An efficient numerical method for general Lp regularization in fluorescence molecular tomography

IEEE Transactions on Medical Imaging

Volumn 29, Issue 4, 2010, Pages 1075-1087

  Baritaux, Jean Charles ^a   Hassler, Kai ^b   Unser, Michael ^a  

^a EPFL   (Switzerland)

^b SCANCO MEDICAL AG   (Switzerland)

Author keywords

Fluorescence; Image reconstruction; Optical tomography

Indexed keywords

COMPUTATIONAL COSTS; EFFICIENT NUMERICAL METHOD; FLUORESCENCE IMAGE; FLUORESCENCE MOLECULAR TOMOGRAPHY; FLUORESCENCE TOMOGRAPHY; ILL-POSEDNESS; MATRIX; NUMERICAL PROBLEMS; PHANTOM EXPERIMENT; RECONSTRUCTION ALGORITHMS; RECONSTRUCTION PROBLEMS; REDUCED MEMORY;

ALGORITHMS; COMPUTATIONAL EFFICIENCY; COST REDUCTION; FLUORESCENCE; IMAGE RECONSTRUCTION; OPTICAL TOMOGRAPHY; REPAIR;

THREE DIMENSIONAL;

ALGORITHM; ARTICLE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; FLUORESCENCE MICROSCOPY; GENETIC PROCEDURES; IMAGE ENHANCEMENT; METHODOLOGY; OPTICAL TOMOGRAPHY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; THREE DIMENSIONAL IMAGING;

ALGORITHMS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; MICROSCOPY, FLUORESCENCE; MOLECULAR PROBE TECHNIQUES; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; TOMOGRAPHY, OPTICAL;

EID: 77950406738     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2010.2042814     Document Type: Article

References (43)

