduction to Generalized Linear Models (CRC press, 2008).

S. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu, “A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers,” Manuscript, University of California, Berkeley, Dept. of Statistics and EECS (2011).

X. Yuan, P. Li, and T. Zhang, “Gradient hard thresholding pursuit for sparsity-constrained optimization,” arXiv preprint arXiv:1311.5750 (2013).

S. M. Kakade, O. Shamir, K. Sridharan, and A. Tewari, “Learning exponential families in high-dimensions: Strong convexity and sparsity,” arXiv preprint arXiv: 0911.0054 (2009).

S. Negahban, B. Yu, M. J. Wainwright, and P. K. Ravikumar, “A unified framework for high-dimensional analysis of M -estimators with decomposable regularizers,” In Proceeding of Advances in Neural Information Processing Systems, Y. Bengio, D. Schuurmans, J. D. Lafferty, C. K. I. Williams and A. Culotta, ed. (MIT, 2009), pp. 1348–1356.

A. Agarwal, S. Negahban, and M. J. Wainwright, “Fast global convergence rates of gradient methods for high-dimensional statistical recovery,” In Proceeding of Advances in Neural Information Processing Systems, J. D. Lafferty, C. K. I. Williams, J. Shawe-Taylor, R. S. Zemel and A. Culotta, ed. (MIT, 2010), pp. 37–45.

T. Blumensath and M. E. Davies, “Gradient pursuit for non-linear sparse signal modelling,” In 2008 16th European Signal Processing Conference (IEEE, 2008), pp. 1–5.

F. Dupé, “Greed is Fine: on Finding Sparse Zeros of Hilbert Operators,” in Proceedings of the 31st International Conference on Machine Learning, E. P. Xing and T. Jebara, ed. (Microtome Publ, 2015), Vol. 37.

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Figures (5)

Fig. 1
Fig. 1 (a) The maximum reconstructed inverse lifetime values of different outer iterations in Expt. 1. Horizontal axis denotes the number of outer iteration and vertical axis denotes the maximum inverse lifetime (unit: s−1). (b-e) The reconstructed inverse lifetime maps of the 1st, 4th, 8th and 13th outer iterations (unit: s−1), the maximum values of which are 0.11 × 10 9   s 1 , 1.28 × 10 9   s 1 , 1.08 × 10 9   s 1 and 1.09 × 10 9   s 1 , respectively.
Fig. 2
Fig. 2 The reconstruction results of Expt. 1 (EED = 9 mm). (a) and (b) are the reconstructed inverse lifetime tomographic images of ANOMP and L1PSD (unit: s−1). (c) shows the inverse lifetime profiles along the dotted lines indicated in (a) and (b). Horizontal and vertical axes denote location (unit: mm) and inverse lifetime (unit: s−1), respectively. (d) and (e) are the FMLT images (unit: s) corresponding to (a) and (b). (f) shows the lifetime profiles along the dotted lines indicated in (d) and (e). Horizontal and vertical axes denote location (unit: mm) and lifetime (unit: s), respectively. In (c) and (f), the red, blue and green lines correspond to the real values, the results of ANOMP and L1PSD, respectively.
Fig. 3
Fig. 3 The reconstruction results of Expt. 2 (EED = 5 mm). (a) and (b) are the reconstructed inverse lifetime tomographic images of ANOMP and L1PSD (unit: s−1). (c) shows the inverse lifetime profiles along the dotted lines indicated in (a) and (b). Horizontal and vertical axes denote location (unit: mm) and inverse lifetime (unit: s−1), respectively. (d) and (e) are the FMLT images (unit: s) corresponding to (a) and (b). (f) shows the lifetime profiles along the dotted lines indicated in (d) and (e). Horizontal and vertical axes denote location (unit: mm) and lifetime (unit: s), respectively. In (c) and (f), the red, blue and green lines correspond to the real values, the results of ANOMP and L1PSD, respectively.
Fig. 4
Fig. 4 The reconstruction results of Expt. 3 (EED = 2 mm). (a) and (b) are the reconstructed inverse lifetime tomographic images of ANOMP and L1PSD (unit: s−1). (c) shows the inverse lifetime profiles along the dotted lines indicated in (a) and (b). Horizontal and vertical axes denote location (unit: mm) and inverse lifetime (unit: s−1), respectively. (d) and (e) are the FMLT images (unit: s) corresponding to (a) and (b). (f) shows the lifetime profiles along the dotted lines indicated in (d) and (e). Horizontal and vertical axes denote location (unit: mm) and lifetime (unit: s), respectively. In (c) and (f), the red, blue and green lines correspond to the real values, the results of ANOMP and L1PSD, respectively.
Fig. 5
Fig. 5 The reconstruction results of the in vivo experiment. (a) and (b) are the reconstructed inverse lifetime tomographic images of ANOMP and L1PSD (unit: s−1). (c) shows the inverse lifetime profiles along the dotted lines indicated in (a) and (b). Horizontal and vertical axes denote location (unit: mm) and inverse lifetime (unit: s−1), respectively. (d) and (e) are the FMLT images (unit: s) corresponding to (a) and (b). (f) shows the lifetime profiles along the dotted lines indicated in (d) and (e). Horizontal and vertical axes denote location (unit: mm) and lifetime (unit: s), respectively. In (c) and (f), the blue lines and green lines correspond to the reconstruction results of ANOMP and L1PSD, respectively.

