Abstract

Mesoscopic fluorescence molecular tomography (MFMT) is a novel imaging technique capable of obtaining 3-D distribution of molecular probes inside biological tissues at depths of a few millimeters with a resolution up to ~100 μm. However, the ill-conditioned nature of the MFMT inverse problem severely deteriorates its reconstruction performances. Furthermore, dense spatial sampling and fine discretization of the imaging volume required for high resolution reconstructions make the sensitivity matrix (Jacobian) highly correlated, which prevents even advanced algorithms from achieving optimal solutions. In this work, we propose two computational methods to respectively increase the incoherence of the sensitivity matrix and improve the convergence rate of the inverse solver. We first apply a compressed sensing (CS) based preconditioner on either the whole sensitivity matrix or sub sensitivity matrices to reduce the coherence between columns of the sensitivity matrix. Then we employed a regularization method based on the weight iterative improvement method (WIIM) to mitigate the ill-condition of the sensitivity matrix and to drive the iterative optimization process towards convergence at a faster rate. We performed numerical simulations and phantom experiments to validate the effectiveness of the proposed strategies. In both in silico and in vitro cases, we were able to improve the quality of MFMT reconstructions significantly.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

Corrections

26 February 2019: A typographical correction was made to the author listing.


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References

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2017 (5)

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. J. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed. Opt. 22(1), 16003 (2017).
[Crossref] [PubMed]

F. Long and X. Intes, “Dental optical tomography with upconversion nanoparticles—a feasibility study,” J. Biomed. Opt. 22(6), 66001 (2017).
[Crossref] [PubMed]

M. T. Schaub, M. Trefois, P. van Dooren, and J.-C. Delvenne, “Sparse matrix factorizations for fast linear solvers with application to Laplacian systems,” SIAM J. Matrix Anal. Appl. 38(2), 505–529 (2017).
[Crossref]

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref] [PubMed]

F. Yang, M. S. Ozturk, R. Yao, and X. Intes, “Improving mesoscopic fluorescence molecular tomography through data reduction,” Biomed. Opt. Express 8(8), 3868–3881 (2017).
[Crossref] [PubMed]

2016 (2)

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics 4(1), 011009 (2016).
[Crossref] [PubMed]

2015 (4)

X. Deng, L. Yin, S. Peng, and M. Ding, “An iterative algorithm for solving ill-conditioned linear least squares problems,” Geod. Geodyn. 6(6), 453–459 (2015).
[Crossref]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref] [PubMed]

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for cancer application,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref] [PubMed]

R. Yao, Q. Pian, and X. Intes, “Wide-field fluorescence molecular tomography with compressive sensing based preconditioning,” Biomed. Opt. Express 6(12), 4887–4898 (2015).
[Crossref] [PubMed]

2014 (3)

L. Zhao, H. Yang, W. Cong, G. Wang, and X. Intes, “Lp regularization for early gate fluorescence molecular tomography,” Opt. Lett. 39(14), 4156–4159 (2014).
[Crossref] [PubMed]

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]

M. S. Ozturk, D. Rohrbach, U. Sunar, and X. Intes, “Mesoscopic fluorescence tomography of a photosensitizer (HPPH) 3D biodistribution in skin cancer,” Acad. Radiol. 21(2), 271–280 (2014).
[Crossref] [PubMed]

2013 (4)

M. S. Ozturk, V. K. Lee, L. Zhao, G. Dai, and X. Intes, “Mesoscopic fluorescence molecular tomography of reporter genes in bioprinted thick tissue,” J. Biomed. Opt. 18(10), 100501 (2013).
[Crossref] [PubMed]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-invasive in vivo imaging of near infrared-labeled transferrin in breast cancer cells and tumors using fluorescence lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref] [PubMed]

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58(11), R37–R61 (2013).
[Crossref] [PubMed]

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 50902 (2013).
[Crossref] [PubMed]

2012 (4)

