Abstract

Diffuse optical tomography (DOT) allows tomographic (3D), non-invasive reconstructions of tissue optical properties for biomedical applications. Severe under-sampling is a common problem in DOT which leads to image artifacts. A large number of measurements is needed in order to minimize these artifacts. In this work, we introduce a compressed sensing (CS) framework for DOT which enables improved reconstructions with under-sampled data. The CS framework uses a sparsifying basis, 1-regularization and random sampling to reduce the number of measurements that are needed to achieve a certain accuracy. We demonstrate the utility of the CS framework using numerical simulations. The CS results show improved DOT results in comparison to “traditional” linear reconstruction methods based on singular-value decomposition (SVD) with 2-regularization and with regular and random sampling. Furthermore, CS is shown to be more robust against the reduction of measurements in comparison to the other methods. Potential benefits and shortcomings of the CS approach in the context of DOT are discussed.

© 2010 Optical Society of America

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  1. D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
    [CrossRef]
  2. T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
    [CrossRef]
  3. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
    [CrossRef]
  4. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
    [CrossRef]
  5. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
    [CrossRef]
  6. R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
    [CrossRef] [PubMed]
  7. S. R. Arridge and M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998).
    [CrossRef] [PubMed]
  8. J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
    [CrossRef]
  9. J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
    [CrossRef] [PubMed]
  10. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Österberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950­–2961 (1999).
    [CrossRef]
  11. E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207 (2006).
    [CrossRef]
  12. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [CrossRef]
  13. C. E. Shannon, “Communication in the presence of noise,” in Proceedings of the IRE 37, 10–21 (1949).
    [CrossRef]
  14. H. Nyquist, “Certain topics in telegraph transmission theory,” in Transactions of the American Institute of Electrical Engineers 47, 617–644 (1928).
    [CrossRef]
  15. D. L. Donoho, “For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution,” Commun. Pure Appl. Math. 59, 797–829 (2006).
    [CrossRef]
  16. D. Needell, and R. Vershynin, “Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit,” Found. Comput. Math. 9, 317–334 (2009).
    [CrossRef]
  17. R. Baraniuk, “Compressive sensing,” Lecture notes in IEEE Signal Process. Mag. 24, 118–120 (2007).
    [CrossRef]
  18. J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655 (2007).
    [CrossRef]
  19. D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
    [CrossRef]
  20. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
    [CrossRef] [PubMed]
  21. H. Yu and G. Wang, “Compressed sensing based interior tomography,” Phys. Med. Biol. 54, 2791–2805 (2009).
    [CrossRef] [PubMed]
  22. J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28, 585–594 (2008).
    [CrossRef]
  23. Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15, 021311 (2010).
    [CrossRef] [PubMed]
  24. D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personalised Med. 2, 394–406 (2009).
    [CrossRef]
  25. G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (piccs): a method to accurately reconstruct dynamic ct images from highly undersampled projection data sets,” Med. Phys. 35, 660 (2008).
    [CrossRef] [PubMed]
  26. Z. Xu and Y. L. Edmund, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A 27, 1638–1646 (2010).
    [CrossRef]
  27. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
    [CrossRef] [PubMed]
  28. J. C. Ye, S. Y. Lee, and Y. Bresler, “Exact reconstruction formula for diffuse optical tomography using simultaneous sparse representation,” in IEEE Fifth International Symposium on Biomedical Imaging: From Nano to Macro, (IEEE, 2008), pp. 1621–1624.
  29. N. Cao, A. Nehorai, and M. Jacob, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express 15, 13695–13707 (2007).
    [CrossRef] [PubMed]
  30. P. Mohajerani, A. A. Eftekhar, J. Huang, and A. Adibi, “Optimal sparse solution for fluorescent diffuse optical tomography: theory and phantom experimental results,” Appl. Opt. 46, 1679–1685 (2007).
    [CrossRef] [PubMed]
  31. H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation part 1: l1 regularization,” Opt. Express 18, 1854–1871 (2010).
    [CrossRef] [PubMed]
  32. M. Süzen, A. Giannoula, P. Zirak, N. Oliverio, U. M. Weigel, P. Farzam, and T. Durduran, “Sparse image reconstruction in diffuse optical tomography: an application of compressed sensing,” in Biomedical Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper BSuE6. http://www.opticsinfobase.org/abstract.cfm?URI=BIOMED-2010-BSuE6.
  33. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, (IEEE Service Center, 1988).
  34. M. A. O’Leary, “Imaging with diffuse photon density waves,” Ph.D. thesis, University of Pennsylvania (1996).
  35. G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” Numerische Mathematik 14, 403–420 (1970).
    [CrossRef]
  36. P. C. Hansen, “Analysis of discrete ill-posed problems by means of the l-curve,” SIAM Rev. 34, 561–580 (1992).
    [CrossRef]
  37. E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
    [CrossRef]
  38. S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
  39. J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50, 2231–2242 (2004).
    [CrossRef]
  40. M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
    [CrossRef]
  41. D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887 (1994).
    [CrossRef] [PubMed]
  42. H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, 137–143 (2009).
    [CrossRef]
  43. H. Ponnekanti, J. Ophir, and Y. Huang, “Fundamental mechanical limitations on the visualization of elasticity contrast in elastography,” Ultrasound Med. Biol. 21, 533–543 (1995).
    [CrossRef]
  44. X. M. Song, B. W. Pogue, S. D. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt. 43, 1053–1062 (2004).
    [CrossRef] [PubMed]
  45. R. D. C. Team, R: A Language and Environment for Statistical Computing, ISBN 3–900051–07–0 (2009). http://www.r-project.org.
  46. M. Süzen and T. Durduran, “Basic dot,” GNU R Simulation Software for Diffuse Optical Tomography and Compressive Sampling (2009,2010).
  47. E. van den Berg and M. P. Friedlander, “Probing the pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. (USA) 31, 890–912 (2008).
    [CrossRef]
  48. R. A. DeVore, “Deterministic constructions of compressed sensing matrices,” J. Complexity 23, 918–925 (2007).
    [CrossRef]
  49. E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted l1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).
    [CrossRef]
  50. J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
    [CrossRef]
  51. U. Gamper, P. Boesiger, and S. Kozerke, “Compressed sensing in dynamic MRI,” Magn. Reson. Med. 59, 365–373 (2008).
    [CrossRef] [PubMed]

