Abstract

In this paper, a flexible edge-preserving regularization algorithm based on the finite element method is proposed to reconstruct the optical-property images of near-infrared diffuse optical tomography. This regularization algorithm can easily incorporate with varied weighting functions, such as a generalized Lorentzian function, an exponential function, or a generalized total variation function. To evaluate the performance, results obtained from Tikhonov or edge-preserving regularization are compared with each other. As found, the edge-preserving regularization with the generalized Lorentzian function is more attractive than that with other functions for the estimation of absorption-coefficient images concerning functional tomographic images to discover functional information of tested phantoms/tissues.

© 2013 Optical Society of America

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  1. P. J. Cassidy and G. K. Radda, “Molecular imaging perspectives,” J. R. Soc. Interface 2, 133–144 (2005).
    [CrossRef]
  2. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
    [CrossRef]
  3. P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997).
    [CrossRef]
  4. V. B. S. Prasath and A. Singh, “A hybrid convex variational model for image restoration,” Appl. Math. Comput. 215, 3655–3664 (2010).
  5. M. Rivera and J. L. Marroquin, “Adaptive rest condition potentials: first and second order edge-preserving regularization,” Comput. Vis. Image Underst. 88, 76–93 (2002).
    [CrossRef]
  6. D. Lazzaro and L. B. Montefusco, “Edge-preserving wavelet thresholding for image denoising,” J. Comput. Appl. Math. 210, 222–231 (2007).
    [CrossRef]
  7. A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Trans. Image Process. 7, 204–221 (1998).
    [CrossRef]
  8. R. Pan and S. J. Reeves, “Efficient Huber-Markov edge-preserving image restoration,” IEEE Trans. Image Process. 15, 3728–3735 (2006).
    [CrossRef]
  9. H. Zhang, Z. Shang, and C. Yang, “A non-linear regularized constrained impedance inversion,” Geophys. Prospect. 55, 819–833 (2007).
    [CrossRef]
  10. H. Zhang, Z. Shang, and C. Yang, “Adaptive reconstruction method of impedance model with absolute and relative constraints,” J. Appl. Geophys. 67, 114–124 (2009).
    [CrossRef]
  11. G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, “Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy,” J. Microsc. 234, 47–61 (2009).
    [CrossRef]
  12. X. Gu and L. Gao, “A new method for parameter estimation of edge-preserving regularization in image restoration,” J. Comput. Appl. Math. 225, 478–486 (2009).
    [CrossRef]
  13. R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. 25, 045010 (2009).
    [CrossRef]
  14. A. Jalobeanu, L. Blance-Feraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method,” Pattern Recogn. 35, 341–352 (2002).
    [CrossRef]
  15. P. Lobel, L. Blanc-Feraud, Ch. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
    [CrossRef]
  16. J. M. Bardsley, and J. Goldes, “An iterative method for edge-preserving MAP estimation when data-noise is Poisson,” SIAM J. Sci. Comput. 32, 171–185 (2010).
    [CrossRef]
  17. B. Omrane, Y. Goussard, and J. Laurin, “Constrained inverse near-field scattering using high resolution wire grid models,” IEEE Trans. Antennas Propag. 59, 3710–3718 (2011).
    [CrossRef]
  18. N. Villain, Y. Goussard, J. Idier, and M. Allain, “Three-dimensional edge-preserving image enhancement for computed tomography,” IEEE Trans. Med. Imag. 22, 1275–1287 (2003).
    [CrossRef]
  19. D. F. Yu, and J. A. Fessler, “Three-dimensional non-local edge-preserving regularization for PET transmission reconstruction,” in Nuclear Science Symposium Conference Record (IEEE, 2000), pp. 1566–1570.
  20. C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, “A variational model for image classification and restoration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 460–472 (2000).
    [CrossRef]
  21. R. Casanova, A. Silva, and A. R. Borges, “MIT image reconstruction based on edge-preserving regularization,” Physiol. Meas. 25, 195–207 (2004).
    [CrossRef]
  22. L. Blanc-Feraud, and M. Barlaud, “Edge preserving restoration of astrophysical images,” Vistas Astron. 40, 531–538 (1996).
    [CrossRef]
  23. L. Y. Chen, M.-C. Pan, and M.-C. Pan, “Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography,” Appl. Opt. 51, 43–54 (2012).
    [CrossRef]
  24. S. Teboul, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Variational approach for edge-preserving regularization using coupled PDE’s,” IEEE Trans. Image Process. 7, 387–397 (1998).
    [CrossRef]
  25. M.-C. Pan, C. H. Chen, L. Y. Chen, M.-C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
    [CrossRef]

