Abstract

The sparse estimation methods that utilize the p-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These p-norm-based regularizations make the optimization function nonconvex, and algorithms that implement p-norm minimization utilize approximations to the original p-norm function. In this work, three such typical methods for implementing the p-norm were considered, namely, iteratively reweighted 1-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of p-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images.

© 2014 Optical Society of America

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2014 (1)

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 6800609 (2014), special issue on Biophotonics.
[CrossRef]

2013 (3)

R. P. K. Jagannath and P. K. Yalavarthy, “Non-quadratic penalization improves near infrared diffuse optical tomography,” J. Opt. Soc. Am. A 30, 1516–1523 (2013).
[CrossRef]

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical ℓp minimization algorithms,” J. Neurocomput. 119, 413–424 (2013).
[CrossRef]

J. Kuntz, B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

2012 (6)

C. B. Shaw and P. K. Yalavarthy, “Prior image-constrained ℓ1-norm-based reconstruction method for effective usage of structural information in diffuse optical tomography,” Opt. Lett. 37, 4353–4355 (2012).
[CrossRef]

J. Meng, L. V. Wang, L. Ying, D. Liang, and L. Song, “Compressed-sensing photoacoustic computed tomography in vivo with partially known support,” Opt. Express 20, 16510–16523 (2012).
[CrossRef]

Y. She, “An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors,” Comput. Stat. Data Anal. 56, 2976–2990 (2012).
[CrossRef]

V. C. Kavuri, Z. Lin, F. Tian, and H. Liu, “Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography,” Biomed. Opt. Express 3, 943–957 (2012).
[CrossRef]

A. Majumdar and R. K. Ward, “On the choice of compressed sensing priors and sparsifying transforms for MR image reconstruction: an experimental study,” Signal Process. Image Commun. 27, 1035–1048 (2012).
[CrossRef]

C. B. Shaw and P. K. Yalavarthy, “Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using ℓ1-norm-based linear image reconstruction method,” J. Biomed. Opt. 17, 086009 (2012).
[CrossRef]

2011 (5)

S. Okawa, Y. Hoshi, and Y. Yamada, “Improvement of image quality of time-domain diffuse optical tomography with ℓp sparsity regularization,” Biomed. Opt. Express 2, 3334–3348 (2011).
[CrossRef]

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30, 1143–1153 (2011).
[CrossRef]

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imaging 30, 1129–1142 (2011).
[CrossRef]

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

M. Lai and J. Wang, “An unconstrained ℓq minimization with 0<q<1 for sparse solution of under-determined linear systems,” SIAM J. Optim. 21, 82–101 (2011).
[CrossRef]

2010 (2)

N. Vaswani and W. Lu, “Modified-CS: modifying compressive sensing for problems with partially known support,” IEEE Trans. Signal Process. 58, 4595–4607 (2010).
[CrossRef]

M. Suzen, A. Giannoula, and T. Durduran, “Compressed sensing in diffuse optical tomography,” Opt. Express 18, 23676–23690 (2010).
[CrossRef]

2009 (3)

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

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Z. Wang and J. Liu, “New model function methods for determining regularization parameters in linear inverse problems,” Appl. Numer. Math. 59, 2489–2506 (2009).
[CrossRef]

2008 (1)

E. J. Candes, M. Wakin, and S. Boyd, “Enhancing sparsity by reweighted ℓ1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[CrossRef]

2007 (4)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express 15, 13695–13708 (2007).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

R. Chartrand, “Exact reconstruction of sparse signals via non-convex minimization,” IEEE Signal Process. Lett. 14, 707–710 (2007).
[CrossRef]

2006 (1)

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006).
[CrossRef]

2005 (1)

P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multi-scale Model. Simul. 4, 1168–1200 (2005).
[CrossRef]

2003 (1)

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

2002 (1)

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

2001 (2)

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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Development and calibration of a parallel modulated near- infrared tomography system for hemoglobin imaging in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

1999 (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. Imaging 18, 262–271 (1999).
[CrossRef]

1995 (1)

Afonso, M.

M. Figueiredo, J. Bioucas-Dias, and M. Afonso, “Fast frame-based image deconvolution using variable splitting and constrained optimization,” in IEEE Worskhop on Statistical Signal Processing, Cardiff, Wales (2009).

Arridge, S. R.

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

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part 2: finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
[CrossRef]

Austin, T.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Baritaux, J. C.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30, 1143–1153 (2011).
[CrossRef]

Bartling, S.