L. Zhao, V. K. Lee, S.-S. Yoo, G. Dai, and X. Intes, “The integration of 3-D cell printing and mesoscopic fluorescence molecular tomography of vascular constructs within thick hydrogel scaffolds,” Biomaterials 33(21), 5325–5332 (2012).
[Crossref] [PubMed]

A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, “Preconditioning of the fluorescence diffuse optical tomography sensing matrix based on compressive sensing,” Opt. Lett. 37(20), 4326–4328 (2012).
[Crossref] [PubMed]

V. Venugopal, J. Chen, M. Barroso, and X. Intes, “Quantitative tomographic imaging of intermolecular FRET in small animals,” Biomed. Opt. Express 3(12), 3161–3175 (2012).
[Crossref] [PubMed]

D. L. Donoho, Y. Tsaig, I. Drori, and J. L. Starck, “Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit,” IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012).
[Crossref]

2011 (2)

J. Chen, V. Venugopal, and X. Intes, “Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates,” Biomed. Opt. Express 2(4), 871–886 (2011).
[Crossref] [PubMed]

J. Chen and X. Intes, “Comparison of Monte Carlo methods for fluorescence molecular tomography-computational efficiency,” Med. Phys. 38(10), 5788–5798 (2011).
[Crossref] [PubMed]

2010 (1)

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

2009 (3)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

S. H. Tseng, C. Hayakawa, J. Spanier, and A. J. Durkin, “Investigation of a probe design for facilitating the uses of the standard photon diffusion equation at short source-detector separations: Monte Carlo simulations,” J. Biomed. Opt. 14(5), 054043 (2009).
[Crossref] [PubMed]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[Crossref] [PubMed]

2007 (1)

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[Crossref]

2004 (2)

2003 (3)

V. A. Markel, V. Mital, and J. C. Schotland, “Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition,” J. Opt. Soc. Am. A 20(5), 890–902 (2003).
[Crossref] [PubMed]

Y. Chen, C. Mu, X. Intes, D. Blessington, and B. Chance, “Near-infrared phase cancellation instrument for fast and accurate localization of fluorescent heterogeneity,” Rev. Sci. Instrum. 74(7), 3466–3473 (2003).
[Crossref]

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via l minimization,” Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197–2202 (2003).
[Crossref] [PubMed]

2002 (2)

2001 (1)

2000 (1)

Y. Saad and H. A. van der Vorst, “Iterative solution of linear systems in the 20th century,” J. Comput. Appl. Math. 123(1–2), 1–33 (2000).
[Crossref]

1993 (1)

Abe, K.

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-invasive in vivo imaging of near infrared-labeled transferrin in breast cancer cells and tumors using fluorescence lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref] [PubMed]

Ale, A.

Azimipour, M.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. J. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed. Opt. 22(1), 16003 (2017).
[Crossref] [PubMed]

Barroso, M.

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for cancer application,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref] [PubMed]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-invasive in vivo imaging of near infrared-labeled transferrin in breast cancer cells and tumors using fluorescence lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref] [PubMed]

V. Venugopal, J. Chen, M. Barroso, and X. Intes, “Quantitative tomographic imaging of intermolecular FRET in small animals,” Biomed. Opt. Express 3(12), 3161–3175 (2012).
[Crossref] [PubMed]

Baumgartner, R.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. J. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed. Opt. 22(1), 16003 (2017).
[Crossref] [PubMed]

Benzi, M.

M. Benzi, “Preconditioning techniques for large linear systems: a survey,” J. Comput. Phys. 182(2), 418–477 (2002).
[Crossref]

Blackwell, T. R.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

Blessington, D.

Y. Chen, C. Mu, X. Intes, D. Blessington, and B. Chance, “Near-infrared phase cancellation instrument for fast and accurate localization of fluorescent heterogeneity,” Rev. Sci. Instrum. 74(7), 3466–3473 (2003).
[Crossref]

Boas, D. A.

Boyd, S.

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[Crossref]

Chance, B.

Chang, W. J.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. J. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed. Opt. 22(1), 16003 (2017).
[Crossref] [PubMed]

Chen, C. W.

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

Chen, J.

Chen, Y.