2012 (1)

2011 (1)

B. Omrane, Y. Goussard, and J. Laurin, “Constrained inverse near-field scattering using high resolution wire grid models,” IEEE Trans. Antennas Propag. 59, 3710–3718 (2011).
[CrossRef]

2010 (2)

J. M. Bardsley, and J. Goldes, “An iterative method for edge-preserving MAP estimation when data-noise is Poisson,” SIAM J. Sci. Comput. 32, 171–185 (2010).
[CrossRef]

V. B. S. Prasath and A. Singh, “A hybrid convex variational model for image restoration,” Appl. Math. Comput. 215, 3655–3664 (2010).

2009 (5)

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

H. Zhang, Z. Shang, and C. Yang, “Adaptive reconstruction method of impedance model with absolute and relative constraints,” J. Appl. Geophys. 67, 114–124 (2009).
[CrossRef]

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, “Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy,” J. Microsc. 234, 47–61 (2009).
[CrossRef]

X. Gu and L. Gao, “A new method for parameter estimation of edge-preserving regularization in image restoration,” J. Comput. Appl. Math. 225, 478–486 (2009).
[CrossRef]

R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. 25, 045010 (2009).
[CrossRef]

2008 (1)

M.-C. Pan, C. H. Chen, L. Y. Chen, M.-C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef]

2007 (2)

H. Zhang, Z. Shang, and C. Yang, “A non-linear regularized constrained impedance inversion,” Geophys. Prospect. 55, 819–833 (2007).
[CrossRef]

D. Lazzaro and L. B. Montefusco, “Edge-preserving wavelet thresholding for image denoising,” J. Comput. Appl. Math. 210, 222–231 (2007).
[CrossRef]

2006 (1)

R. Pan and S. J. Reeves, “Efficient Huber-Markov edge-preserving image restoration,” IEEE Trans. Image Process. 15, 3728–3735 (2006).
[CrossRef]

2005 (1)

P. J. Cassidy and G. K. Radda, “Molecular imaging perspectives,” J. R. Soc. Interface 2, 133–144 (2005).
[CrossRef]

2004 (1)

R. Casanova, A. Silva, and A. R. Borges, “MIT image reconstruction based on edge-preserving regularization,” Physiol. Meas. 25, 195–207 (2004).
[CrossRef]

2003 (1)

N. Villain, Y. Goussard, J. Idier, and M. Allain, “Three-dimensional edge-preserving image enhancement for computed tomography,” IEEE Trans. Med. Imag. 22, 1275–1287 (2003).
[CrossRef]

2002 (2)

A. Jalobeanu, L. Blance-Feraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method,” Pattern Recogn. 35, 341–352 (2002).
[CrossRef]

M. Rivera and J. L. Marroquin, “Adaptive rest condition potentials: first and second order edge-preserving regularization,” Comput. Vis. Image Underst. 88, 76–93 (2002).
[CrossRef]

2000 (1)

C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, “A variational model for image classification and restoration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 460–472 (2000).
[CrossRef]

1998 (2)

A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Trans. Image Process. 7, 204–221 (1998).
[CrossRef]

S. Teboul, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Variational approach for edge-preserving regularization using coupled PDE’s,” IEEE Trans. Image Process. 7, 387–397 (1998).
[CrossRef]

1997 (2)

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997).
[CrossRef]

P. Lobel, L. Blanc-Feraud, Ch. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

1996 (1)

L. Blanc-Feraud, and M. Barlaud, “Edge preserving restoration of astrophysical images,” Vistas Astron. 40, 531–538 (1996).
[CrossRef]

Allain, M.