J. Kuntz, B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Bioucas-Dias, J.

M. Figueiredo, J. Bioucas-Dias, and M. Afonso, “Fast frame-based image deconvolution using variable splitting and constrained optimization,” in IEEE Worskhop on Statistical Signal Processing, Cardiff, Wales (2009).

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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

Boyd, S.

E. J. Candes, M. Wakin, and S. Boyd, “Enhancing sparsity by reweighted ℓ1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[CrossRef]

Bresler, Y.

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imaging 30, 1129–1142 (2011).
[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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

Bucher, M.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30, 1143–1153 (2011).
[CrossRef]

Candes, E. J.

E. J. Candes, M. Wakin, and S. Boyd, “Enhancing sparsity by reweighted ℓ1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[CrossRef]

Cao, N.

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

Chartrand, R.

R. Chartrand, “Exact reconstruction of sparse signals via non-convex minimization,” IEEE Signal Process. Lett. 14, 707–710 (2007).
[CrossRef]

Combettes, P. L.

P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multi-scale Model. Simul. 4, 1168–1200 (2005).
[CrossRef]

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Dehghani, H.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

Delpy, D. T.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

Durduran, T.

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Everdell, N.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Feng, J.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Figueiredo, M.

M. Figueiredo, J. Bioucas-Dias, and M. Afonso, “Fast frame-based image deconvolution using variable splitting and constrained optimization,” in IEEE Worskhop on Statistical Signal Processing, Cardiff, Wales (2009).

Figueiredo, M. A.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

Flach, B.

J. Kuntz, B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

Giannoula, A.

Gibson, A.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Gibson, J. J.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

Han, D.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Hanson, K. M.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

Hassler, K.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30, 1143–1153 (2011).
[CrossRef]

Hebden, J. C.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Hielscher, A. H.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

Hillman, E. M. C.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Hoshi, Y.

Jacobs, M.

Jagannath, R. P. K.

Jia, K.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Jiang, S.

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Development and calibration of a parallel modulated near- infrared tomography system for hemoglobin imaging in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

Kachelrie, M.

J. Kuntz, B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Kanhirodan, R.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 6800609 (2014), special issue on Biophotonics.
[CrossRef]

Kavuri, V. C.

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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

Kim, J. M.

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imaging 30, 1129–1142 (2011).
[CrossRef]

Klose, A. D.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

Kogel, C.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

Kueres, R.

J. Kuntz, B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Kuntz, J.

J. Kuntz, B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Lai, M.

M. Lai and J. Wang, “An unconstrained ℓq minimization with 0<q<1 for sparse solution of under-determined linear systems,” SIAM J. Optim. 21, 82–101 (2011).
[CrossRef]

Lee, O.

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imaging 30, 1129–1142 (2011).
[CrossRef]

Liang, D.

Lin, Z.

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical ℓp minimization algorithms,” J. Neurocomput. 119, 413–424 (2013).
[CrossRef]

V. C. Kavuri, Z. Lin, F. Tian, and H. Liu, “Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography,” Biomed. Opt. Express 3, 943–957 (2012).
[CrossRef]

Liu, H.

Liu, J.

Z. Wang and J. Liu, “New model function methods for determining regularization parameters in linear inverse problems,” Appl. Numer. Math. 59, 2489–2506 (2009).
[CrossRef]

Liu, K.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Lu, W.

N. Vaswani and W. Lu, “Modified-CS: modifying compressive sensing for problems with partially known support,” IEEE Trans. Signal Process. 58, 4595–4607 (2010).
[CrossRef]

Lyu, Q.

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical ℓp minimization algorithms,” J. Neurocomput. 119, 413–424 (2013).
[CrossRef]

Majumdar, A.

A. Majumdar and R. K. Ward, “On the choice of compressed sensing priors and sparsifying transforms for MR image reconstruction: an experimental study,” Signal Process. Image Commun. 27, 1035–1048 (2012).
[CrossRef]

Manjappa, R.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 6800609 (2014), special issue on Biophotonics.
[CrossRef]

McBride, T. O.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Development and calibration of a parallel modulated near- infrared tomography system for hemoglobin imaging in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

Meek, J. H.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Meng, J.

Miller, E. L.

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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

Nehorai, A.

Nowak, R. D.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

Okawa, S.