Tables (1)

Tables Icon

Table 1 Quantitative metrics of reconstruction results of the phantom experiments

Equations (19)

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D ( r ) c 2 Φ 2 ( r , t ) t 2 + 1 c ( 3 D ( r ) μ a + 1 ) Φ ( r , t ) t + μ a Φ ( r , t ) [ D ( r ) Φ ( r , t ) ] = S ( r , t ) ,
Φ m ( r s , r d , t ) = Ω Φ x ( r s , r , t ) G m ( r , r d , t ) E ( r , t ) d 3 r ,
Φ m = F ( I τ ) ,
Φ m i = F i = n = 1 N G F n i Δ V = n = 1 N G Δ V [ Φ x ( r s i , n , t ) G m ( n , r d i , t ) . ( c η μ a f ( n ) I τ ( n ) e I τ ( n ) t ) ] | t = t i
min | | I τ | | 0 s . t . F ( I τ ) = Φ m .
i k = arg i max | F T ( I τ k 1 ) ( Φ m F ( I τ k 1 ) ) | ,
z = | F T ( I τ k 1 ) ( Φ m F ( I τ k 1 ) ) | ,
Z = S u p p ( z N s ) ,
F = ( F 1 1 F N G 1 F 1 S × D × I F N G S × D × I ) ,
F n i = Δ V [ Φ x ( r s i , n , t ) G m ( n , r d i , t ) . ( c η μ a f ( n ) ( 1 I τ ( n ) t ) e I τ ( n ) t ) ] | t = t i
Γ k = Γ k 1 Z ,
min 0.5 ( | | F ( I τ ) Φ m | | 2 2 + λ | | I τ | | 2 2 + μ ) s . t . I τ | Γ k 0 ; I τ | Γ k c = 0.
Φ m i = F i = n = 1 N G k F Γ k n i Δ V = n = 1 N G k Δ V [ Φ x ( r s i , Γ k n , t ) G m ( Γ k n , r d i , t ) , ( c η μ a f ( Γ k n ) I τ ( Γ k n ) e I τ ( Γ k n ) t ) ] | t = t i
F = ( F Γ k 1 1 F Γ k N G k 1 F Γ k 1 S × D × I F Γ k N G k S × D × I ) ,
max ( Γ v k ) min ( Γ v k ) < ω .
max ( Γ v k ) min ( Γ v k ) + ζ n u m ( Γ v k ) 1 < ζ ,
M A E = | | I τ r e c o n I τ t r u e | | 1 N G ,
C N R = I τ R O I ¯ I τ B C K ¯ ( w R O I σ R O I 2 + w B C K σ B C K 2 ) 1 / 2 ,
R E = | τ r e c o n τ t r u e | τ t r u e ,

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