Spatial location weighted optimization scheme for DC optical tomography
Optics Express, Vol. 11, Issue 2, pp. 141-150 (2003)
http://dx.doi.org/10.1364/OE.11.000141
Acrobat PDF (399 KB)
Abstract
In this paper, a spatial location weighted gradient-based optimization scheme for reducing the computation burden and increasing the reconstruction precision is stated. The method applies to DC diffusion-based optical tomography, where otherwise the reconstruction suffers slow convergence. The inverse approach employs a weighted steepest descent method combined with a conjugate gradient method. A reverse differentiation method is used to efficiently derive the gradient. The reconstruction results confirm that the spatial location weighted optimization method offers a more efficient approach to the DC optical imaging problem than unweighted method does.
© 2002 Optical Society of America
1. Introduction
12. Y. Q. Yao, Y. Wang, Y. L. Pei, W. W. Zhu, and R. L. Barbour. “Frequency-domain optical imaging of absorption and scattering distributions by Born iterative method,” J. Opt. Soc. Amer. A 14, 325–342 (1997) [CrossRef]
13. K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995) [CrossRef] [PubMed]
1. A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-Based Iterative Image-Reconstruction Scheme for Time-Resolved Optical Tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999) [CrossRef]
2. R. Roy and E. M. Sevick-MUraca, “Active constrained truncated Newton method for simple-bound optical tomography,” J. Opt. Soc. Am. A 17, 1627–1641 (2000) [CrossRef]
4. R. Roy and E. M. Sevick-MUraca, “Truncated Newton’s optimization scheme for absorption and fluorescence optical tomography: Part I theory and formulation,” Opt. Express 4, 353–371 (1999), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-10-353 [CrossRef] [PubMed]
6. A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, and A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-6-272 [CrossRef] [PubMed]
14. A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, and P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Advances in Engineering Software 28, 217–221 (1997) [CrossRef]
1. A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-Based Iterative Image-Reconstruction Scheme for Time-Resolved Optical Tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999) [CrossRef]
5. S. R. Arridge and M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213 [CrossRef] [PubMed]
14. A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, and P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Advances in Engineering Software 28, 217–221 (1997) [CrossRef]
15. A. D. Klose and A. H. Hielscher, “Optical tomography using the time-independent equation of radiative transfer — Part 2: inverse model,” J. Quant. Spectrosc. Radiat. Transfer 72, 715–732 (2002) [CrossRef]
1. A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-Based Iterative Image-Reconstruction Scheme for Time-Resolved Optical Tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999) [CrossRef]
5. S. R. Arridge and M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213 [CrossRef] [PubMed]
5. S. R. Arridge and M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213 [CrossRef] [PubMed]
1. A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-Based Iterative Image-Reconstruction Scheme for Time-Resolved Optical Tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999) [CrossRef]
5. S. R. Arridge and M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213 [CrossRef] [PubMed]
14. A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, and P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Advances in Engineering Software 28, 217–221 (1997) [CrossRef]
2. Theory review
2.1 Forward and inverse problems in OT
a) Forward model
17. R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994) [CrossRef]
b) The inverse formulation
2.2 The gradient calculation
5. S. R. Arridge and M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213 [CrossRef] [PubMed]
11. S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part2: Zinite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995) [CrossRef] [PubMed]
11. S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part2: Zinite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995) [CrossRef] [PubMed]
1. A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-Based Iterative Image-Reconstruction Scheme for Time-Resolved Optical Tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999) [CrossRef]
