Comparative studies of l_{p}-regularization-based reconstruction algorithms for bioluminescence tomography |
Biomedical Optics Express, Vol. 3, Issue 11, pp. 2916-2936 (2012)
http://dx.doi.org/10.1364/BOE.3.002916
Acrobat PDF (5004 KB)
Abstract
Inverse source reconstruction is the most challenging aspect of bioluminescence tomography (BLT) because of its ill-posedness. Although many efforts have been devoted to this problem, so far, there is no generally accepted method. Due to the ill-posedness property of the BLT inverse problem, the regularization method plays an important role in the inverse reconstruction. In this paper, six reconstruction algorithms based on l_{p} regularization are surveyed. The effects of the permissible source region, measurement noise, optical properties, tissue specificity and source locations on the performance of the reconstruction algorithms are investigated using a series of single source experiments. In order to further inspect the performance of the reconstruction algorithms, we present the double sources and the in vivo mouse experiments to study their resolution ability and potential for a practical heterogeneous mouse experiment. It is hoped to provide useful guidance on algorithm development and application in the related fields.
© 2012 OSA
1. Introduction
1. R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008). [CrossRef] [PubMed]
5. 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] [PubMed]
5. 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] [PubMed]
6. G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004). [CrossRef] [PubMed]
9. G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, “Overview of bioluminescence tomography--a new molecular imaging modality,” Front. Biosci. 13(13), 1281–1293 (2008). [CrossRef] [PubMed]
3. M. Rodriguez-Porcel, J. Wu, and S. Gambhir, “Molecular imaging of stem cells,” in StemBook [Internet] (Harvard Stem Cell Institute,Cambridge, MA, 2008), available from http://www.ncbi.nlm.nih.gov/books/NBK27079/
8. W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005). [CrossRef] [PubMed]
10. 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] [PubMed]
28. Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the l_{p} regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012). [CrossRef]
10. 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] [PubMed]
14. H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008). [CrossRef] [PubMed]
16. C. Qin, J. Tian, X. Yang, J. Feng, K. Liu, J. Liu, G. Yan, S. Zhu, and M. Xu, “Adaptive improved element free Galerkin method for quasi- or multi-spectral bioluminescence tomography,” Opt. Express 17(24), 21925–21934 (2009). [CrossRef] [PubMed]
17. 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] [PubMed]
15. J. Feng, K. Jia, C. Qin, G. Yan, S. Zhu, X. Zhang, J. Liu, and J. Tian, “Three-dimensional bioluminescence tomography based on Bayesian approach,” Opt. Express 17(19), 16834–16848 (2009). [CrossRef] [PubMed]
18. H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization,” Opt. Express 18(3), 1854–1871 (2010). [CrossRef] [PubMed]
26. Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun. 284(24), 5871–5876 (2011). [CrossRef]
29. D. Donoho, “Compresse sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006). [CrossRef]
17. 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] [PubMed]
22. W. Cong and G. Wang, “Bioluminescence tomography based on the phase approximation model,” J. Opt. Soc. Am. A 27(2), 174–179 (2010). [CrossRef] [PubMed]
24. X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, “Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method,” Int. J. Biomed. Imaging 2011, 203537 (2011). [CrossRef] [PubMed]
26. Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun. 284(24), 5871–5876 (2011). [CrossRef]
22. W. Cong and G. Wang, “Bioluminescence tomography based on the phase approximation model,” J. Opt. Soc. Am. A 27(2), 174–179 (2010). [CrossRef] [PubMed]
24. X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, “Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method,” Int. J. Biomed. Imaging 2011, 203537 (2011). [CrossRef] [PubMed]
26. Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun. 284(24), 5871–5876 (2011). [CrossRef]
33. D. Donoho, “For most large underdetermined systems of linear equations the minimal l1-norm near solution is also the sparest solution,” Commun. Pure Appl. Math. 59(6), 797–829 (2006). [CrossRef]
34. Z. Xu, H. Zhang, Y. Wang, X. Chang, and L. Yong, “L1/2 regularization,” Sci. China Inform. Sci. 53(6), 1159–1169 (2010). [CrossRef]
34. Z. Xu, H. Zhang, Y. Wang, X. Chang, and L. Yong, “L1/2 regularization,” Sci. China Inform. Sci. 53(6), 1159–1169 (2010). [CrossRef]
36. M. Wei, W. Scott, J. James, H. McClellan, and G. Larson, “Estimation of the discrete spectrum of relaxations for electromagnetic induction responses using l_{p}-regularized least squares for 0 ≤ p ≤ 1,” IEEE Geosci. Remote Sens. Lett. 8(2), 233–237 (2011). [CrossRef]
28. Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the l_{p} regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012). [CrossRef]
27. X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010). [CrossRef] [PubMed]
25. X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18(24), 24825–24841 (2010). [CrossRef] [PubMed]
