Abstract

In this paper we study an l1-regularized multilevel approach for bioluminescence tomography based on radiative transfer equation with the emphasis on improving imaging resolution and reducing computational time. Simulations are performed to validate that our algorithms are potential for efficient high-resolution imaging. Besides, we study and compare reconstructions with boundary angular-averaged data, boundary angular-resolved data and internal angular-averaged data respectively.

© 2010 OSA

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    [CrossRef]

2009

H. Gao and H. K. Zhao, “A fast forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38(3), 149–192 (2009).
[CrossRef]

Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17(10), 8062–8080 (2009).
[CrossRef]

T. Goldstein and S. Osher, “The split bregman method for l1 regularized problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
[CrossRef]

J. Yang, Y. Zhang, and W. Yin, “An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise,” SIAM J. Sci. Comput. 31(4), 2842–2865 (2009).
[CrossRef]

2008

W. Yin, S. Osher, D. Goldfarb, and J. Darbon, “Bregman iterative algorithms for l1-minimization with applications to compressed sensing,” SIAM J. Imaging Sciences 1(1), 143–168 (2008).
[CrossRef]

M. Boffety, M. Allain, A. Sentenac, M. Massonneau, and R. Carminati, “Analysis of the depth resolution limit of luminescence diffuse optical imaging,” Opt. Lett. 33(20), 2290–2292 (2008).
[CrossRef]

P. Stefanov and G. Uhlmann, “An inverse source problem in optical molecular imaging,” Analysis and PDE 1, 115–126 (2008).

A. Charette, J. Boulanger, and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2743–2766 (2008).
[CrossRef]

E. J. Candes and M. B. Wakin, “A introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

2007

V. Markel and J. Schotland, “Fourier-laplace structure of the linearized inverse scattering problem for the radiative transport equation,” Inv. Prob. Imag. 1, 181–189 (2007).

Y. Lv, J. Tian, W. Cong, and G. Wang, “Experimental study on bioluminescence tomography with multimodality fusion,” Int. J. Biomed. Imaging 2007, 86741 (2007).
[CrossRef]

G. Bal and A. Tamasan, “Inverse source problems in transport equations,” SIAM J. Math. Anal. 39(1), 57–76 (2007).
[CrossRef]

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]

2006

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101–1-041101–22 (2006).

Y. Lv, J. Tian, W. X. Cong, G. Wang, J. Luo, W. Yang, H. Li, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006).
[CrossRef]

E. J. Candes and T. Tao, “Near optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[CrossRef]

P. Zhao and B. Yu, “On model selection consistency of Lasso,” J. Mach. Learn. Res. 7, 2541–2563 (2006).

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

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[CrossRef]

E. J. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[CrossRef]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. McLennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14(17), 7801–7809 (2006).
[CrossRef]

G. Wang, X. Qian, W. Cong, H. Shen, Y. Li, W. Han, K. Durairaj, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo, “Recent development in bioluminescence tomography,” Current Medical Imaging Reviews 2(4), 453–457 (2006).
[CrossRef]

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, “The first bioluminescence tomography system for simultaneous acquisition of multi-view and multi-spectral data,” Int. J. Biomed. Imaging 2006, 1–8 (2006).
[CrossRef]

2005

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[CrossRef]

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. Wang, E. Hoffman, G. McLennan, P. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005).
[CrossRef]

C. Kuo, O. Coquoz, T. Troy, D. Zwarg, and B. Rice, “Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system,” Mol. Imaging 4, 370 (2005).

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]

E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[CrossRef]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202(1), 323–345 (2005).
[CrossRef]

2004

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
[CrossRef]

X. Gu, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12(17), 3996–4000 (2004).
[CrossRef]

2003

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

2002

C. H. Contag and B. D. Ross, “It’s not just about anatomy: in vivo bioluminescence imaging as an eyepiece into biology,” J. Magn. Reson. Imaging 16(4), 378–387 (2002).
[CrossRef]

2001

R. Weissleder and U. U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).

1999

A. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[CrossRef]

1996

R. Tibshirani, “Regression shrinkage and selection via the Lasso,” J. R. Stat. Soc., B 58, 267–288 (1996).

1995

K. D. Paulsen, P. M. Meaney, M. J. Moskowitz, and J. R. Sullivan, “A dual mesh scheme for finite element based reconstruction algorithms,” IEEE Trans. Med. Imaging 14(3), 504–514 (1995).
[CrossRef]