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics 4(1), 011009 (2016).
[Crossref] [PubMed]

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

Y. Chen, C. Mu, X. Intes, D. Blessington, and B. Chance, “Near-infrared phase cancellation instrument for fast and accurate localization of fluorescent heterogeneity,” Rev. Sci. Instrum. 74(7), 3466–3473 (2003).
[Crossref]

Cong, W.

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref] [PubMed]

L. Zhao, H. Yang, W. Cong, G. Wang, and X. Intes, “Lp regularization for early gate fluorescence molecular tomography,” Opt. Lett. 39(14), 4156–4159 (2014).
[Crossref] [PubMed]

Cullen, P. K.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. J. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed. Opt. 22(1), 16003 (2017).
[Crossref] [PubMed]

Dai, G.

M. S. Ozturk, V. K. Lee, L. Zhao, G. Dai, and X. Intes, “Mesoscopic fluorescence molecular tomography of reporter genes in bioprinted thick tissue,” J. Biomed. Opt. 18(10), 100501 (2013).
[Crossref] [PubMed]

L. Zhao, V. K. Lee, S.-S. Yoo, G. Dai, and X. Intes, “The integration of 3-D cell printing and mesoscopic fluorescence molecular tomography of vascular constructs within thick hydrogel scaffolds,” Biomaterials 33(21), 5325–5332 (2012).
[Crossref] [PubMed]

Dale, A. M.

Delvenne, J.-C.

M. T. Schaub, M. Trefois, P. van Dooren, and J.-C. Delvenne, “Sparse matrix factorizations for fast linear solvers with application to Laplacian systems,” SIAM J. Matrix Anal. Appl. 38(2), 505–529 (2017).
[Crossref]

Deng, X.

X. Deng, L. Yin, S. Peng, and M. Ding, “An iterative algorithm for solving ill-conditioned linear least squares problems,” Geod. Geodyn. 6(6), 453–459 (2015).
[Crossref]

Ding, M.

X. Deng, L. Yin, S. Peng, and M. Ding, “An iterative algorithm for solving ill-conditioned linear least squares problems,” Geod. Geodyn. 6(6), 453–459 (2015).
[Crossref]

Donoho, D. L.

D. L. Donoho, Y. Tsaig, I. Drori, and J. L. Starck, “Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit,” IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012).
[Crossref]

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via l minimization,” Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197–2202 (2003).
[Crossref] [PubMed]

Drori, I.

D. L. Donoho, Y. Tsaig, I. Drori, and J. L. Starck, “Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit,” IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012).
[Crossref]

Duarte-Carvajalino, J. M.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

Dunn, A. K.

Durkin, A. J.

S. H. Tseng, C. Hayakawa, J. Spanier, and A. J. Durkin, “Investigation of a probe design for facilitating the uses of the standard photon diffusion equation at short source-detector separations: Monte Carlo simulations,” J. Biomed. Opt. 14(5), 054043 (2009).
[Crossref] [PubMed]

Elad, M.

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via l minimization,” Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197–2202 (2003).
[Crossref] [PubMed]

Erzurumlu, R. S.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics 4(1), 011009 (2016).
[Crossref] [PubMed]

Fang, Q.

Fisher, J. P.

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

Gorinevsky, D.

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[Crossref]

Hayakawa, C.

S. H. Tseng, C. Hayakawa, J. Spanier, and A. J. Durkin, “Investigation of a probe design for facilitating the uses of the standard photon diffusion equation at short source-detector separations: Monte Carlo simulations,” J. Biomed. Opt. 14(5), 054043 (2009).
[Crossref] [PubMed]

Helmstetter, F. J.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. J. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed. Opt. 22(1), 16003 (2017).
[Crossref] [PubMed]

Hillman, E. M. C.

Holboke, M.

Intes, X.