24. X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, “Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method,” Int. J. Biomed. Imaging 2011, 203537 (2011). [CrossRef] [PubMed]
26. Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun. 284(24), 5871–5876 (2011). [CrossRef]
28. Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the l_{p} regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012). [CrossRef]
2. Methodology
2.1. Inverse reconstruction formula of BLT
37. M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009). [CrossRef] [PubMed]
8. W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005). [CrossRef] [PubMed]
38. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11), 1779–1792 (1995). [CrossRef] [PubMed]
8. W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005). [CrossRef] [PubMed]
39. Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006). [CrossRef] [PubMed]
2.2. Regularization methods
2.2.1. Tikhonov regularization
40. A. Ribés and F. Schmitt, “Linear inverse problems in imaging,” IEEE Signal Process. Mag. 25(4), 84–99 (2008). [CrossRef]
2.2.2. Truncated Total Least Squares Method
27. X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010). [CrossRef] [PubMed]
2.2.3. Incomplete Variables Truncated Conjugate Gradient (IVTCG) Method
25. X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18(24), 24825–24841 (2010). [CrossRef] [PubMed]
2.2.4. Truncated Newton interior-point method (TNIPM)
24. X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, “Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method,” Int. J. Biomed. Imaging 2011, 203537 (2011). [CrossRef] [PubMed]
2.2.5. Primal-dual interior-point method (PDIP)
26. Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun. 284(24), 5871–5876 (2011). [CrossRef]
26. Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun. 284(24), 5871–5876 (2011). [CrossRef]
2.2.6. Weighted iterative shrinkage/thresholding algorithm
28. Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the l_{p} regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012). [CrossRef]
28. Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the l_{p} regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012). [CrossRef]
3. Experiments and results
3.1. Numerical Experiments
3.1.1. Reconstruction in a single source
39. Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006). [CrossRef] [PubMed]
1. Reconstruction using different permissible source regions
2. Reconstruction at different measurement noise levels
41. R. Han, J. Liang, X. Qu, Y. Hou, N. Ren, J. Mao, and J. Tian, “A source reconstruction algorithm based on adaptive hp-FEM for bioluminescence tomography,” Opt. Express 17(17), 14481–14494 (2009). [CrossRef] [PubMed]
3. Reconstruction using different optical parameters
4. Reconstruction in tissue specificity
5. Reconstruction at different source locations
3.1.2. Reconstruction of double sources
3.2. In vivo mouse experiment
26. Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun. 284(24), 5871–5876 (2011). [CrossRef]
4. Discussion and Conclusions
Acknowledgments
References and links
1. | R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008). [CrossRef] [PubMed] |
2. | G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. F. Meinel, “Development of the first bioluminescence CT scanner,” Radiology 229(P), 566 (2003). |
3. | M. Rodriguez-Porcel, J. Wu, and S. Gambhir, “Molecular imaging of stem cells,” in StemBook [Internet] (Harvard Stem Cell Institute,Cambridge, MA, 2008), available from http://www.ncbi.nlm.nih.gov/books/NBK27079/ |
4. | F. S. Azar and X. Intes, Translational Multimodality Optical Imaging (Artech House, 2008), Chap. 17. |
5. | 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] [PubMed] |
6. | G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004). [CrossRef] [PubMed] |
7. | 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] [PubMed] |
8. | W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005). [CrossRef] [PubMed] |
9. | G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, “Overview of bioluminescence tomography--a new molecular imaging modality,” Front. Biosci. 13(13), 1281–1293 (2008). [CrossRef] [PubMed] |
10. | 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] [PubMed] |
11. | 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] [PubMed] |
12. | Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52(15), 4497–4512 (2007). [CrossRef] [PubMed] |
13. | J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16(20), 15640–15654 (2008). [CrossRef] [PubMed] |
14. | H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008). [CrossRef] [PubMed] |
15. | J. Feng, K. Jia, C. Qin, G. Yan, S. Zhu, X. Zhang, J. Liu, and J. Tian, “Three-dimensional bioluminescence tomography based on Bayesian approach,” Opt. Express 17(19), 16834–16848 (2009). [CrossRef] [PubMed] |
16. | C. Qin, J. Tian, X. Yang, J. Feng, K. Liu, J. Liu, G. Yan, S. Zhu, and M. Xu, “Adaptive improved element free Galerkin method for quasi- or multi-spectral bioluminescence tomography,” Opt. Express 17(24), 21925–21934 (2009). [CrossRef] [PubMed] |
17. | 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] [PubMed] |
18. | H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization,” Opt. Express 18(3), 1854–1871 (2010). [CrossRef] [PubMed] |