2010

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

Z. Xu and Y. L. Edmund, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A 27, 1638–1646 (2010).
[CrossRef]

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15, 021311 (2010).
[CrossRef] [PubMed]

H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation part 1: l1 regularization,” Opt. Express 18, 1854–1871 (2010).
[CrossRef] [PubMed]

2009

D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personalised Med. 2, 394–406 (2009).
[CrossRef]

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
[CrossRef] [PubMed]

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, 137–143 (2009).
[CrossRef]

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

D. Needell, and R. Vershynin, “Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit,” Found. Comput. Math. 9, 317–334 (2009).
[CrossRef]

D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

H. Yu and G. Wang, “Compressed sensing based interior tomography,” Phys. Med. Biol. 54, 2791–2805 (2009).
[CrossRef] [PubMed]

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[CrossRef]

2008

U. Gamper, P. Boesiger, and S. Kozerke, “Compressed sensing in dynamic MRI,” Magn. Reson. Med. 59, 365–373 (2008).
[CrossRef] [PubMed]

E. van den Berg and M. P. Friedlander, “Probing the pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. (USA) 31, 890–912 (2008).
[CrossRef]

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

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28, 585–594 (2008).
[CrossRef]

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (piccs): a method to accurately reconstruct dynamic ct images from highly undersampled projection data sets,” Med. Phys. 35, 660 (2008).
[CrossRef] [PubMed]

2007

N. Cao, A. Nehorai, and M. Jacob, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express 15, 13695–13707 (2007).
[CrossRef] [PubMed]

P. Mohajerani, A. A. Eftekhar, J. Huang, and A. Adibi, “Optimal sparse solution for fluorescent diffuse optical tomography: theory and phantom experimental results,” Appl. Opt. 46, 1679–1685 (2007).
[CrossRef] [PubMed]

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
[CrossRef] [PubMed]

R. Baraniuk, “Compressive sensing,” Lecture notes in IEEE Signal Process. Mag. 24, 118–120 (2007).
[CrossRef]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655 (2007).
[CrossRef]