Osterberg, U. L.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Development and calibration of a parallel modulated near- infrared tomography system for hemoglobin imaging in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

Patterson, M. S.

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006).
[CrossRef]

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Development and calibration of a parallel modulated near- infrared tomography system for hemoglobin imaging in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

Pogue, B. W.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006).
[CrossRef]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Development and calibration of a parallel modulated near- infrared tomography system for hemoglobin imaging in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

Poplack, S. P.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

Prakash, J.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 6800609 (2014), special issue on Biophotonics.
[CrossRef]

Qin, C.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Sanyal, S.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30, 1143–1153 (2011).
[CrossRef]

Schotland, J. C.

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

Schweiger, M.

Semmler, W.

J. Kuntz, B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Shaw, C. B.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 6800609 (2014), special issue on Biophotonics.
[CrossRef]

C. B. Shaw and P. K. Yalavarthy, “Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using ℓ1-norm-based linear image reconstruction method,” J. Biomed. Opt. 17, 086009 (2012).
[CrossRef]

C. B. Shaw and P. K. Yalavarthy, “Prior image-constrained ℓ1-norm-based reconstruction method for effective usage of structural information in diffuse optical tomography,” Opt. Lett. 37, 4353–4355 (2012).
[CrossRef]

She, Y.

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical ℓp minimization algorithms,” J. Neurocomput. 119, 413–424 (2013).
[CrossRef]

Y. She, “An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors,” Comput. Stat. Data Anal. 56, 2976–2990 (2012).
[CrossRef]

Soho, S.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

Song, L.

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

Suzen, M.

Tian, F.

Tian, J.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Tosteson, T. D.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

Unser, M.

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30, 1143–1153 (2011).
[CrossRef]

Vaswani, N.

N. Vaswani and W. Lu, “Modified-CS: modifying compressive sensing for problems with partially known support,” IEEE Trans. Signal Process. 58, 4595–4607 (2010).
[CrossRef]

Wajs, V. R.

P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multi-scale Model. Simul. 4, 1168–1200 (2005).
[CrossRef]

Wakin, M.

E. J. Candes, M. Wakin, and S. Boyd, “Enhancing sparsity by reweighted ℓ1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[CrossRef]

Wang, J.

M. Lai and J. Wang, “An unconstrained ℓq minimization with 0<q<1 for sparse solution of under-determined linear systems,” SIAM J. Optim. 21, 82–101 (2011).
[CrossRef]

Wang, L. V.

Wang, Z.

Z. Wang and J. Liu, “New model function methods for determining regularization parameters in linear inverse problems,” Appl. Numer. Math. 59, 2489–2506 (2009).
[CrossRef]

Ward, R. K.

A. Majumdar and R. K. Ward, “On the choice of compressed sensing priors and sparsifying transforms for MR image reconstruction: an experimental study,” Signal Process. Image Commun. 27, 1035–1048 (2012).
[CrossRef]

Wright, S. J.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

Wyatt, J. S.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Yalavarthy, P. K.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 6800609 (2014), special issue on Biophotonics.
[CrossRef]

R. P. K. Jagannath and P. K. Yalavarthy, “Non-quadratic penalization improves near infrared diffuse optical tomography,” J. Opt. Soc. Am. A 30, 1516–1523 (2013).
[CrossRef]

C. B. Shaw and P. K. Yalavarthy, “Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using ℓ1-norm-based linear image reconstruction method,” J. Biomed. Opt. 17, 086009 (2012).
[CrossRef]

C. B. Shaw and P. K. Yalavarthy, “Prior image-constrained ℓ1-norm-based reconstruction method for effective usage of structural information in diffuse optical tomography,” Opt. Lett. 37, 4353–4355 (2012).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

Yamada, Y.

Yang, X.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Ye, J. C.

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imaging 30, 1129–1142 (2011).
[CrossRef]

Ying, L.

Yusof, R. M.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Zhang, C.