N. Villain, Y. Goussard, J. Idier, and M. Allain, “Three-dimensional edge-preserving image enhancement for computed tomography,” IEEE Trans. Med. Imag. 22, 1275–1287 (2003).
[CrossRef]

Arridge, S. R.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

Aubert, G.

C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, “A variational model for image classification and restoration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 460–472 (2000).
[CrossRef]

S. Teboul, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Variational approach for edge-preserving regularization using coupled PDE’s,” IEEE Trans. Image Process. 7, 387–397 (1998).
[CrossRef]

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997).
[CrossRef]

Bardsley, J. M.

J. M. Bardsley, and J. Goldes, “An iterative method for edge-preserving MAP estimation when data-noise is Poisson,” SIAM J. Sci. Comput. 32, 171–185 (2010).
[CrossRef]

Barlaud, M.

S. Teboul, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Variational approach for edge-preserving regularization using coupled PDE’s,” IEEE Trans. Image Process. 7, 387–397 (1998).
[CrossRef]

P. Lobel, L. Blanc-Feraud, Ch. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997).
[CrossRef]

L. Blanc-Feraud, and M. Barlaud, “Edge preserving restoration of astrophysical images,” Vistas Astron. 40, 531–538 (1996).
[CrossRef]

Bertero, M.

R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. 25, 045010 (2009).
[CrossRef]

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, “Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy,” J. Microsc. 234, 47–61 (2009).
[CrossRef]

Blance-Feraud, L.

A. Jalobeanu, L. Blance-Feraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method,” Pattern Recogn. 35, 341–352 (2002).
[CrossRef]

Blanc-Feraud, L.

C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, “A variational model for image classification and restoration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 460–472 (2000).
[CrossRef]

S. Teboul, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Variational approach for edge-preserving regularization using coupled PDE’s,” IEEE Trans. Image Process. 7, 387–397 (1998).
[CrossRef]

P. Lobel, L. Blanc-Feraud, Ch. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997).
[CrossRef]

L. Blanc-Feraud, and M. Barlaud, “Edge preserving restoration of astrophysical images,” Vistas Astron. 40, 531–538 (1996).
[CrossRef]

Boccacci, P.

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, “Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy,” J. Microsc. 234, 47–61 (2009).
[CrossRef]

R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. 25, 045010 (2009).
[CrossRef]

Borges, A. R.

R. Casanova, A. Silva, and A. R. Borges, “MIT image reconstruction based on edge-preserving regularization,” Physiol. Meas. 25, 195–207 (2004).
[CrossRef]

Bresler, Y.

A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Trans. Image Process. 7, 204–221 (1998).
[CrossRef]

Casanova, R.

R. Casanova, A. Silva, and A. R. Borges, “MIT image reconstruction based on edge-preserving regularization,” Physiol. Meas. 25, 195–207 (2004).
[CrossRef]

Cassidy, P. J.

P. J. Cassidy and G. K. Radda, “Molecular imaging perspectives,” J. R. Soc. Interface 2, 133–144 (2005).
[CrossRef]

Charbonnier, P.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997).
[CrossRef]

Chen, C. H.

M.-C. Pan, C. H. Chen, L. Y. Chen, M.-C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef]

Chen, L. Y.

L. Y. Chen, M.-C. Pan, and M.-C. Pan, “Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography,” Appl. Opt. 51, 43–54 (2012).
[CrossRef]

M.-C. Pan, C. H. Chen, L. Y. Chen, M.-C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef]

Delaney, A. H.

A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Trans. Image Process. 7, 204–221 (1998).
[CrossRef]

Diaspro, A.

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, “Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy,” J. Microsc. 234, 47–61 (2009).
[CrossRef]

Fessler, J. A.