R. A. DeVore, “Deterministic constructions of compressed sensing matrices,” J. Complexity 23, 918–925 (2007).
[CrossRef]

2006

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution,” Commun. Pure Appl. Math. 59, 797–829 (2006).
[CrossRef]

2005

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

2004

2003

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

2001

2000

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

1999

1998

1995

H. Ponnekanti, J. Ophir, and Y. Huang, “Fundamental mechanical limitations on the visualization of elasticity contrast in elastography,” Ultrasound Med. Biol. 21, 533–543 (1995).
[CrossRef]

1994

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887 (1994).
[CrossRef] [PubMed]

1992

P. C. Hansen, “Analysis of discrete ill-posed problems by means of the l-curve,” SIAM Rev. 34, 561–580 (1992).
[CrossRef]

1970

G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” Numerische Mathematik 14, 403–420 (1970).
[CrossRef]

Adibi, A.

Arridge, S. R.

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

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[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]

Athanasiou, T.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

Baraniuk, R.

R. Baraniuk, “Compressive sensing,” Lecture notes in IEEE Signal Process. Mag. 24, 118–120 (2007).
[CrossRef]

Boas, D. A.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887 (1994).
[CrossRef] [PubMed]

Boesiger, P.

U. Gamper, P. Boesiger, and S. Kozerke, “Compressed sensing in dynamic MRI,” Magn. Reson. Med. 59, 365–373 (2008).
[CrossRef] [PubMed]

Boyd, S.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).

Boyd, S. P.

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

Brady, D. J.

Brooks, D. H.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Candes, E. J.

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

Candès, E.

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

Candès, E. J.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Cao, N.

Chance, B.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887 (1994).
[CrossRef] [PubMed]

Chen, G. H.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (piccs): a method to accurately reconstruct dynamic ct images from highly undersampled projection data sets,” Med. Phys. 35, 660 (2008).
[CrossRef] [PubMed]

Choe, R.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

Choi, K.

Culver, J. P.

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, 137–143 (2009).
[CrossRef]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

Darzi, A.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Dehghani, H.

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, 137–143 (2009).
[CrossRef]

X. M. Song, B. W. Pogue, S. D. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt. 43, 1053–1062 (2004).
[CrossRef] [PubMed]

DeVore, R. A.

R. A. DeVore, “Deterministic constructions of compressed sensing matrices,” J. Complexity 23, 918–925 (2007).
[CrossRef]

DiMarzio, C. A.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Donoho, D.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
[CrossRef] [PubMed]

Donoho, D. L.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution,” Commun. Pure Appl. Math. 59, 797–829 (2006).
[CrossRef]

Doyley, M. M.

Duarte-Carvajalino, J. M.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[CrossRef]

Durduran, T.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

Edmund, Y. L.

Eftekhar, A. A.

Enfield, L. C.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Friedlander, M. P.

E. van den Berg and M. P. Friedlander, “Probing the pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. (USA) 31, 890–912 (2008).
[CrossRef]

Gamper, U.

U. Gamper, P. Boesiger, and S. Kozerke, “Compressed sensing in dynamic MRI,” Magn. Reson. Med. 59, 365–373 (2008).
[CrossRef] [PubMed]

Gao, H.

Gaudette, R. J.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Gaudette, T.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Gibson, A.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

Gilbert, A. C.

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655 (2007).
[CrossRef]

Golub, G. H.

G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” Numerische Mathematik 14, 403–420 (1970).
[CrossRef]

Gorinevsky, D.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).

Guo, Z.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15, 021311 (2010).
[CrossRef] [PubMed]

Hansen, P. C.

P. C. Hansen, “Analysis of discrete ill-posed problems by means of the l-curve,” SIAM Rev. 34, 561–580 (1992).
[CrossRef]

Hebden, J.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

Holboke, M. J.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

Horisaki, R.

Huang, J.

Huang, Y.

H. Ponnekanti, J. Ophir, and Y. Huang, “Fundamental mechanical limitations on the visualization of elasticity contrast in elastography,” Ultrasound Med. Biol. 21, 533–543 (1995).
[CrossRef]

Jacob, M.

Jiang, S. D.