1. S. R. Cherry, "In vivo molecular and genomic imaging: New challenges for imaging physics," Phys. Med. Biol., vol.49, no.3, pp. R13-R48, 2004.
2. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: The evolution of whole-body photonic imaging," Nat. Biotech., vol.23, pp. 313-320, Mar. 2005. (Pubitemid 41094419)
3. J. Rao, A. Dragulescu-Andrasi, and H. Yao, "Fluorescence imaging in vivo: Recent advances," Current Opin. Biotechnol., vol.18, no.1, pp. 17-25, 2007. (Pubitemid 46237739)
4. M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, "Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo," Proc. Nat. Acad. Sci., vol.105, no.49, pp. 19126-19131, 2008.
5. J. Haller, D. Hyde, N. Deliolanis, R. de Kleine, M. Niedre, and V. Ntzi-achristos, "Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging," J. Appl. Physiol., vol.104, no.3, pp. 795-802, 2008. (Pubitemid 351468809)
6. K. M. Kozloff, R. Weissleder, and U. Mahmood, "Noninvasive optical detection of bone mineral," J. Bone Mineral Res., vol.22, no.8, pp. 1208-1216, 2007. (Pubitemid 351339703)
7. A. H. Hielscher, "Optical tomographic imaging of small animals," Current Opin. Biotechnol., vol.16, no.1, pp. 79-88, 2005, Analytical biotechnology.
8. V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, "Concur-rent MRI and diffuse optical tomography of breast after indocyanine green enhancement," Proc. Nat. Acad. Sci. USA, vol.97, no.6, pp. 2767-2772, 2000. (Pubitemid 30159246)
9. A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, "Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans," Opt. Express, vol.15, no.11, pp. 6696-6716, 2007. (Pubitemid 46827669)
10. Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, "Frequency- domain optical imaging of absorption and scattering distributions by a born iterative method," J. Opt. Soc. Am. A, vol.14, no.1, pp. 325-342, 1997. (Pubitemid 127573831)
11. A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, "Fluorescence optical diffusion tomography," Appl. Opt., vol.42, no.16, pp. 3081-3094, 2003.
12. A. Joshi, W. Bangerth, and E. Sevick-Muraca, "Adaptive finite element based tomography for fluorescence optical imaging in tissue," Opt. Express, vol.12, no.22, pp. 5402-5417, 2004.
13. R. Roy and E. Sevick-Muraca, "Truncated newton's optimization scheme forabsorption and fluorescence optical tomography: Part I Theory and formulation," Opt. Express, vol.4, no.10, pp. 353-371, 1999.
14. R. Roy and E. Sevick-Muraca, "Truncated newton's optimization scheme for absorption and fluorescence optical tomography: Part II Reconstruction from synthetic measurements," Opt. Express, vol.4, no.10, pp. 372-382, 1999.
15. D. T. Delpy, M. Schweiger, and S. R. Arridge, "Application of the finite-element method for the forward and inverse models in optical tomography," J. Math. Imag. Vis., vol.3, pp. 263-283, 1993.
16. K. D. Paulsen and H. Jiang, "Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization," Appl. Opt., vol.35, no.19, pp. 3447-3458, 1996. (Pubitemid 126622158)
17. H. Jiang, "Frequency-domain fluorescent diffusion tomography: A fi-nite-element-based algorithm and simulations," Appl. Opt., vol.37, no.22, pp. 5337-5343, 1998. (Pubitemid 128658563)
18. A. D. Klose and A. H. Hielscher, "Fluorescence tomography with sim-ulated data based on the equation of radiative transfer," Opt. Lett., vol.28, no.12, pp. 1019-1021, 2003.
19. A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Computat. Phys., vol.202, no.1, pp. 323-345, 2005. (Pubitemid 39518860)
20. R. Roy and E. Sevick-Muraca, "A numerical study of gradient-based nonlinear optimization methods for contrast enhanced optical tomog-raphy," Opt. Express, vol.9, no.1, pp. 49-65, 2001.
21. A. Cong and G. Wang, "A finite-element-based reconstruction method for 3-D fluorescence tomography," Opt. Express, vol.13, no.24, pp. 9847-9857, 2005. (Pubitemid 41692757)
22. R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, "A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient," Phys. Med. Biol., vol.45, no.4, pp. 1051-1070, 2000. (Pubitemid 30196395)
23. R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluores-cence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imag., vol.23, no.4, pp. 492-500, Apr. 2004.
24. V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, "Fluorescence lifetime imaging by using time-gated data acquisition," Appl. Opt., vol.46, no.30, pp. 7384-7391, 2007.
25. L. Hervé, A. Koenig, A. Da Silva, M. Berger, J. Boutet, J. M. Dinten, P. Peltié, and P. Rizo, "Noncontact fluorescence diffuse optical to-mography of heterogeneous media," Appl. Opt., vol.46, no.22, pp. 4896-4906, 2007. (Pubitemid 47632043)
26. A. M. Bruckstein, D. L. Donoho, and M. Elad, "From sparse solutions of systems of equations to sparse modeling of signals and images," SIAM Rev., vol.51, no.1, pp. 34-81, 2009.
27. T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 2000.
28. N. Cao, A. Nehorai, and M. Jacobs, "Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-max-imization algorithm," Opt. Express, vol.15, no.21, pp. 13695-13708, 2007. (Pubitemid 47608583)
29. 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., vol.46, no.10, pp. 1679-1685, 2007. (Pubitemid 46659534)
30. S. R. Arridge and M. Schweiger, "Photon-measurement density func-tions. Part 2: Finite-element-method calculations," Appl. Opt., vol.34, no.34, p. 8026, 1995.
31. A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based it-erative image reconstruction scheme for time-resolved optical tomog-raphy," IEEE Trans. Med. Imag., vol.18, no.3, pp. 262-271, Mar. 1999.
32. S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, "Fast iterative image reconstruction methods for fully 3-D multispec-tral bioluminescence tomography," Phys. Med. Biol., vol.53, no.14, pp. 3921-3942, 2008. (Pubitemid 352020273)
33. A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, "A matrix-free algorithm for mul-tiple wavelength fluorescence tomography," Opt. Express, vol.17, no.5, pp. 3042-3051, 2009.
34. X. Song, B. W. Pogue, S. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, "Automated region detection based on the contrast-to-noise ratio in near-infrared tomography," Appl. Opt., vol.43, no.5, pp. 1053-1062, 2004.
35. A. Ishimaru, Wave Propagation and Scattering in Random Media. New York: Academic, 1978.
36. S. R. Arridge, "Optical tomography in medical imaging," Inverse Prob-lems, vol.15, no.2, pp. R41-R93, 1999.
37. J. Dieudonne, Foundations of Modern Analysis. New York: Aca-demic, 1969.
38. F. Natterer and F. Wubbeling, Mathematical Methods in Image Recon-struction. Philadelphia, PA: SIAM, 2001.
39. G. Strang, Computational Science and Engineering. Cambridge, MA: Wellesley-Cambridge, November 2007.
40. I. Daubechies, R. Devore, M. Fornasier, and S. Gunturk, "Iteratively re-weighted least squares minimization: Proof of faster than linear rate for sparse recovery," in Proc. 42nd Annu. Conf. Inf. Sci. Syst., 2008, pp. 26-29.
41. M. Rudin, Molecular Imaging: Basic Principles and Applications in Biomedical Research. London, U.K.: Imperial College Press, 2005.
42. S. C. Davis, B. W. Pogue, H. Dehghani, and K. D. Paulsen, "Contrast-detail analysis characterizing diffuse optical fluorescence tomography image reconstruction," J. Biomed. Optics, vol.10, no.5, p. 050501, 2005. (Pubitemid 44255994)
43. W. Bangerth, "A framework for the adaptive finite element solution of large-scale inverse problems," SIAM J. Sci. Comput., vol.30, no.6, pp. 2965-2989, 2008