D. F. Yu, and J. A. Fessler, “Three-dimensional non-local edge-preserving regularization for PET transmission reconstruction,” in Nuclear Science Symposium Conference Record (IEEE, 2000), pp. 1566–1570.

Gao, L.

X. Gu and L. Gao, “A new method for parameter estimation of edge-preserving regularization in image restoration,” J. Comput. Appl. Math. 225, 478–486 (2009).
[CrossRef]

Goldes, J.

J. M. Bardsley, and J. Goldes, “An iterative method for edge-preserving MAP estimation when data-noise is Poisson,” SIAM J. Sci. Comput. 32, 171–185 (2010).
[CrossRef]

Goussard, Y.

B. Omrane, Y. Goussard, and J. Laurin, “Constrained inverse near-field scattering using high resolution wire grid models,” IEEE Trans. Antennas Propag. 59, 3710–3718 (2011).
[CrossRef]

N. Villain, Y. Goussard, J. Idier, and M. Allain, “Three-dimensional edge-preserving image enhancement for computed tomography,” IEEE Trans. Med. Imag. 22, 1275–1287 (2003).
[CrossRef]

Gu, X.

X. Gu and L. Gao, “A new method for parameter estimation of edge-preserving regularization in image restoration,” J. Comput. Appl. Math. 225, 478–486 (2009).
[CrossRef]

Idier, J.

N. Villain, Y. Goussard, J. Idier, and M. Allain, “Three-dimensional edge-preserving image enhancement for computed tomography,” IEEE Trans. Med. Imag. 22, 1275–1287 (2003).
[CrossRef]

Jalobeanu, A.

A. Jalobeanu, L. Blance-Feraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method,” Pattern Recogn. 35, 341–352 (2002).
[CrossRef]

Laurin, J.

B. Omrane, Y. Goussard, and J. Laurin, “Constrained inverse near-field scattering using high resolution wire grid models,” IEEE Trans. Antennas Propag. 59, 3710–3718 (2011).
[CrossRef]

Lazzaro, D.

D. Lazzaro and L. B. Montefusco, “Edge-preserving wavelet thresholding for image denoising,” J. Comput. Appl. Math. 210, 222–231 (2007).
[CrossRef]

Lobel, P.

P. Lobel, L. Blanc-Feraud, Ch. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

Marroquin, J. L.

M. Rivera and J. L. Marroquin, “Adaptive rest condition potentials: first and second order edge-preserving regularization,” Comput. Vis. Image Underst. 88, 76–93 (2002).
[CrossRef]

Montefusco, L. B.

D. Lazzaro and L. B. Montefusco, “Edge-preserving wavelet thresholding for image denoising,” J. Comput. Appl. Math. 210, 222–231 (2007).
[CrossRef]

Omrane, B.

B. Omrane, Y. Goussard, and J. Laurin, “Constrained inverse near-field scattering using high resolution wire grid models,” IEEE Trans. Antennas Propag. 59, 3710–3718 (2011).
[CrossRef]

Pan, M.-C.

L. Y. Chen, M.-C. Pan, and M.-C. Pan, “Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography,” Appl. Opt. 51, 43–54 (2012).
[CrossRef]

L. Y. Chen, M.-C. Pan, and M.-C. Pan, “Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography,” Appl. Opt. 51, 43–54 (2012).
[CrossRef]

M.-C. Pan, C. H. Chen, L. Y. Chen, M.-C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef]

M.-C. Pan, C. H. Chen, L. Y. Chen, M.-C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef]

Pan, R.

R. Pan and S. J. Reeves, “Efficient Huber-Markov edge-preserving image restoration,” IEEE Trans. Image Process. 15, 3728–3735 (2006).
[CrossRef]

Pichot, Ch.

P. Lobel, L. Blanc-Feraud, Ch. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

Prasath, V. B. S.

V. B. S. Prasath and A. Singh, “A hybrid convex variational model for image restoration,” Appl. Math. Comput. 215, 3655–3664 (2010).

Radda, G. K.