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical ℓp minimization algorithms,” J. Neurocomput. 119, 413–424 (2013).
[CrossRef]

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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

Zhu, S.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Appl. Numer. Math. (1)

Z. Wang and J. Liu, “New model function methods for determining regularization parameters in linear inverse problems,” Appl. Numer. Math. 59, 2489–2506 (2009).
[CrossRef]

Appl. Opt. (1)

Biomed. Opt. Express (2)

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Comput. Stat. Data Anal. (1)

Y. She, “An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors,” Comput. Stat. Data Anal. 56, 2976–2990 (2012).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 6800609 (2014), special issue on Biophotonics.
[CrossRef]

IEEE J. Sel. Top. Signal Process. (1)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[CrossRef]

IEEE Signal Process. Lett. (1)

R. Chartrand, “Exact reconstruction of sparse signals via non-convex minimization,” IEEE Signal Process. Lett. 14, 707–710 (2007).
[CrossRef]

IEEE Signal Process. Mag. (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 Signal Process. Mag. 18(6), 57–75 (2001).
[CrossRef]

IEEE Trans. Med. Imaging (3)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

J. C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser, “Sparsity-driven reconstruction for FDOT with anatomical priors,” IEEE Trans. Med. Imaging 30, 1143–1153 (2011).
[CrossRef]

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imaging 30, 1129–1142 (2011).
[CrossRef]

IEEE Trans. Signal Process. (1)

N. Vaswani and W. Lu, “Modified-CS: modifying compressive sensing for problems with partially known support,” IEEE Trans. Signal Process. 58, 4595–4607 (2010).
[CrossRef]

Inverse Probl. (1)

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

J. Biomed. Opt. (2)

C. B. Shaw and P. K. Yalavarthy, “Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using ℓ1-norm-based linear image reconstruction method,” J. Biomed. Opt. 17, 086009 (2012).
[CrossRef]

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11, 041102 (2006).
[CrossRef]

J. Fourier Anal. Appl. (1)

E. J. Candes, M. Wakin, and S. Boyd, “Enhancing sparsity by reweighted ℓ1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
[CrossRef]

J. Neurocomput. (1)

Q. Lyu, Z. Lin, Y. She, and C. Zhang, “A comparison of typical ℓp minimization algorithms,” J. Neurocomput. 119, 413–424 (2013).
[CrossRef]

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

Med. Phys. (1)

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).

Multi-scale Model. Simul. (1)

P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multi-scale Model. Simul. 4, 1168–1200 (2005).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Med. Biol. (2)

J. Kuntz, B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47, 4155–4166 (2002).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. USA 100, 12349–12354 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Development and calibration of a parallel modulated near- infrared tomography system for hemoglobin imaging in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

SIAM J. Optim. (1)

M. Lai and J. Wang, “An unconstrained ℓq minimization with 0<q<1 for sparse solution of under-determined linear systems,” SIAM J. Optim. 21, 82–101 (2011).
[CrossRef]

Signal Process. Image Commun. (1)

A. Majumdar and R. K. Ward, “On the choice of compressed sensing priors and sparsifying transforms for MR image reconstruction: an experimental study,” Signal Process. Image Commun. 27, 1035–1048 (2012).
[CrossRef]

Other (3)

https://sites.google.com/site/sercmig/home/complpnorm .

M. Figueiredo, J. Bioucas-Dias, and M. Afonso, “Fast frame-based image deconvolution using variable splitting and constrained optimization,” in IEEE Worskhop on Statistical Signal Processing, Cardiff, Wales (2009).

I. Selesnick, “Introduction to sparsity in signal processing [Connexions Web site],” available at http://cnx.org/content/m43545/1.3/ . (2012).

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Figures (5)

Fig. 1.
Fig. 1.

(a)  Reconstructed μa images using IRL1, IRLS, and ITM algorithms in the numerical experiment with 1% and 5% noisy data collected using the target distribution (given in the first column). The first and second rows show the reconstructed images obtained for the 1% and 5% noisy data, respectively. The reconstruction methods used are given at the top of each reconstructed image. The optimal value of p and optimal regularization parameter (λ) are also indicated at the bottom of each reconstructed image. The 1D cross-sectional profile along the dashed line of the target distribution for reconstructed μa images for 1% and 5% noisy cases are given in (b) and (c), respectively.

Fig. 2.
Fig. 2.

(a) Reconstructed μa images using IRL1, IRLS, and ITM algorithms in the numerical experiment with 1% noisy data collected using the target distribution, which is rectangular in shape and placed close to the center of the imaging domain (given in the first column). The second, third, and fourth columns show the reconstructed images obtained for the 1% noisy data. The reconstruction methods used are given at the top of each reconstructed image. The optimal value of p and optimal regularization parameter (λ) are also indicated at the bottom of each reconstructed image. The 1D cross-sectional profile along the dashed line of the target distribution for reconstructed μa images is given in (b).