19. | H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation part 2: total variation and l1 data fidelity,” Opt. Express 18(3), 2894–2912 (2010). [CrossRef] [PubMed] |
20. | K. Liu, J. Tian, Y. Lu, C. Qin, X. Yang, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18(4), 3732–3745 (2010). [CrossRef] [PubMed] |
21. | B. Zhang, X. Yang, C. Qin, D. Liu, S. Zhu, J. Feng, L. Sun, K. Liu, D. Han, X. Ma, X. Zhang, J. Zhong, X. Li, X. Yang, and J. Tian, “A trust region method in adaptive finite element framework for bioluminescence tomography,” Opt. Express 18(7), 6477–6491 (2010). [CrossRef] [PubMed] |
22. | W. Cong and G. Wang, “Bioluminescence tomography based on the phase approximation model,” J. Opt. Soc. Am. A 27(2), 174–179 (2010). [CrossRef] [PubMed] |
23. | H. Huang, X. Qu, J. Liang, X. He, X. Chen, D. Yang, and J. Tian, “A multi-phase level set framework for source reconstruction in bioluminescence tomography,” J. Comput. Phys. 229(13), 5246–5256 (2010). [CrossRef] |
24. | X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, “Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method,” Int. J. Biomed. Imaging 2011, 203537 (2011). [CrossRef] [PubMed] |
25. | X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18(24), 24825–24841 (2010). [CrossRef] [PubMed] |
26. | Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun. 284(24), 5871–5876 (2011). [CrossRef] |
27. | X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010). [CrossRef] [PubMed] |
28. | Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the l_{p} regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012). [CrossRef] |
29. | D. Donoho, “Compresse sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006). [CrossRef] |
30. | E. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians (ICM, 2006), pp. 1433–1452. |
31. | H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Springer, 2000). |
32. | A. N. Tikhonov, “Solution of incorrectly formulated problems and the regularization method,” Soviet Math. Dokl. 4, 1035–1038 (1963). |
33. | D. Donoho, “For most large underdetermined systems of linear equations the minimal l1-norm near solution is also the sparest solution,” Commun. Pure Appl. Math. 59(6), 797–829 (2006). [CrossRef] |
34. | Z. Xu, H. Zhang, Y. Wang, X. Chang, and L. Yong, “L1/2 regularization,” Sci. China Inform. Sci. 53(6), 1159–1169 (2010). [CrossRef] |
35. | X. Chen, F. Xu, and Y. Ye, “Lower bound theory of nonzero entries in solutions of l_{2}-l_{p} minimization,” SIAM J. Sci. Comput. 32(5), 2832–2852 (2010). [CrossRef] |
36. | M. Wei, W. Scott, J. James, H. McClellan, and G. Larson, “Estimation of the discrete spectrum of relaxations for electromagnetic induction responses using l_{p}-regularized least squares for 0 ≤ p ≤ 1,” IEEE Geosci. Remote Sens. Lett. 8(2), 233–237 (2011). [CrossRef] |
37. | M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009). [CrossRef] [PubMed] |
38. | M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11), 1779–1792 (1995). [CrossRef] [PubMed] |
39. | Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006). [CrossRef] [PubMed] |
40. | A. Ribés and F. Schmitt, “Linear inverse problems in imaging,” IEEE Signal Process. Mag. 25(4), 84–99 (2008). [CrossRef] |
41. | R. Han, J. Liang, X. Qu, Y. Hou, N. Ren, J. Mao, and J. Tian, “A source reconstruction algorithm based on adaptive hp-FEM for bioluminescence tomography,” Opt. Express 17(17), 14481–14494 (2009). [CrossRef] [PubMed] |
OCIS Codes
(100.3190) Image processing : Inverse problems
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.6960) Medical optics and biotechnology : Tomography
ToC Category:
Image Reconstruction and Inverse Problems
History
Original Manuscript: August 15, 2012
Revised Manuscript: October 18, 2012
Manuscript Accepted: October 19, 2012
Published: October 23, 2012
Citation
Qitan Zhang, Xueli Chen, Xiaochao Qu, Jimin Liang, and Jie Tian, "Comparative studies of l_{p}-regularization-based
reconstruction algorithms for bioluminescence tomography," Biomed. Opt. Express 3, 2916-2936 (2012)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-11-2916
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References
- R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature452(7187), 580–589 (2008). [CrossRef] [PubMed]
- G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. F. Meinel, “Development of the first bioluminescence CT scanner,” Radiology229(P), 566 (2003).
- M. Rodriguez-Porcel, J. Wu, and S. Gambhir, “Molecular imaging of stem cells,” in StemBook [Internet] (Harvard Stem Cell Institute,Cambridge, MA, 2008), available from http://www.ncbi.nlm.nih.gov/books/NBK27079/
- F. S. Azar and X. Intes, Translational Multimodality Optical Imaging (Artech House, 2008), Chap. 17.
- 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. Express14(17), 7801–7809 (2006). [CrossRef] [PubMed]
- G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys.31(8), 2289–2299 (2004). [CrossRef] [PubMed]
- X. Gu, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express12(17), 3996–4000 (2004). [CrossRef] [PubMed]
- W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express13(18), 6756–6771 (2005). [CrossRef] [PubMed]
- G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, “Overview of bioluminescence tomography--a new molecular imaging modality,” Front. Biosci.13(13), 1281–1293 (2008). [CrossRef] [PubMed]
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