Abstract

The level set technique is an implicit shape-based image reconstruction method that allows the recovery of the location, size and shape of objects of distinct contrast with well-defined boundaries embedded in a medium of homogeneous or moderately varying background parameters. In the case of diffuse optical tomography, level sets can be employed to simultaneously recover inclusions that differ in their absorption or scattering parameters from the background medium. This paper applies the level set method to the three-dimensional reconstruction of objects from simulated model data and from experimental frequency-domain data of light transmission obtained from a cylindrical phantom with tissue-like parameters. The shape and contrast of two inclusions, differing in absorption and diffusion parameters from the background, respectively, are reconstructed simultaneously. We compare the performance of level set reconstruction with results from an image-based method using a Gauss-Newton iterative approach, and show that the level set technique can improve the detection and localisation of small, high-contrast targets.

© 2010 Optical Society of America

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  4. A. Zacharopoulos, M. Schweiger, V. Kolehmainen, and S. R. Arridge, "3D shape based reconstruction of experimental data in diffuse optical tomography," Opt. Express 17, 18940-18956 (2009).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (2)

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

A. Zacharopoulos, M. Schweiger, V. Kolehmainen, and S. R. Arridge, "3D shape based reconstruction of experimental data in diffuse optical tomography," Opt. Express 17, 18940-18956 (2009).
[CrossRef]

2006 (3)

M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos, and V. Kolehmainen, "Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique," Opt. Lett. 31, 471-473 (2006).
[CrossRef] [PubMed]

O. Dorn and D. Lesselier, "Level set methods for inverse scattering," Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

G. Bal and K. Ren, "Reconstruction of singular surfaces by shape sensitivity analysis and level set method," Math. Mod. Methods Appl. Sci. 16, 1347-1373 (2006).
[CrossRef]

2005 (5)

P. Gonzalez-Rodriguez, M. Kindelan, M. Moscoso, and O. Dorn, "History matching problem in reservoir engineering using the propagation back-projection method," Inverse Probl. 21, 565-590 (2005).
[CrossRef]

M. Schweiger, S. R. Arridge, and I. Nissila, "Gauss-Newton method for image reconstruction in diffuse optical tomography," Phys. Med. Biol. 50, 2365-2386 (2005).
[CrossRef] [PubMed]

E. T. Chung, T. F. Chan, and X.-C. Tai, "Electrical impedance tomography using level set representation and total variational regularization," J. Comp. Phys. 205, 357-372 (2005).
[CrossRef]

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, "Hybrid radiative-transfer-diffusion model for optical tomography," Appl. Opt. 44, 876-886 (2005).
[CrossRef] [PubMed]

2004 (2)

K. Ren, G. S. Abdoulaev, G. Bal, and A. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004).
[CrossRef] [PubMed]

X.-C. Tai and T. F. Chan, "A survey on multiple level set methods with applications for identifying piecewise constant functions," Int. J. Numer. Anal. Mod. 1, 25-47 (2004).

2003 (3)

M. Schweiger and S. R. Arridge, "Image reconstruction in optical tomography using local basis functions," J. Electron. Imaging 12, 583-593 (2003).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

M. E. Kilmer, E. L. Miller, A. Barbaro, and D. Boas, "Three-dimensional shape-based imaging of absorption perturbation for diffuse optical tomography," Appl. Opt. 42, 3129-3144 (2003).
[CrossRef] [PubMed]

2002 (1)

I. Nissila, K. Kotilahti, K. Fallstrom, and T. Katila, "Instrumentation for the accurate measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 73, 3306-3312 (2002).
[CrossRef]

2001 (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

2000 (2)

B. W. Pogue, K. D. Paulsen, C. Abele, and H. Kaufman, "Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms," J. Biomed. Opt. 5, 185-193 (2000).
[CrossRef] [PubMed]