F. Long and X. Intes, “Dental optical tomography with upconversion nanoparticles—a feasibility study,” J. Biomed. Opt. 22(6), 66001 (2017).
[Crossref] [PubMed]

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref] [PubMed]

F. Yang, M. S. Ozturk, R. Yao, and X. Intes, “Improving mesoscopic fluorescence molecular tomography through data reduction,” Biomed. Opt. Express 8(8), 3868–3881 (2017).
[Crossref] [PubMed]

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref] [PubMed]

R. Yao, Q. Pian, and X. Intes, “Wide-field fluorescence molecular tomography with compressive sensing based preconditioning,” Biomed. Opt. Express 6(12), 4887–4898 (2015).
[Crossref] [PubMed]

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for cancer application,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref] [PubMed]

L. Zhao, H. Yang, W. Cong, G. Wang, and X. Intes, “Lp regularization for early gate fluorescence molecular tomography,” Opt. Lett. 39(14), 4156–4159 (2014).
[Crossref] [PubMed]

M. S. Ozturk, D. Rohrbach, U. Sunar, and X. Intes, “Mesoscopic fluorescence tomography of a photosensitizer (HPPH) 3D biodistribution in skin cancer,” Acad. Radiol. 21(2), 271–280 (2014).
[Crossref] [PubMed]

M. S. Ozturk, V. K. Lee, L. Zhao, G. Dai, and X. Intes, “Mesoscopic fluorescence molecular tomography of reporter genes in bioprinted thick tissue,” J. Biomed. Opt. 18(10), 100501 (2013).
[Crossref] [PubMed]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-invasive in vivo imaging of near infrared-labeled transferrin in breast cancer cells and tumors using fluorescence lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref] [PubMed]

L. Zhao, V. K. Lee, S.-S. Yoo, G. Dai, and X. Intes, “The integration of 3-D cell printing and mesoscopic fluorescence molecular tomography of vascular constructs within thick hydrogel scaffolds,” Biomaterials 33(21), 5325–5332 (2012).
[Crossref] [PubMed]

V. Venugopal, J. Chen, M. Barroso, and X. Intes, “Quantitative tomographic imaging of intermolecular FRET in small animals,” Biomed. Opt. Express 3(12), 3161–3175 (2012).
[Crossref] [PubMed]

J. Chen, V. Venugopal, and X. Intes, “Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates,” Biomed. Opt. Express 2(4), 871–886 (2011).
[Crossref] [PubMed]

J. Chen and X. Intes, “Comparison of Monte Carlo methods for fluorescence molecular tomography-computational efficiency,” Med. Phys. 38(10), 5788–5798 (2011).
[Crossref] [PubMed]

Y. Chen, C. Mu, X. Intes, D. Blessington, and B. Chance, “Near-infrared phase cancellation instrument for fast and accurate localization of fluorescent heterogeneity,” Rev. Sci. Instrum. 74(7), 3466–3473 (2003).
[Crossref]

X. Intes, V. Ntziachristos, and B. Chance, “Analytical model for dual-interfering sources Diffuse Optical Tomography,” Opt. Express 10(1), 2–14 (2002).
[Crossref] [PubMed]

X. Intes, B. Chance, M. Holboke, and A. Yodh, “Interfering diffusive photon-density waves with an absorbing-fluorescent inhomogeneity,” Opt. Express 8(3), 223–231 (2001).
[Crossref] [PubMed]

Jacques, S. L.

Ji, R.

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[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]

A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, “Preconditioning of the fluorescence diffuse optical tomography sensing matrix based on compressive sensing,” Opt. Lett. 37(20), 4326–4328 (2012).
[Crossref] [PubMed]

Kim, S.-J.

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[Crossref]

Koh, K.

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[Crossref]

Kristine, G.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

Lee, V. K.

M. S. Ozturk, V. K. Lee, L. Zhao, G. Dai, and X. Intes, “Mesoscopic fluorescence molecular tomography of reporter genes in bioprinted thick tissue,” J. Biomed. Opt. 18(10), 100501 (2013).
[Crossref] [PubMed]

L. Zhao, V. K. Lee, S.-S. Yoo, G. Dai, and X. Intes, “The integration of 3-D cell printing and mesoscopic fluorescence molecular tomography of vascular constructs within thick hydrogel scaffolds,” Biomaterials 33(21), 5325–5332 (2012).
[Crossref] [PubMed]

Li, Q.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

Lin, J.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics 4(1), 011009 (2016).
[Crossref] [PubMed]

Liu, Q.