Fig. 3.
Fig. 3.

(a) Reconstructed μa images using IRL1, IRLS, and ITM algorithms in the numerical experiment with 1% noisy data collected using the target distribution, which is rectangular in shape, placed horizontally close to the boundary of the imaging domain (given in the first column) for varying values of p (given below each reconstructed image). The first, second, and third rows show the reconstructed images obtained for the 1% noisy data using IRL1, IRLS, and ITM, respectively. The 1D cross-sectional profile along the dashed line of the target distribution for reconstructed μa images for the optimized p-value (last but one column) is given in (b).

Fig. 4.
Fig. 4.

(a) Comparison of reconstructed μa images obtained for the case of experimental gelatin phantom, mimicking a typical breast, using IRL1, IRLS, and ITM algorithms. (b) Similar to Fig. 2, the 1D cross-section of the reconstructed results along the dotted line of the target image.

Fig. 5.
Fig. 5.

(a) Plot showing the variation of p in the p-norm (0<p1) in steps of 0.05 versus the data model misfit function, yG(μa)22 for IRLS, IRL1, and ITM algorithms corresponding to the case of Fig. 1(a) (5% noise). The optimal value of p is the one that results in minimum value of the data model misfit (y axis). (b) Similar to (a), except the y axis gives the mean squared error, where the error is defined as reconstructed μa minus expected μa.

Tables (6)

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Algorithm 1. Iteratively Reweighted 1 Minimization Algorithm Using Weighted SALSA

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Algorithm 2. Iteratively Reweighted Least Squares Minimization Algorithm

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Algorithm 3. Iteratively Thresholding Method

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Algorithm 4. Adaptive Estimation of Regularization Parameter (λ)

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Table 1. Pearson Correlation of the Reconstructed Optical Properties for the Results Presented in This Worka

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Table 2. Mean Reconstructed μa in the Region of Interest [Target(s)] for the Results Presented in This Worka

Equations (25)

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·[D(r)Φ(r)]+μa(r)Φ(r)=Qo(r),
Ω(μa)=yG(μa)22.
G(μa)=G(μa0)+JΔμa+(Δμa)THΔμa+
Ω(Δμa)=δJΔμa22,
Ω(Δμa)=δJΔμa22+λΔμapp.
Δμa(k+1)=argminΔμa{δJΔμa22+i=1Nw(i)(k+1)|Δμa(i)|},
w(i)(k+1)=λ*p(|Δμa(i)(k)|+ϵk)1p,
ΩIRLS(Δμa)=argminΔμa{λi=1N(Δμa(i)2+ϵ)p2+12δJΔμa22}.
i=1N(λ*p*Δμa(i)(ϵ+Δμa(i)2)1p2)+JT(JΔμaδ)=0.
i=1N(λ*p*Δμa(i)(k+1)(ϵ+(Δμa(i)(k))2)1p2)+JT(JΔμa(k+1)δ)=0,
{JTJ+diag(λ*p(ϵ+(Δμa(i)(k))2)1p2)}Δμa(k+1)=JTδ.
{JTJ+diag(λ*p(ϵk+(Δμa(i)(k))2)1p2)}Δμa=JTδ
ΩITM(Δμa)=argminΔμa{12δJΔμa22+P(Δμa;λ)},
ΩITM(Δμa,z)=12δJΔμa22+P(Δμa;λ)+12(Δμaz)T(IJTJ)(Δμaz).
Δμa(k+1)=argminΔμa{12Δμa((IJTJ)z(k)+JTδ)22+P(Δμa;λ)}.
Δμa(k+1)=Γ((lJTJ)Δμa(k)+JTδ;λ),
Γp(Δμa;λ)={0,forΔμaτ(λ)sgn(Δμa)max(θ:g(θ)=|Δμa|),forΔμa>τ(λ),
Δμa(k+1)=Γp((IJ22JTJ)Δμa(k)+J22JTδ;λJ22).
Δμa=Γp((IJ22JTJ)Δμa(k)+J22JTδ;λJ22)
F(λ)=δJΔμa(λ)22+λΔμa(λ)pp.
λk+1=Ckσm˜bTk,
Ck=(bF(λk))2F(λk),Tk=bF(λk)F(λk)λk.
PC(μatarget,μarecon)=COV(μatarget,μarecon)σ(μatarget)σ(μarecon),
m>Cklogβ(n),
mC1k+pklog(n),

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