O. Dorn, E. L. Miller, and C. Rappaport, "A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets," Inverse Probl. 16, 1119-1156 (2000).
[CrossRef]

1999 (3)

A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

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).
[CrossRef] [PubMed]

1998 (2)

S. R. Arridge and M. Schweiger, "A gradient-based optimisation scheme for optical tomography," Opt. Express 2, 213-226 (1998).
[CrossRef] [PubMed]

O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
[CrossRef]

1997 (1)

1995 (2)

S. R. Arridge, "Photon measurement density functions. Part 1: Analytical forms," Appl. Opt. 34, 7395-7409 (1995).
[CrossRef] [PubMed]

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]

1993 (1)

M. Firbank and D. T. Delpy, "A design for a stable and reproducible phantom for use in near infrared imaging and spectroscopy," Phys. Med. Biol. 38, 847-853 (1993).
[CrossRef]

1988 (1)

M. Cope and D. T. Delpy, "System for long term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination," Med. Biol. Eng. Comput. 26, 289-294 (1988).
[CrossRef] [PubMed]

Abdoulaev, G. S.

Abele, C.

B. W. Pogue, K. D. Paulsen, C. Abele, and H. Kaufman, "Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms," J. Biomed. Opt. 5, 185-193 (2000).
[CrossRef] [PubMed]

Arridge, S. R.

A. Zacharopoulos, M. Schweiger, V. Kolehmainen, and S. R. Arridge, "3D shape based reconstruction of experimental data in diffuse optical tomography," Opt. Express 17, 18940-18956 (2009).
[CrossRef]

M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos, and V. Kolehmainen, "Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique," Opt. Lett. 31, 471-473 (2006).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, and I. Nissila, "Gauss-Newton method for image reconstruction in diffuse optical tomography," Phys. Med. Biol. 50, 2365-2386 (2005).
[CrossRef] [PubMed]

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

M. Schweiger and S. R. Arridge, "Image reconstruction in optical tomography using local basis functions," J. Electron. Imaging 12, 583-593 (2003).
[CrossRef]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

S. R. Arridge and M. Schweiger, "A gradient-based optimisation scheme for optical tomography," Opt. Express 2, 213-226 (1998).
[CrossRef] [PubMed]

S. R. Arridge, "Photon measurement density functions. Part 1: Analytical forms," Appl. Opt. 34, 7395-7409 (1995).
[CrossRef] [PubMed]

Bal, G.

G. Bal and K. Ren, "Reconstruction of singular surfaces by shape sensitivity analysis and level set method," Math. Mod. Methods Appl. Sci. 16, 1347-1373 (2006).
[CrossRef]

K. Ren, G. S. Abdoulaev, G. Bal, and A. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004).
[CrossRef] [PubMed]

Barbaro, A.

Boas, D.

Boas, D. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

Chan, T. F.

E. T. Chung, T. F. Chan, and X.-C. Tai, "Electrical impedance tomography using level set representation and total variational regularization," J. Comp. Phys. 205, 357-372 (2005).
[CrossRef]

X.-C. Tai and T. F. Chan, "A survey on multiple level set methods with applications for identifying piecewise constant functions," Int. J. Numer. Anal. Mod. 1, 25-47 (2004).

Chung, E. T.

E. T. Chung, T. F. Chan, and X.-C. Tai, "Electrical impedance tomography using level set representation and total variational regularization," J. Comp. Phys. 205, 357-372 (2005).
[CrossRef]

Cope, M.

M. Cope and D. T. Delpy, "System for long term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination," Med. Biol. Eng. Comput. 26, 289-294 (1988).
[CrossRef] [PubMed]

Delpy, D. T.

M. Firbank and D. T. Delpy, "A design for a stable and reproducible phantom for use in near infrared imaging and spectroscopy," Phys. Med. Biol. 38, 847-853 (1993).
[CrossRef]

M. Cope and D. T. Delpy, "System for long term measurement of cerebral blood and tissue oxygenation on newborn infants by near infrared transillumination," Med. Biol. Eng. Comput. 26, 289-294 (1988).
[CrossRef] [PubMed]

DiMarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

Dorn, O.