Kilmer, M. E.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Kim, S.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).

Koh, K.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).

Kozerke, S.

U. Gamper, P. Boesiger, and S. Kozerke, “Compressed sensing in dynamic MRI,” Magn. Reson. Med. 59, 365–373 (2008).
[CrossRef] [PubMed]

Leff, D. R.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Leng, S.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (piccs): a method to accurately reconstruct dynamic ct images from highly undersampled projection data sets,” Med. Phys. 35, 660 (2008).
[CrossRef] [PubMed]

Lesage, F.

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28, 585–594 (2008).
[CrossRef]

Li, C.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15, 021311 (2010).
[CrossRef] [PubMed]

Liang, D.

D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personalised Med. 2, 394–406 (2009).
[CrossRef]

Lim, S.

Lustig, M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
[CrossRef] [PubMed]

Marks, D. L.

McBride, T. O.

Miller, E. L.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Mohajerani, P.

Needell, D.

D. Needell, and R. Vershynin, “Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit,” Found. Comput. Math. 9, 317–334 (2009).
[CrossRef]

D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

Nehorai, A.

Ntziachristos, V.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887 (1994).
[CrossRef] [PubMed]

Ophir, J.

H. Ponnekanti, J. Ophir, and Y. Huang, “Fundamental mechanical limitations on the visualization of elasticity contrast in elastography,” Ultrasound Med. Biol. 21, 533–543 (1995).
[CrossRef]

Österberg, U. L.

Patten, D. K.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Paulsen, K. D.

Pauly, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
[CrossRef] [PubMed]

Pogue, B. W.

Ponnekanti, H.

H. Ponnekanti, J. Ophir, and Y. Huang, “Fundamental mechanical limitations on the visualization of elasticity contrast in elastography,” Ultrasound Med. Biol. 21, 533–543 (1995).
[CrossRef]

Prewitt, J.

Provost, J.

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28, 585–594 (2008).
[CrossRef]

Reinsch, C.

G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” Numerische Mathematik 14, 403–420 (1970).
[CrossRef]

Romberg, J.

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

Romberg, J. K.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Santos, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

Sapiro, G.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[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.

Slemp, A.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

Song, L.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15, 021311 (2010).
[CrossRef] [PubMed]

Song, X. M.

Tang, J.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (piccs): a method to accurately reconstruct dynamic ct images from highly undersampled projection data sets,” Med. Phys. 35, 660 (2008).
[CrossRef] [PubMed]

Tao, T.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Tizzard, A.

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, 137–143 (2009).
[CrossRef]

Tosteson, T. D.

Tropp, J. A.

D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655 (2007).
[CrossRef]

J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50, 2231–2242 (2004).
[CrossRef]

van den Berg, E.

E. van den Berg and M. P. Friedlander, “Probing the pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. (USA) 31, 890–912 (2008).
[CrossRef]

Vershynin, R.

D. Needell, and R. Vershynin, “Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit,” Found. Comput. Math. 9, 317–334 (2009).
[CrossRef]

Wakin, M. B.

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

Wang, G.

H. Yu and G. Wang, “Compressed sensing based interior tomography,” Phys. Med. Biol. 54, 2791–2805 (2009).
[CrossRef] [PubMed]

Wang, L. V.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15, 021311 (2010).
[CrossRef] [PubMed]

Warren, O. J.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

White, B. R.

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, 137–143 (2009).
[CrossRef]

Xu, Z.

Yang, G. Z.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Ying, L.

D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personalised Med. 2, 394–406 (2009).
[CrossRef]

Yodh, A. G.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887 (1994).
[CrossRef] [PubMed]

Yu, H.

H. Yu and G. Wang, “Compressed sensing based interior tomography,” Phys. Med. Biol. 54, 2791–2805 (2009).
[CrossRef] [PubMed]

Zeff, B. W.

H. Dehghani, B. R. White, B. W. Zeff, A. Tizzard, and J. P. Culver, “Depth sensitivity and image reconstruction analysis of dense imaging arrays for mapping brain function with diffuse optical tomography,” Appl. Opt. 48, 137–143 (2009).
[CrossRef]

Zhang, H. F.

D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personalised Med. 2, 394–406 (2009).
[CrossRef]

Zhao, H.