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 50902 (2013).
[Crossref] [PubMed]

Liu, Y.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics 4(1), 011009 (2016).
[Crossref] [PubMed]

Long, F.

F. Long and X. Intes, “Dental optical tomography with upconversion nanoparticles—a feasibility study,” J. Biomed. Opt. 22(6), 66001 (2017).
[Crossref] [PubMed]

Lustig, M.

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[Crossref]

Markel, V. A.

Mital, V.

Mu, C.

Y. Chen, C. Mu, X. Intes, D. Blessington, and B. Chance, “Near-infrared phase cancellation instrument for fast and accurate localization of fluorescent heterogeneity,” Rev. Sci. Instrum. 74(7), 3466–3473 (2003).
[Crossref]

Naphas, R.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

Nguyen, B. N.

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

Ntziachristos, V.

Ozturk, M. S.

F. Yang, M. S. Ozturk, R. Yao, and X. Intes, “Improving mesoscopic fluorescence molecular tomography through data reduction,” Biomed. Opt. Express 8(8), 3868–3881 (2017).
[Crossref] [PubMed]

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref] [PubMed]

M. S. Ozturk, D. Rohrbach, U. Sunar, and X. Intes, “Mesoscopic fluorescence tomography of a photosensitizer (HPPH) 3D biodistribution in skin cancer,” Acad. Radiol. 21(2), 271–280 (2014).
[Crossref] [PubMed]

M. S. Ozturk, V. K. Lee, L. Zhao, G. Dai, and X. Intes, “Mesoscopic fluorescence molecular tomography of reporter genes in bioprinted thick tissue,” J. Biomed. Opt. 18(10), 100501 (2013).
[Crossref] [PubMed]

Pashaie, R.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. J. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed. Opt. 22(1), 16003 (2017).
[Crossref] [PubMed]

Paul, T. W.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

Peng, S.

X. Deng, L. Yin, S. Peng, and M. Ding, “An iterative algorithm for solving ill-conditioned linear least squares problems,” Geod. Geodyn. 6(6), 453–459 (2015).
[Crossref]

Periasamy, A.

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-invasive in vivo imaging of near infrared-labeled transferrin in breast cancer cells and tumors using fluorescence lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref] [PubMed]

Pian, Q.

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref] [PubMed]

R. Yao, Q. Pian, and X. Intes, “Wide-field fluorescence molecular tomography with compressive sensing based preconditioning,” Biomed. Opt. Express 6(12), 4887–4898 (2015).
[Crossref] [PubMed]

Rajoria, S.

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for cancer application,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref] [PubMed]

Rohrbach, D.

M. S. Ozturk, D. Rohrbach, U. Sunar, and X. Intes, “Mesoscopic fluorescence tomography of a photosensitizer (HPPH) 3D biodistribution in skin cancer,” Acad. Radiol. 21(2), 271–280 (2014).
[Crossref] [PubMed]

Saad, Y.

Y. Saad and H. A. van der Vorst, “Iterative solution of linear systems in the 20th century,” J. Comput. Appl. Math. 123(1–2), 1–33 (2000).
[Crossref]

Sapiro, G.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

Schaub, M. T.

M. T. Schaub, M. Trefois, P. van Dooren, and J.-C. Delvenne, “Sparse matrix factorizations for fast linear solvers with application to Laplacian systems,” SIAM J. Matrix Anal. Appl. 38(2), 505–529 (2017).
[Crossref]

Schotland, J. C.

Sheikhzadeh, M.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. J. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed. Opt. 22(1), 16003 (2017).
[Crossref] [PubMed]

Sinsuebphon, N.

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref] [PubMed]

Spanier, J.