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

O. Dorn and D. Lesselier, "Level set methods for inverse scattering," Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos, and V. Kolehmainen, "Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique," Opt. Lett. 31, 471-473 (2006).
[CrossRef] [PubMed]

P. Gonzalez-Rodriguez, M. Kindelan, M. Moscoso, and O. Dorn, "History matching problem in reservoir engineering using the propagation back-projection method," Inverse Probl. 21, 565-590 (2005).
[CrossRef]

O. Dorn, E. L. Miller, and C. Rappaport, "A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets," Inverse Probl. 16, 1119-1156 (2000).
[CrossRef]

O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
[CrossRef]

Fallstrom, K.

I. Nissila, K. Kotilahti, K. Fallstrom, and T. Katila, "Instrumentation for the accurate measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 73, 3306-3312 (2002).
[CrossRef]

Firbank, M.

M. Firbank and D. T. Delpy, "A design for a stable and reproducible phantom for use in near infrared imaging and spectroscopy," Phys. Med. Biol. 38, 847-853 (1993).
[CrossRef]

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

Gonzalez-Rodriguez, P.

P. Gonzalez-Rodriguez, M. Kindelan, M. Moscoso, and O. Dorn, "History matching problem in reservoir engineering using the propagation back-projection method," Inverse Probl. 21, 565-590 (2005).
[CrossRef]

Hielscher, A.

Hielscher, A. H.

A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

Irishina, N.

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

Jiang, H.

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]

Kaipio, J. P.

Katila, T.

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

I. Nissila, K. Kotilahti, K. Fallstrom, and T. Katila, "Instrumentation for the accurate measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 73, 3306-3312 (2002).
[CrossRef]

Kaufman, H.

B. W. Pogue, K. D. Paulsen, C. Abele, and H. Kaufman, "Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms," J. Biomed. Opt. 5, 185-193 (2000).
[CrossRef] [PubMed]

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

Kilmer, M. E.

Kindelan, M.

P. Gonzalez-Rodriguez, M. Kindelan, M. Moscoso, and O. Dorn, "History matching problem in reservoir engineering using the propagation back-projection method," Inverse Probl. 21, 565-590 (2005).
[CrossRef]

Klose, A. D.

A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

Kolehmainen, V.

Kotilahti, K.

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

I. Nissila, K. Kotilahti, K. Fallstrom, and T. Katila, "Instrumentation for the accurate measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 73, 3306-3312 (2002).
[CrossRef]

Lesselier, D.

O. Dorn and D. Lesselier, "Level set methods for inverse scattering," Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

Lipiainen, L.

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

Miller, E. L.

M. E. Kilmer, E. L. Miller, A. Barbaro, and D. Boas, "Three-dimensional shape-based imaging of absorption perturbation for diffuse optical tomography," Appl. Opt. 42, 3129-3144 (2003).
[CrossRef] [PubMed]

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

O. Dorn, E. L. Miller, and C. Rappaport, "A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets," Inverse Probl. 16, 1119-1156 (2000).
[CrossRef]

Moscoso, M.

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

P. Gonzalez-Rodriguez, M. Kindelan, M. Moscoso, and O. Dorn, "History matching problem in reservoir engineering using the propagation back-projection method," Inverse Probl. 21, 565-590 (2005).
[CrossRef]

Nissila, I.

M. Schweiger, S. R. Arridge, and I. Nissila, "Gauss-Newton method for image reconstruction in diffuse optical tomography," Phys. Med. Biol. 50, 2365-2386 (2005).
[CrossRef] [PubMed]

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

I. Nissila, K. Kotilahti, K. Fallstrom, and T. Katila, "Instrumentation for the accurate measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 73, 3306-3312 (2002).
[CrossRef]

Noponen, T.