P. J. Cassidy and G. K. Radda, “Molecular imaging perspectives,” J. R. Soc. Interface 2, 133–144 (2005).
[CrossRef]

Reeves, S. J.

R. Pan and S. J. Reeves, “Efficient Huber-Markov edge-preserving image restoration,” IEEE Trans. Image Process. 15, 3728–3735 (2006).
[CrossRef]

Rivera, M.

M. Rivera and J. L. Marroquin, “Adaptive rest condition potentials: first and second order edge-preserving regularization,” Comput. Vis. Image Underst. 88, 76–93 (2002).
[CrossRef]

Samson, C.

C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, “A variational model for image classification and restoration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 460–472 (2000).
[CrossRef]

Schotland, J. C.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

Shang, Z.

H. Zhang, Z. Shang, and C. Yang, “Adaptive reconstruction method of impedance model with absolute and relative constraints,” J. Appl. Geophys. 67, 114–124 (2009).
[CrossRef]

H. Zhang, Z. Shang, and C. Yang, “A non-linear regularized constrained impedance inversion,” Geophys. Prospect. 55, 819–833 (2007).
[CrossRef]

Shyr, Y. M.

M.-C. Pan, C. H. Chen, L. Y. Chen, M.-C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef]

Silva, A.

R. Casanova, A. Silva, and A. R. Borges, “MIT image reconstruction based on edge-preserving regularization,” Physiol. Meas. 25, 195–207 (2004).
[CrossRef]

Singh, A.

V. B. S. Prasath and A. Singh, “A hybrid convex variational model for image restoration,” Appl. Math. Comput. 215, 3655–3664 (2010).

Teboul, S.

S. Teboul, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Variational approach for edge-preserving regularization using coupled PDE’s,” IEEE Trans. Image Process. 7, 387–397 (1998).
[CrossRef]

Vicidomini, G.

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, “Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy,” J. Microsc. 234, 47–61 (2009).
[CrossRef]

Villain, N.

N. Villain, Y. Goussard, J. Idier, and M. Allain, “Three-dimensional edge-preserving image enhancement for computed tomography,” IEEE Trans. Med. Imag. 22, 1275–1287 (2003).
[CrossRef]

Yang, C.

H. Zhang, Z. Shang, and C. Yang, “Adaptive reconstruction method of impedance model with absolute and relative constraints,” J. Appl. Geophys. 67, 114–124 (2009).
[CrossRef]

H. Zhang, Z. Shang, and C. Yang, “A non-linear regularized constrained impedance inversion,” Geophys. Prospect. 55, 819–833 (2007).
[CrossRef]

Yu, D. F.

D. F. Yu, and J. A. Fessler, “Three-dimensional non-local edge-preserving regularization for PET transmission reconstruction,” in Nuclear Science Symposium Conference Record (IEEE, 2000), pp. 1566–1570.

Zanella, R.

R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. 25, 045010 (2009).
[CrossRef]

Zanni, L.

R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. 25, 045010 (2009).
[CrossRef]

Zerubia, J.

A. Jalobeanu, L. Blance-Feraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method,” Pattern Recogn. 35, 341–352 (2002).
[CrossRef]

C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, “A variational model for image classification and restoration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 460–472 (2000).
[CrossRef]

Zhang, H.

H. Zhang, Z. Shang, and C. Yang, “Adaptive reconstruction method of impedance model with absolute and relative constraints,” J. Appl. Geophys. 67, 114–124 (2009).
[CrossRef]

H. Zhang, Z. Shang, and C. Yang, “A non-linear regularized constrained impedance inversion,” Geophys. Prospect. 55, 819–833 (2007).
[CrossRef]

Appl. Math. Comput. (1)

V. B. S. Prasath and A. Singh, “A hybrid convex variational model for image restoration,” Appl. Math. Comput. 215, 3655–3664 (2010).