14. A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, and P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Advances in Engineering Software 28, 217–221 (1997) [CrossRef]
14. A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, and P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Advances in Engineering Software 28, 217–221 (1997) [CrossRef]
3. The spatial location weighted reconstruction scheme
14. A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, and P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Advances in Engineering Software 28, 217–221 (1997) [CrossRef]
3.1 Steepest descent directions: A-norm of z⃑
3.2 The choice of the weighting factor β
Algorithm 1. Spatial location weighted optimization method |
---|
Set initial guess x⃑^{(0)} |
Calculate the gradient of the initial guess Z⃑(x ^{(0)}) |
Set initial β = 0 |
Repeat |
Construct the matrix A |
Calculate the steepest descent direction d⃑^{(β)} in A-measurement. |
Find γ^{(β)} that minimizes E ^{(β)} = E(x ^{(0)} + γ^{(β)}d⃑^{(β)}) |
β = β + 1 |
Until E ^{(β)} < E ^{(β - 1)} |
x ^{(1)} = x ^{(0)} + r ^{(β-1)}d⃑^{(β-1)} |
Use x ^{(1)} as the initial guess for the conjugate-gradient method |
4. Simulation results
20. S. R. Arridge, M. Schweiger, M. Hiraoka, and D.T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993) [CrossRef] [PubMed]
9. S. R. Arridge and W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998) [CrossRef]
10. Y. Pei, H. L. Graber, and R. L. Barbour, “Normalized-constraint algorithm for minimizing inter-parameter crosstalk in DC optical tomography,” Opt. Express 9, 97- (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-2-97 [CrossRef] [PubMed]
5. Conclusions
Acknowledgments
References and links
1. | A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-Based Iterative Image-Reconstruction Scheme for Time-Resolved Optical Tomography,” IEEE Trans. Med. Imag. 18, 262–271 (1999) [CrossRef] |
2. | R. Roy and E. M. Sevick-MUraca, “Active constrained truncated Newton method for simple-bound optical tomography,” J. Opt. Soc. Am. A 17, 1627–1641 (2000) [CrossRef] |
3. | F. E. W. Schmidt, Development of a Time-Resolved Optical Tomography System for Neonatal Brain Imaging, Ph. D thesis (1999), University College London |
4. | R. Roy and E. M. Sevick-MUraca, “Truncated Newton’s optimization scheme for absorption and fluorescence optical tomography: Part I theory and formulation,” Opt. Express 4, 353–371 (1999), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-10-353 [CrossRef] [PubMed] |
5. | S. R. Arridge and M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213 [CrossRef] [PubMed] |
6. | A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, and A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-6-272 [CrossRef] [PubMed] |
7. | Y. Pei, Optical Tomographic Imaging Using the Finite Element Method, Ph. D. Thesis (1999), Polytechnic University. |
8. | C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S. S. Barbour, and R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 9, 6466–6486 (2000) [CrossRef] |
9. | S. R. Arridge and W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998) [CrossRef] |
10. | Y. Pei, H. L. Graber, and R. L. Barbour, “Normalized-constraint algorithm for minimizing inter-parameter crosstalk in DC optical tomography,” Opt. Express 9, 97- (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-2-97 [CrossRef] [PubMed] |
11. | S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part2: Zinite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995) [CrossRef] [PubMed] |
12. | Y. Q. Yao, Y. Wang, Y. L. Pei, W. W. Zhu, and R. L. Barbour. “Frequency-domain optical imaging of absorption and scattering distributions by Born iterative method,” J. Opt. Soc. Amer. A 14, 325–342 (1997) [CrossRef] |
13. | K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995) [CrossRef] [PubMed] |
14. | A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, and P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Advances in Engineering Software 28, 217–221 (1997) [CrossRef] |
15. | A. D. Klose and A. H. Hielscher, “Optical tomography using the time-independent equation of radiative transfer — Part 2: inverse model,” J. Quant. Spectrosc. Radiat. Transfer 72, 715–732 (2002) [CrossRef] |
16. | A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chap. 9 |
17. | R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994) [CrossRef] |
18. | I. W. Kwee, Towards a Bayesian Framework for Optical Tomography, Ph. D. Thesis (1999), University College London. |
19. | S. G. Nash and A. Sofer, Linear and nonlinear programming (McGraw-Hill, New York, 1996) |