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

Paulsen, K. D.

B. W. Pogue, K. D. Paulsen, C. Abele, and H. Kaufman, "Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms," J. Biomed. Opt. 5, 185-193 (2000).
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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]

Pogue, B. W.

B. W. Pogue, K. D. Paulsen, C. Abele, and H. Kaufman, "Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms," J. Biomed. Opt. 5, 185-193 (2000).
[CrossRef] [PubMed]

Rappaport, C.

O. Dorn, E. L. Miller, and C. Rappaport, "A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets," Inverse Probl. 16, 1119-1156 (2000).
[CrossRef]

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G. Bal and K. Ren, "Reconstruction of singular surfaces by shape sensitivity analysis and level set method," Math. Mod. Methods Appl. Sci. 16, 1347-1373 (2006).
[CrossRef]

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[CrossRef] [PubMed]

Roy, R.

Schotland, J. C.

Schweiger, M.

A. Zacharopoulos, M. Schweiger, V. Kolehmainen, and S. R. Arridge, "3D shape based reconstruction of experimental data in diffuse optical tomography," Opt. Express 17, 18940-18956 (2009).
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M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos, and V. Kolehmainen, "Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique," Opt. Lett. 31, 471-473 (2006).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, and I. Nissila, "Gauss-Newton method for image reconstruction in diffuse optical tomography," Phys. Med. Biol. 50, 2365-2386 (2005).
[CrossRef] [PubMed]

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

M. Schweiger and S. R. Arridge, "Image reconstruction in optical tomography using local basis functions," J. Electron. Imaging 12, 583-593 (2003).
[CrossRef]

S. R. Arridge and M. Schweiger, "A gradient-based optimisation scheme for optical tomography," Opt. Express 2, 213-226 (1998).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

Tai, X.-C.

E. T. Chung, T. F. Chan, and X.-C. Tai, "Electrical impedance tomography using level set representation and total variational regularization," J. Comp. Phys. 205, 357-372 (2005).
[CrossRef]

X.-C. Tai and T. F. Chan, "A survey on multiple level set methods with applications for identifying piecewise constant functions," Int. J. Numer. Anal. Mod. 1, 25-47 (2004).

Tarvainen, T.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, "Hybrid radiative-transfer-diffusion model for optical tomography," Appl. Opt. 44, 876-886 (2005).
[CrossRef] [PubMed]

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

Vauhkonen, M.

Zacharopoulos, A.

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

Appl. Opt. (3)

IEEE Sig. Proc. Magazine (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Sig. Proc. Magazine 18, 57-75 (2001).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
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Int. J. Numer. Anal. Mod. (1)

X.-C. Tai and T. F. Chan, "A survey on multiple level set methods with applications for identifying piecewise constant functions," Int. J. Numer. Anal. Mod. 1, 25-47 (2004).

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O. Dorn and D. Lesselier, "Level set methods for inverse scattering," Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
[CrossRef]

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[CrossRef]

P. Gonzalez-Rodriguez, M. Kindelan, M. Moscoso, and O. Dorn, "History matching problem in reservoir engineering using the propagation back-projection method," Inverse Probl. 21, 565-590 (2005).
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A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

J. Biomed. Opt. (1)

B. W. Pogue, K. D. Paulsen, C. Abele, and H. Kaufman, "Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms," J. Biomed. Opt. 5, 185-193 (2000).
[CrossRef] [PubMed]

J. Comp. Phys. (1)

E. T. Chung, T. F. Chan, and X.-C. Tai, "Electrical impedance tomography using level set representation and total variational regularization," J. Comp. Phys. 205, 357-372 (2005).
[CrossRef]

J. Electron. Imaging (1)

M. Schweiger and S. R. Arridge, "Image reconstruction in optical tomography using local basis functions," J. Electron. Imaging 12, 583-593 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