Appl. Opt. (1)

Comput. Vis. Image Underst. (1)

M. Rivera and J. L. Marroquin, “Adaptive rest condition potentials: first and second order edge-preserving regularization,” Comput. Vis. Image Underst. 88, 76–93 (2002).
[CrossRef]

Geophys. Prospect. (1)

H. Zhang, Z. Shang, and C. Yang, “A non-linear regularized constrained impedance inversion,” Geophys. Prospect. 55, 819–833 (2007).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

B. Omrane, Y. Goussard, and J. Laurin, “Constrained inverse near-field scattering using high resolution wire grid models,” IEEE Trans. Antennas Propag. 59, 3710–3718 (2011).
[CrossRef]

IEEE Trans. Image Process. (4)

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311 (1997).
[CrossRef]

A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Trans. Image Process. 7, 204–221 (1998).
[CrossRef]

R. Pan and S. J. Reeves, “Efficient Huber-Markov edge-preserving image restoration,” IEEE Trans. Image Process. 15, 3728–3735 (2006).
[CrossRef]

S. Teboul, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Variational approach for edge-preserving regularization using coupled PDE’s,” IEEE Trans. Image Process. 7, 387–397 (1998).
[CrossRef]

IEEE Trans. Med. Imag. (1)

N. Villain, Y. Goussard, J. Idier, and M. Allain, “Three-dimensional edge-preserving image enhancement for computed tomography,” IEEE Trans. Med. Imag. 22, 1275–1287 (2003).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, “A variational model for image classification and restoration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 460–472 (2000).
[CrossRef]

Inverse Probl. (3)

P. Lobel, L. Blanc-Feraud, Ch. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, “Efficient gradient projection methods for edge-preserving removal of Poisson noise,” Inverse Probl. 25, 045010 (2009).
[CrossRef]

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

J. Appl. Geophys. (1)

H. Zhang, Z. Shang, and C. Yang, “Adaptive reconstruction method of impedance model with absolute and relative constraints,” J. Appl. Geophys. 67, 114–124 (2009).
[CrossRef]

J. Biomed. Opt. (1)

M.-C. Pan, C. H. Chen, L. Y. Chen, M.-C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef]

J. Comput. Appl. Math. (2)

D. Lazzaro and L. B. Montefusco, “Edge-preserving wavelet thresholding for image denoising,” J. Comput. Appl. Math. 210, 222–231 (2007).
[CrossRef]

X. Gu and L. Gao, “A new method for parameter estimation of edge-preserving regularization in image restoration,” J. Comput. Appl. Math. 225, 478–486 (2009).
[CrossRef]

J. Microsc. (1)

G. Vicidomini, P. Boccacci, A. Diaspro, and M. Bertero, “Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy,” J. Microsc. 234, 47–61 (2009).
[CrossRef]

J. R. Soc. Interface (1)

P. J. Cassidy and G. K. Radda, “Molecular imaging perspectives,” J. R. Soc. Interface 2, 133–144 (2005).
[CrossRef]

Pattern Recogn. (1)

A. Jalobeanu, L. Blance-Feraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method,” Pattern Recogn. 35, 341–352 (2002).
[CrossRef]

Physiol. Meas. (1)

R. Casanova, A. Silva, and A. R. Borges, “MIT image reconstruction based on edge-preserving regularization,” Physiol. Meas. 25, 195–207 (2004).
[CrossRef]

SIAM J. Sci. Comput. (1)

J. M. Bardsley, and J. Goldes, “An iterative method for edge-preserving MAP estimation when data-noise is Poisson,” SIAM J. Sci. Comput. 32, 171–185 (2010).
[CrossRef]

Vistas Astron. (1)

L. Blanc-Feraud, and M. Barlaud, “Edge preserving restoration of astrophysical images,” Vistas Astron. 40, 531–538 (1996).
[CrossRef]

Other (1)

D. F. Yu, and J. A. Fessler, “Three-dimensional non-local edge-preserving regularization for PET transmission reconstruction,” in Nuclear Science Symposium Conference Record (IEEE, 2000), pp. 1566–1570.

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Figures (7)

Fig. 1.
Fig. 1.