S. H. Tseng, C. Hayakawa, J. Spanier, and A. J. Durkin, “Investigation of a probe design for facilitating the uses of the standard photon diffusion equation at short source-detector separations: Monte Carlo simulations,” J. Biomed. Opt. 14(5), 054043 (2009).
[Crossref] [PubMed]

Starck, J. L.

D. L. Donoho, Y. Tsaig, I. Drori, and J. L. Starck, “Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit,” IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012).
[Crossref]

Sunar, U.

M. S. Ozturk, D. Rohrbach, U. Sunar, and X. Intes, “Mesoscopic fluorescence tomography of a photosensitizer (HPPH) 3D biodistribution in skin cancer,” Acad. Radiol. 21(2), 271–280 (2014).
[Crossref] [PubMed]

Tang, Q.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics 4(1), 011009 (2016).
[Crossref] [PubMed]

Trefois, M.

M. T. Schaub, M. Trefois, P. van Dooren, and J.-C. Delvenne, “Sparse matrix factorizations for fast linear solvers with application to Laplacian systems,” SIAM J. Matrix Anal. Appl. 38(2), 505–529 (2017).
[Crossref]

Tropp, J. A.

J. A. Tropp, “Greed is Good: Algorithmic Results for Sparse Approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

Tsaig, Y.

D. L. Donoho, Y. Tsaig, I. Drori, and J. L. Starck, “Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit,” IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012).
[Crossref]

Tseng, S. H.

S. H. Tseng, C. Hayakawa, J. Spanier, and A. J. Durkin, “Investigation of a probe design for facilitating the uses of the standard photon diffusion equation at short source-detector separations: Monte Carlo simulations,” J. Biomed. Opt. 14(5), 054043 (2009).
[Crossref] [PubMed]

Tsytsarev, V.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics 4(1), 011009 (2016).
[Crossref] [PubMed]

van der Vorst, H. A.

Y. Saad and H. A. van der Vorst, “Iterative solution of linear systems in the 20th century,” J. Comput. Appl. Math. 123(1–2), 1–33 (2000).
[Crossref]

van Dooren, P.

M. T. Schaub, M. Trefois, P. van Dooren, and J.-C. Delvenne, “Sparse matrix factorizations for fast linear solvers with application to Laplacian systems,” SIAM J. Matrix Anal. Appl. 38(2), 505–529 (2017).
[Crossref]

Venugopal, V.

Wang, G.

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref] [PubMed]

L. Zhao, H. Yang, W. Cong, G. Wang, and X. Intes, “Lp regularization for early gate fluorescence molecular tomography,” Opt. Lett. 39(14), 4156–4159 (2014).
[Crossref] [PubMed]

Wang, L.

Wierwille, J.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

Yang, F.

F. Yang, M. S. Ozturk, R. Yao, and X. Intes, “Improving mesoscopic fluorescence molecular tomography through data reduction,” Biomed. Opt. Express 8(8), 3868–3881 (2017).
[Crossref] [PubMed]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref] [PubMed]

Yang, H.

Yao, R.

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]

A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, “Preconditioning of the fluorescence diffuse optical tomography sensing matrix based on compressive sensing,” Opt. Lett. 37(20), 4326–4328 (2012).
[Crossref] [PubMed]

Yin, L.

X. Deng, L. Yin, S. Peng, and M. Ding, “An iterative algorithm for solving ill-conditioned linear least squares problems,” Geod. Geodyn. 6(6), 453–459 (2015).
[Crossref]

Yodh, A.

Yoo, S.-S.

L. Zhao, V. K. Lee, S.-S. Yoo, G. Dai, and X. Intes, “The integration of 3-D cell printing and mesoscopic fluorescence molecular tomography of vascular constructs within thick hydrogel scaffolds,” Biomaterials 33(21), 5325–5332 (2012).
[Crossref] [PubMed]

Yuan, S.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

Zhao, L.