Math. Mod. Methods Appl. Sci. (1)

G. Bal and K. Ren, "Reconstruction of singular surfaces by shape sensitivity analysis and level set method," Math. Mod. Methods Appl. Sci. 16, 1347-1373 (2006).
[CrossRef]

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[CrossRef] [PubMed]

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I. Nissila, K. Kotilahti, K. Fallstrom, and T. Katila, "Instrumentation for the accurate measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 73, 3306-3312 (2002).
[CrossRef]

I. Nissila, T. Noponen, K. Kotilahti, T. Tarvainen, M. Schweiger, L. Lipiainen, S. R. Arridge, and T. Katila, "Instrumentation and calibration methods for the multichannel measurement of phase and amplitude in optical tomography," Rev. Sci. Instrum. 76 (2005). Art. no. 044302.
[CrossRef]

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M. Schweiger, O. Dorn, and S. R. Arridge, "3-D shape and contrast reconstruction in optical tomography with level sets," in "First International Congress of the International Association of Inverse Problems (IPIA)," J. Phys.: Conf. Ser.124, 012043. Institute of Physics, 2007.
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M. Jacob, Y. Bresler, V. Toronov, X. Zhang, and A. Webb, "Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging," J. Biomed. Opt. 11,064029-1 - 064029-12 (2006).
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Supplementary Material (3)

» Media 1: AVI (265 KB)     
» Media 2: AVI (320 KB)     
» Media 3: AVI (213 KB)     

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Figures (12)

Fig. 1.
Fig. 1.

Object geometry for simulated model data, and phantom for experimental data. The object is a cylinder with embedded cylindrical targets in the central plane. Source and detector locations on the surface are marked with ‘x’ and ‘o’, respectively (a). Cross sections in the central xy plane show the position of the absorption (b) and diffusion target (c).

Fig. 2.
Fig. 2.

Cross sections through target parameter distributions for absorption (top) and diffusion coefficient (bottom) in the central plane z = 0 of the cylinder object. Background parameter noise levels σp in columns from left to right: 0, 10, 20 and 50%.

Fig. 3.
Fig. 3.

Cross sections through mean and variance images of shape-only level set reconstructions of absorption and scattering from 50 background noise realisations. Rows from top to bottom: absorption mean, absorption variance, diffusion mean and diffusion variance. In each row, images from left to right are for background variation levels of 0, 10, 20 and 50% Media 1.

Fig. 4.
Fig. 4.

Cross sections through the absorption (left) and diffusion (right) target distributions (dashed line) and level set shape reconstructions for one sample of each of the background variation levels. Note that the lines for 0, 10 and 20% background variation overlap.

Fig. 5.
Fig. 5.

Level set shape errors ε for absorption (blue) and diffusion images (red) as a function of background noise level. Plotted are the results for both the shape-only (solid lines) and combined shape and contrast reconstructions (dashed lines).

Fig. 6.
Fig. 6.

Cross sections through mean and variance images of combined shape and contrast level set reconstructions of absorption and scattering from 50 background noise realisations. Rows from top to bottom: absorption mean, absorption variance, diffusion mean and diffusion variance. In each row, images from left to right correspond to background variation levels of 0%, 10%, 20% and 50% (Media 2).

Fig. 7.
Fig. 7.

Evolution of absorption parameter x 1,i (n) (left) and diffusion parameter x 2,i (n) (right) as a function of iteration number corresponding to the two difference reconstruction problems in Fig. 6. Target values are plotted as dashed lines.

Fig. 8.
Fig. 8.

Cross sections through the absorption (left) and diffusion (right) target distributions (dashed line) and level set shape+contrast difference reconstructions for one sample of each of the background variation levels.

Fig. 9.
Fig. 9.

Cross sections for Gauss-Newton-Krylov image-based difference reconstructions. Top row: absorption, second row: diffusion images. Columns from left to right are reconstructions of data from the four background realisations shown in Fig. 2.