Zubkov, L.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

Appl. Comput. Harmon. Anal.

D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

Appl. Opt.

Breast Cancer Res. Treat.

D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athanasiou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Diffuse optical imaging of the healthy and diseased breast: a systematic review,” Breast Cancer Res. Treat. 108, 9–22 (2008).
[CrossRef]

Commun. Pure Appl. Math.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution,” Commun. Pure Appl. Math. 59, 797–829 (2006).
[CrossRef]

Found. Comput. Math.

D. Needell, and R. Vershynin, “Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit,” Found. Comput. Math. 9, 317–334 (2009).
[CrossRef]

IEEE J. Sel. Top. Signal Process.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).

IEEE Signal Process. Mag.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25, 72–82 (2008).
[CrossRef]

R. Baraniuk, “Compressive sensing,” Lecture notes in IEEE Signal Process. Mag. 24, 118–120 (2007).
[CrossRef]

IEEE Trans. Image Process.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[CrossRef]

IEEE Trans. Inf. Theory

J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50, 2231–2242 (2004).
[CrossRef]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655 (2007).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

IEEE Trans. Med. Imaging

J. Provost and F. Lesage, “The application of compressed sensing for photo-acoustic tomography,” IEEE Trans. Med. Imaging 28, 585–594 (2008).
[CrossRef]

Int. J. Funct. Inform. Personalised Med.

D. Liang, H. F. Zhang, and L. Ying, “Compressed-sensing photoacoustic imaging based on random optical illumination,” Int. J. Funct. Inform. Personalised Med. 2, 394–406 (2009).
[CrossRef]

Inverse Probl.

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

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

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

J. Biomed. Opt.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15, 021311 (2010).
[CrossRef] [PubMed]

J. Complexity

R. A. DeVore, “Deterministic constructions of compressed sensing matrices,” J. Complexity 23, 918–925 (2007).
[CrossRef]

J. Fourier Anal. Appl.

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

J. Opt. Soc. Am. A

Magn. Reson. Med.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
[CrossRef] [PubMed]

U. Gamper, P. Boesiger, and S. Kozerke, “Compressed sensing in dynamic MRI,” Magn. Reson. Med. 59, 365–373 (2008).
[CrossRef] [PubMed]

Med. Phys.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (piccs): a method to accurately reconstruct dynamic ct images from highly undersampled projection data sets,” Med. Phys. 35, 660 (2008).
[CrossRef] [PubMed]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235 (2003).
[CrossRef] [PubMed]

Numerische Mathematik

G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” Numerische Mathematik 14, 403–420 (1970).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, 1–43 (2005).
[CrossRef]

H. Yu and G. Wang, “Compressed sensing based interior tomography,” Phys. Med. Biol. 54, 2791–2805 (2009).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887 (1994).
[CrossRef] [PubMed]

Rep. Prog. Phys.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

SIAM J. Sci. Comput. (USA)

E. van den Berg and M. P. Friedlander, “Probing the pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. (USA) 31, 890–912 (2008).
[CrossRef]

SIAM Rev.

P. C. Hansen, “Analysis of discrete ill-posed problems by means of the l-curve,” SIAM Rev. 34, 561–580 (1992).
[CrossRef]

Ultrasound Med. Biol.

H. Ponnekanti, J. Ophir, and Y. Huang, “Fundamental mechanical limitations on the visualization of elasticity contrast in elastography,” Ultrasound Med. Biol. 21, 533–543 (1995).
[CrossRef]

Other

R. D. C. Team, R: A Language and Environment for Statistical Computing, ISBN 3–900051–07–0 (2009). http://www.r-project.org.

M. Süzen and T. Durduran, “Basic dot,” GNU R Simulation Software for Diffuse Optical Tomography and Compressive Sampling (2009,2010).

M. Süzen, A. Giannoula, P. Zirak, N. Oliverio, U. M. Weigel, P. Farzam, and T. Durduran, “Sparse image reconstruction in diffuse optical tomography: an application of compressed sensing,” in Biomedical Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper BSuE6. http://www.opticsinfobase.org/abstract.cfm?URI=BIOMED-2010-BSuE6.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, (IEEE Service Center, 1988).