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref] [PubMed]

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for cancer application,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref] [PubMed]

L. Zhao, H. Yang, W. Cong, G. Wang, and X. Intes, “Lp regularization for early gate fluorescence molecular tomography,” Opt. Lett. 39(14), 4156–4159 (2014).
[Crossref] [PubMed]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-invasive in vivo imaging of near infrared-labeled transferrin in breast cancer cells and tumors using fluorescence lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref] [PubMed]

M. S. Ozturk, V. K. Lee, L. Zhao, G. Dai, and X. Intes, “Mesoscopic fluorescence molecular tomography of reporter genes in bioprinted thick tissue,” J. Biomed. Opt. 18(10), 100501 (2013).
[Crossref] [PubMed]

L. Zhao, V. K. Lee, S.-S. Yoo, G. Dai, and X. Intes, “The integration of 3-D cell printing and mesoscopic fluorescence molecular tomography of vascular constructs within thick hydrogel scaffolds,” Biomaterials 33(21), 5325–5332 (2012).
[Crossref] [PubMed]

Zhu, C.

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 50902 (2013).
[Crossref] [PubMed]

Acad. Radiol. (1)

M. S. Ozturk, D. Rohrbach, U. Sunar, and X. Intes, “Mesoscopic fluorescence tomography of a photosensitizer (HPPH) 3D biodistribution in skin cancer,” Acad. Radiol. 21(2), 271–280 (2014).
[Crossref] [PubMed]

Ann. Biomed. Eng. (1)

M. S. Ozturk, C. W. Chen, R. Ji, L. Zhao, B. N. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref] [PubMed]

Biomaterials (1)

L. Zhao, V. K. Lee, S.-S. Yoo, G. Dai, and X. Intes, “The integration of 3-D cell printing and mesoscopic fluorescence molecular tomography of vascular constructs within thick hydrogel scaffolds,” Biomaterials 33(21), 5325–5332 (2012).
[Crossref] [PubMed]

Biomed. Opt. Express (4)

Curr. Mol. Imaging (1)

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for cancer application,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref] [PubMed]

Geod. Geodyn. (1)

X. Deng, L. Yin, S. Peng, and M. Ding, “An iterative algorithm for solving ill-conditioned linear least squares problems,” Geod. Geodyn. 6(6), 453–459 (2015).
[Crossref]

IEEE J. Sel. Top. Quant. (1)

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, T. W. Paul, and G. Kristine, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Top. Quant. 16(4), 755–766 (2010).
[Crossref]

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

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref] [PubMed]

IEEE Trans. Image Process. (2)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7), 1395–1408 (2009).
[Crossref] [PubMed]

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 (2)

D. L. Donoho, Y. Tsaig, I. Drori, and J. L. Starck, “Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit,” IEEE Trans. Inf. Theory 58(2), 1094–1121 (2012).
[Crossref]

J. A. Tropp, “Greed is Good: Algorithmic Results for Sparse Approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

J. Biomed. Opt. (5)

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F. Long and X. Intes, “Dental optical tomography with upconversion nanoparticles—a feasibility study,” J. Biomed. Opt. 22(6), 66001 (2017).
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M. S. Ozturk, V. K. Lee, L. Zhao, G. Dai, and X. Intes, “Mesoscopic fluorescence molecular tomography of reporter genes in bioprinted thick tissue,” J. Biomed. Opt. 18(10), 100501 (2013).
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Med. Phys. (1)

J. Chen and X. Intes, “Comparison of Monte Carlo methods for fluorescence molecular tomography-computational efficiency,” Med. Phys. 38(10), 5788–5798 (2011).
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Nat. Photonics (1)

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
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Neurophotonics (1)

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics 4(1), 011009 (2016).
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Other (2)

M. S. Ozturk, X. Intes, G. dai, and V. K. Lee, “Longitudinal Volumetric Assessment of Glioblastoma Brain Tumor in 3D Bio-Printed Environment by Mesoscopic Fluorescence Molecular Tomography,” in Biomedical Optics 2016, OSA Technical Digest (online) (Optical Society of America, 2016), paper JM3A.46.