Fig. 10.
Fig. 10.

Cross sections through the absorption (left) and diffusion (right) target distributions (dashed line) and Gauss-Newton-Krylov image-based difference reconstructions R-1 to R-3a.

Fig. 11.
Fig. 11.

Horizontal cross sections through reconstructions from experimental data. Top row: absorption, second row: diffusion parameter distributions. Columns from left to right: Level set reconstruction for shape only, for shape and contrast, and damped Gauss-Newton-Krylov reconstruction. Outlines indicate the target inclusions (Media 3).

Fig. 12.
Fig. 12.

Cross sections through absorption (left) and diffusion (right) target distributions, and results of level set shape-only, level set shape and contrast, and DGN-K image-based reconstructions of experimental phantom data.

Equations (26)

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( · κ ( r ) + μ a ( r ) + c ) Φ ( r , ω ) = 0 , r Ω ,
Φ ( m , ω ) + 2 κ ( m ) ζ Φ ( m , ω ) ν = q ( m , ω ) , m Ω ,
q i ( m , ω ) = u i ( m m i ( S ) ) δ ( ω ω 0 ) ,
y ij = Ω Γ i ( m , ω ) w j ( m m j ( D ) ) d m ,
Γ i ( m , ω ) = κ ( m ) Φ i ( m , ω ) ν = 1 2 ζ Φ i ( m , ω ) , m Ω .
x l ( r ) k x lk b k ( r ) , l = { 1,2 } , k = 1 N / 2 ,
: N M , ( x ) = y .
x ̂ = arg min x 𝓙 M ( x ) ,
𝓙 M ( x ) = 1 2 𝓡 M ( x ) 2 + τQ ( x ) ,
𝓡 M ( x ) = ( x ) M ,
x l ( r ) = { x l , i if r S l x l , e if r Ω \ S l ,
x l ( r ) = { x l , i if ψ l ( r ) 0 x l , e if ψ l ( r ) > 0 .
𝓙 M ( S ) ( ψ 1 , ψ 2 ) = 1 2 𝓡 M ( ψ 1 , ψ 2 ) 2 ,
𝓙 M ( S + C ) ( ψ 1 , ψ 2 , x 1 , i , x 2 , i ) = 1 2 𝓡 M ( ψ 1 , ψ 2 , x 1 , i , x 2 , i ) 2 ,
d ψ l ( t ) dt = f l ( r , t ) , d x l , i ( t ) dt = g l ( t ) ,
𝓙 M ( t 2 ) < 𝓙 M ( t 1 ) for t 2 > t 1 .
d 𝓙 M ( S ) dt = l = 1 2 Re Ω 𝓡 l ( x l ) * 𝓙 ( x l , e x l , i ) δ ( ψ l ) f l d r ,
d 𝓙 M ( S + C ) dt = d 𝓙 M ( S ) dt + l = 1 2 Re ( g l Ω ( 1 H ( ψ l ) ) 𝓡 l ( x l ) * 𝓡 d r ) ,
f l , d ( r , t ) = Re ( x l , e ( r ) x l , i ) 𝓡 l ( x l ) * 𝓡
g l , d ( t ) = Re ( S l 𝓡 l ( x l ) * 𝓡 d r ) ,
𝓟 = ( αI β Δ ) 1 ,
ψ l ( 0 ) = 1 , x l , i ( 0 ) = x l , i , 0 ,
ψ l ( n + 1 ) = ψ l ( n ) + 𝓟 Δ t f l , d ( n ) ,
x l , i ( n + 1 ) = x l , i ( n ) + Δ t g l , d ( n ) .
M ˜ = M ( sig ) M ( bkg ) + y ,
ε l = 1 Ω Ω H l ( tgt ) ( r ) H l ( rec ) ( r ) d r where H l ( r ) = { 1 if r S l 0 if r Ω \ S l ,

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