Architecture of the frequency domain optoelectronic measurement module associated with a ring-based scanning device.

Fig. 2.
Fig. 2.

Demonstration of reconstructed absorption and reduced scattering images of a breast-like phantom from simulated data: (a) designated distribution of absorption coefficient with no variation and the reconstructed absorption images using (b) Tikhonov, (c) generalized Lorentzian function, (d) exponential function, and (e) generalized total variation function as well as (f) designated distribution of reduced scattering coefficient with no variation and the reconstructed reduced scattering images using (g) Tikhonov, (h) generalized Lorentzian function, (i) exponential function, and (j) generalized total variation function.

Fig. 3.
Fig. 3.

1D circular profiles corresponding to Fig. 2.

Fig. 4.
Fig. 4.

Comparison of contrast and size resolutions of simulation cases for Tikhonov and edge-preserving regularization corresponding to Table 1: 1D cases, (a) contrast resolution of μa, (b) size resolution of μa, (c) contrast resolution of μs, (d) size resolution of μs, and 2D cases, (e) contrast resolution of μa, (f) size resolution of μa, (g) contrast resolution of μs, (h) size resolution of μs.

Fig. 5.
Fig. 5.

Demonstration of reconstructed absorption and reduced scattering images of a breast-like phantom from experimental data: (a) phantom with designated absorption properties and the reconstructed absorption images using (b) Tikhonov, (c) generalized Lorentzian function, (d) exponential function, and (e) generalized total variation function as well as (f) phantom with designated reduced scattering properties and the reconstructed reduced scattering images using (g) Tikhonov, (h) generalized Lorentzian function, (i) exponential function, and (j) generalized total variation function.

Fig. 6.
Fig. 6.

1D circular profiles corresponding to Fig. 5.

Fig. 7.
Fig. 7.

Comparison of contrast and size resolutions of experiment cases for Tikhonov and edge-preserving regularization corresponding to Table 2: 1D cases, (a) contrast resolution of μa, (b) size resolution of μa, (c) contrast resolution of μs, (d) size resolution of μs, and 2D cases, (e) contrast resolution of μa, (f) size resolution of μa, (g) contrast resolution of μs, (h) size resolution of μs.

Tables (2)

Tables Icon

Table 1. Evaluation on Contrast and Size Resolutions of Simulation Cases for Tikhonov and Edge Preserving Regularization

Tables Icon

Table 2. Evaluation on Contrast and Size Resolutions of Experiment Cases for Tikhonov and Edge-Preserving Regularization

Equations (12)

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·κ(r)Φ(r,ω)[μa(r)iωc]Φ(r,ω)=S(r,ω),
AΦ=C,
Aij=Ωκ(r)ϕi(r)·ϕj(r)[μa(r)iωc]ϕi(r)ϕj(r)dr+αΩϕi(r)ϕj(r)dr,Ci=ΩS(r,ω)ϕi(r)dr.
Φμa=A1AμaΦ+A1CμaΦκ=A1AκΦ+A1Cκ.
JΔχ=ΔΦ,
QEp*(Δχ,b)=JΔχΔΦ22+λ2lk{(bl)k(DlΔχ)k2+φ[(bl)k]},
(bln+1)k=argmin(bl)k{QEp*(Δχn,(bl)k)}=φ[(DlΔχn)k]2(DlΔχn)k.
Δχn+1=arg minΔχ{QEp*(Δχ,bn+1)}=[JTJ+λ2ΔEpn+1]1JTΔΦ,
Rcontrast1D,2D=(max¯inclusion/min¯background)reconstruction(max¯inclusion/min¯background)Exact
Rcontrast1D,2D=2Rcontrast1D,2D,if1<Rcontrast1D,2D<2,
Rsize1D,2D={[1(MSEinclusion)Recon.2.Exact(MSEinclusion)Exact.2.baseline]Rcontrast1D,2D}1/2,
Φheterocomputed=ΦheteromeasuredΦhomocomputedΦhomomeasured.

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