1994

Z. Tao, N. J. McCormick, and R. Sanchez, “Ocean source and optical property estimation from explicit and implicit algorithms,” Appl. Opt. 33(15), 3265 (1994).
[CrossRef]

1993

A. N. Panchenko, “Inverse source problem of radiative transfer: a special case of the attenuated Radon transform,” Inverse Probl. 9(2), 321–337 (1993).
[CrossRef]

C. E. Siewert, “An inverse source problem in radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 50(6), 603–609 (1993).
[CrossRef]

1992

N. J. McCormick, “Inverse radiative transfer problems: a review,” Nucl. Sci. Eng. 112, 185–198 (1992).

1963

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963).
[CrossRef]

1944

K. Levenberg, “A method for the solution of certain nonlinear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

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]

Allain, M.

M. Boffety, M. Allain, A. Sentenac, M. Massonneau, and R. Carminati, “Analysis of the depth resolution limit of luminescence diffuse optical imaging,” Opt. Lett. 33(20), 2290–2292 (2008).
[CrossRef]

Arridge, A. R.

A. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[CrossRef]

Bading, J. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[CrossRef]

Bal, G.

G. Bal and A. Tamasan, “Inverse source problems in transport equations,” SIAM J. Math. Anal. 39(1), 57–76 (2007).
[CrossRef]

Boffety, M.

M. Boffety, M. Allain, A. Sentenac, M. Massonneau, and R. Carminati, “Analysis of the depth resolution limit of luminescence diffuse optical imaging,” Opt. Lett. 33(20), 2290–2292 (2008).
[CrossRef]

Boulanger, J.

A. Charette, J. Boulanger, and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2743–2766 (2008).
[CrossRef]

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]

Candes, E. J.

E. J. Candes and M. B. Wakin, “A introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[CrossRef]

E. J. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

E. J. Candes and T. Tao, “Near optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[CrossRef]

E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[CrossRef]

Carminati, R.

M. Boffety, M. Allain, A. Sentenac, M. Massonneau, and R. Carminati, “Analysis of the depth resolution limit of luminescence diffuse optical imaging,” Opt. Lett. 33(20), 2290–2292 (2008).
[CrossRef]

Chan, T. F.

Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17(10), 8062–8080 (2009).
[CrossRef]

Charette, A.

A. Charette, J. Boulanger, and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2743–2766 (2008).
[CrossRef]

Chatziioannou, A. F.

Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17(10), 8062–8080 (2009).
[CrossRef]

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]

Chaudhari, A. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[CrossRef]

Cheng, J.

G. Wang, X. Qian, W. Cong, H. Shen, Y. Li, W. Han, K. Durairaj, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo, “Recent development in bioluminescence tomography,” Current Medical Imaging Reviews 2(4), 453–457 (2006).
[CrossRef]

Cherry, S. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[CrossRef]

Cong, A.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. Wang, E. Hoffman, G. McLennan, P. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005).
[CrossRef]

Cong, W.

Y. Lv, J. Tian, W. Cong, and G. Wang, “Experimental study on bioluminescence tomography with multimodality fusion,” Int. J. Biomed. Imaging 2007, 86741 (2007).
[CrossRef]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. McLennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14(17), 7801–7809 (2006).
[CrossRef]

G. Wang, X. Qian, W. Cong, H. Shen, Y. Li, W. Han, K. Durairaj, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo, “Recent development in bioluminescence tomography,” Current Medical Imaging Reviews 2(4), 453–457 (2006).
[CrossRef]

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, “The first bioluminescence tomography system for simultaneous acquisition of multi-view and multi-spectral data,” Int. J. Biomed. Imaging 2006, 1–8 (2006).
[CrossRef]

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. Wang, E. Hoffman, G. McLennan, P. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005).
[CrossRef]

Cong, W. X.

Y. Lv, J. Tian, W. X. Cong, G. Wang, J. Luo, W. Yang, H. Li, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006).
[CrossRef]

Contag, C. H.

C. H. Contag and B. D. Ross, “It’s not just about anatomy: in vivo bioluminescence imaging as an eyepiece into biology,” J. Magn. Reson. Imaging 16(4), 378–387 (2002).
[CrossRef]

Conti, P. S.

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