M. A. O’Leary, “Imaging with diffuse photon density waves,” Ph.D. thesis, University of Pennsylvania (1996).

J. C. Ye, S. Y. Lee, and Y. Bresler, “Exact reconstruction formula for diffuse optical tomography using simultaneous sparse representation,” in IEEE Fifth International Symposium on Biomedical Imaging: From Nano to Macro, (IEEE, 2008), pp. 1621–1624.

C. E. Shannon, “Communication in the presence of noise,” in Proceedings of the IRE 37, 10–21 (1949).
[CrossRef]

H. Nyquist, “Certain topics in telegraph transmission theory,” in Transactions of the American Institute of Electrical Engineers 47, 617–644 (1928).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Illustrating the geometry of the simulated optical domain (infinite-medium). For the field-of-view, 3-D volume of size 4 × 4 × 3 cm3 and voxel dimensions 0.4 × 0.4 × 0.6 cm3 is considered. A spherical inhomogeneity is embedded in the medium at z = −1.5 cm. A 5 × 5 array of sources and detectors is placed on a plane at z = 0 cm.

Fig. 2
Fig. 2

(a) Full set of S/D pairs (0% removal), (b) remaining S/D pairs after ∼ 90% “random” sampling (removal) for CS and SVD, (c) remaining S/D pairs after ∼ 90% “regular” sampling for SVD-reg.

Fig. 3
Fig. 3

Cumulative coherence function (CCF) between the Jacobian (J) and the discrete Fourier transform (T) for several scaled orders m/N (m = 2 – 15, N = 16). The CCF was scaled with respect to order m = 1, i.e. (CCF(m/N) – CCF(1/N))/CCF(m/N).

Fig. 4
Fig. 4

From top to bottom: “Forward” imaging data, SVD-reg, SVD, and CS reconstructed images for a simulated inhomogeneity of μa,I = 0.08 cm−1 and a case of ∼ 50% reduced S/D pairs. Five layers along the z-axis were considered, ranging from z = −0.3 cm (S/D plane) to z = −2.7 cm (from left to right). The inhomogeneity was taken to be localized at z = −1.5 cm (layer 3). Please note the use of differences in colorbars in each row.

Fig. 5
Fig. 5

(a) Normalized observed contrast versus the investigated range of removed S/D pairs for CS, SVD and SVD-reg. The contrast was normalized according to that for 0% removal and the absorption coefficient of the inhomogeneity was μa,I = 0.08 cm−1. (b) Observed contrast versus the true absorption coefficient of the inhomogeneity μa,I, for 0% and 92% S/D removal.

Fig. 6
Fig. 6

Normalized contrast-to-noise ratio (CNR) versus the range of removed S/D pairs. The CNR was normalized according to that for 0% removal. The absorption coefficient of the inhomogeneity was assumed to be μa,I = 0.08 cm−1.

Fig. 7
Fig. 7

(a) Normalized root mean square error (nRM SE) and (b) localization error (LE) for several percent values of removed S/D pairs. The absorption coefficient of the inhomogeneity was assumed μa,I = 0.08 cm−1.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

Φ sc = J Δ μ a .
J l k = v V G ( r i , r k ) Φ 0 ( r k , r j ) / ( G ( r j , r i ) D 0 ) ,
min ( || J Δ μ a Φ sc || 2 2 + λ 2 || Δ μ a || 2 2 ) ,
min || T x ¯ || 1 s . t . y = Φ T x ¯ ,
min || Δ μ a || 1 s . t . J Δ μ a = Φ sc ,
min ( || J T Δ μ ¯ a Φ sc || 2 2 + Λ | | T Δ μ ¯ a || 1 ) .
μ = max J i , T j ,
CCF ( m ) = max max Ω k J k , T j ,
C o = 20 log 10 ( Δ μ ^ a , I Δ μ ^ a , B ) ,
CNR = 20 log 10 [ 2 ( Δ μ ^ a , I Δ μ ^ a , B ) 2 σ I 2 + σ B 2 ] ,
nRMSE = Σ r V ( Δ μ a ( r V ) Δ μ a , true ( r V ) ) 2 / N ( Δ μ a max Δ μ a min ) ,
LE = | r max r true , I | .

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