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of scanning mode of the 2nd generation MFMT system. (a) displays the discretization of imaging volume. (b) shows the dimension of the emCCD with super pixels (blue squares) binned by 2 × 2 pixels(red squares) used as detectors. (c) and (d) illustrate the scanning trajectory (blue dash) from start scanning spot (c) to the last one (d).
Fig. 2
Fig. 2 The numerical phantom designed to mimic a bio-printed vascular channel and sprouting capillaries. (a), (b) and (c) are the full view, xy view, and xz view of the phantom, respectively.
Fig. 3
Fig. 3 Curves of the normalized products (a) and cumulative coherence (b) before and after applying the preconditioner on whole sensitivity matrix and block by block sensitivity matrix.
Fig. 4
Fig. 4 Reconstruction results and evaluation metrics before and after applying preconditioning. (a) shows the metrics of reconstructions of non-pre and whole-pre at different SNR levels. (b) shows the metrics of reconstructions of whole-pre and sub-pre at different SNR levels. (c-e) display the 3-D reconstruction of non-pre, whole-pre and sub-pre, respectively.
Fig. 5
Fig. 5 Comparison of convergence rate and visual reconstruction results among four scenarios without and with WIIM embedded in them. (a-c) plots the convergence rate and iteration number of the scenarios at three noise levels, respectively. (d-f) visualize the reconstruction of three scenarios at SNR of 4, respectively.
Fig. 6
Fig. 6 Experimental phantom (a-c) are the x-y, x-z cross-sectional, and 3D view of phantom obtained from micro-MRI, overlaid with the best reconstruction result, respectively.
Fig. 7
Fig. 7 Reconstruction results of experimental phantom. (a) L-curve for experimental data to determine the optimal regularization parameter when applying sub-preconditioning. (b-d) are results without preconditioning, with whole-pre and WIIM, and with sub-pre and WIIM, respectively. (e) is the result when applying sub-pre, WIIM and noise suppression on the experimental phantom .

Tables (2)

Tables Icon

Table 1 Quantification results of the preconditioning for numerical data (Targeted tolerance = 10−3, Preset max Iteration = 9,000)

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Table 2 Quantification results of the preconditioning for experimental data (Targeted tolerance = 10−3, Preset max Iteration = 9,000, SNR = 4)

Equations (22)

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W( r s , r d ,r)= G x ( r s ,r) × G m (r, r d )
U( r s , r d )= Ω W( r s , r d ,r)η(r)d r 3
AX=b
min { AX-b 2 2 X 1
A pre = M A A
A pre T A pre = A T M A T M A A I
A A p r e T A p r e A T = A A T M A T M A A A T A A T
( Σ A Σ A T ) U A T M A T M A U A ( Σ A Σ A T ) Σ A Σ A T
M A = ( Σ A Σ A T ) 1 2 U A T
M A = ( Σ A Σ A T + ϵ I ) 1 2 U A T
( Λ + γ I ) x k + 1 = y + γ x k
γ γ + δ 2 0.1 , ( γ > 0 )
{ γ = β 10 0.5 | log ( β ) | + 1 β = min ( | e i g ( Λ ) |
( Λ + γ I ) e k = r k
δ x x c o n d ( A ) δ b b
M ( A ) = p , q , p q m a x | a p , a q | a p 2 a q 2
M 1 ( k , A ) = p m a x | Q | = k , p Q m a x p Q | a p , a q | a p 2 a q 2
SNR = μ ( | S f S b | ) σ ( | S b S r | )
nSSD ( A , B ) = 1 1 N i = 1 R j = 1 C k = 1 Z [ A ( i , j , k ) B ( i , j , k ) ] 2
nSAD ( A , B ) = 1 1 N i = 1 R j = 1 C k = 1 Z | A ( i , j , k ) B ( i , j , k ) |
nR= i = 1 R j = 1 C k = 1 Z A ( i , j , k ) × B ( i , j , k ) i = 1 R j = 1 C k = 1 Z A ( i , j , k ) 2 × i = 1 R j = 1 C k = 1 Z B ( i , j , k ) 2
nD = 1 1 N i = 1 R j = 1 C k = 1 Z A ( i , j , k ) B ( i , j , k )

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