20. | S. R. Arridge, M. Schweiger, M. Hiraoka, and D.T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993) [CrossRef] [PubMed] |
OCIS Codes
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.6960) Medical optics and biotechnology : Tomography
ToC Category:
Research Papers
History
Original Manuscript: December 12, 2002
Revised Manuscript: January 16, 2003
Published: January 27, 2003
Citation
Jun Zhou, Jing Bai, and Ping He, "Spatial location weighted optimization scheme for DC optical tomography," Opt. Express 11, 141-150 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-2-141
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References
- A. H. Hielscher, A. D. Klose, K. M. Hanson, �??Gradient-Based Iterative Image-Reconstruction Scheme for Time-Resolved Optical Tomography,�?? IEEE Trans. Med. Imag. 18, 262-271 (1999) [CrossRef]
- R. Roy and E. M. Sevick-Muraca, �??Active constrained truncated Newton method for simple-bound optical tomography,�?? J. Opt. Soc. Am. A 17, 1627-1641 (2000) [CrossRef]
- F. E. W. Schmidt, Development of a Time-Resolved Optical Tomography System for Neonatal Brain Imaging, Ph. D thesis (1999), University College London
- R. Roy and E. M. Sevick-MUraca, �??Truncated Newton�??s optimization scheme for absorption and fluorescence optical tomography: Part I theory and formulation,�?? Opt. Express 4, 353-371 (1999), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-10-353">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-10-353</a> [CrossRef] [PubMed]
- S. R. Arridge, M. Schweiger, �??A gradient-based optimisation scheme for optical tomography,�?? Opt. Express 2, 213-226 (1998), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213</a> [CrossRef] [PubMed]
- A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, A. H. Hielscher, �??Three-dimensional optical tomography of hemodynamics in the human head,�?? Opt. Express 9, 272-286 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-6-272">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-6-272</a> [CrossRef] [PubMed]
- Y. Pei, Optical Tomographic Imaging Using the Finite Element Method, Ph. D. Thesis (1999), Polytechnic University.
- C. H. Schmitz, H. L. Graber, H. Luo, I. Arif, J. Hira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S. S. Barbour, R. L. Barbour, �??Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,�?? Appl. Opt. 9, 6466-6486 (2000) [CrossRef]
- S. R. Arridge, W. R. B. Lionheart, �??Nonuniqueness in diffusion-based optical tomography,�?? Opt. Lett. 23, 882-884 (1998) [CrossRef]
- Y. Pei, H. L. Graber, R. L. Barbour, �??Normalized-constraint algorithm for minimizing inter-parameter crosstalk in DC optical tomography,�?? Opt. Express 9, 97- (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-2-97">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-2-97</a> [CrossRef] [PubMed]
- S. R. Arridge, M. Schweiger, �??Photon-measurement density functions. Part2: Finite-element-method calculations,�?? Appl. Opt. 34, 8026-8037 (1995) [CrossRef] [PubMed]
- Y. Q. Yao, Y. Wang, Y. L. Pei, W. W. Zhu, R. L. Barbour. �??Frequency-domain optical imaging of absorption and scattering distributions by Born iterative method,�?? J. Opt. Soc. Am. A 14, 325-342 (1997) [CrossRef]
- K. D. Paulsen and H. Jiang, �??Spatially varying optical property reconstruction using a finite element diffusion equation approximation,�?? Med. Phys. 22, 691-701 (1995) [CrossRef] [PubMed]
- A. J. Davies, D. B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, �??Reverse differentiation and the inverse diffusion problem,�?? Advances in Engineering Software 28, 217-221 (1997) [CrossRef]
- A. D. Klose and A. H. Hielscher, �??Optical tomography using the time-independent equation of radiative transfer �?? Part 2: inverse model,�?? J. Quant. Spectrosc. Radiat. Transfer 72, 715-732 (2002) [CrossRef]
- A Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chap. 9
- R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, B. J. Tromberg, �??Boundary conditions for the diffusion equation in radiative transfer,�?? J. Opt. Soc. Am. A 11, 2727-2741 (1994) [CrossRef]
- I. W. Kwee, Towards a Bayesian Framework for Optical Tomography, Ph. D. Thesis (1999), University College London.
- S. G. Nash, A. Sofer, Linear and nonlinear programming(McGraw-Hill, New York, 1996)
- S. R. Arridge, M. Schweiger, M. Hiraoka, D.T. Delpy, �??A finite element approach for modeling photon transport in tissue,�?? Med. Phys. 20, 299-309 (1993). [CrossRef] [PubMed]
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