Abstract

The resolution in optical coherence tomography imaging is an important parameter which determines the size of the smallest features that can be visualized. Sparse sampling approaches have shown considerable promise in producing high resolution OCT images with fewer camera pixels, reducing both the cost and the complexity of an imaging system. In this paper, we propose a non-local approach to the reconstruction of high resolution OCT images from sparsely sampled measurements. An iterative strategy is introduced for minimizing a homotopic, non-local regularized functional in the spatial domain, subject to data fidelity constraints in the k-space domain. The novel algorithm was tested on human retinal, corneal, and limbus images, acquired in-vivo, demonstrating the effectiveness of the proposed approach in generating high resolution reconstructions from a limited number of camera pixels.

© 2012 OSA

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References

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  1. S. A. Boppart, “Optical coherence tomography: technology and applications for neuroimaging,” Psychophysiology 40, 529–541 (2003).
    [CrossRef] [PubMed]
  2. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  3. B. E. Bouma and G. J. Tearney, Handbook of Optical Coherence Tomography (Informa Healthcare, 2001).
  4. M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
    [CrossRef] [PubMed]
  5. W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer, 2008).
    [CrossRef]
  6. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
    [CrossRef]
  7. R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express 12, 2156–2165 (2004).
    [CrossRef] [PubMed]
  8. R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express 11, 889–894 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. E. Candës, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
    [CrossRef]
  11. D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [CrossRef]
  12. M. Lustig, D. Donoho, and J. Pauly, “Sparse MRI: the application of compressed sesing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
    [CrossRef] [PubMed]
  13. J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Imag. 28, 106–121 (2009).
    [CrossRef]
  14. A. Wong, A. Mishra, D. Clausi, and P. Fieguth, “Sparse reconstruction of breast MRI using homotopic L0 minimization in a regional sparsified domain,” Biomed. Eng. IEEE Trans, 1–10 (2010).
  15. D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc., 1032–1035 (2009).
  16. N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
    [CrossRef]
  17. X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express 18, 22010–22019 (2010).
    [CrossRef] [PubMed]
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  19. P. Fieguth, Statistical Image Processing and Multidimensional Modeling (Springer, 2010).
  20. B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. 24, 227–234 (1995).
    [CrossRef]
  21. W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag, 101–104 (2009).
  22. P. Puvanathasan, P. Forbes, Z. Ren, D. Malchow, S. Boyd, and K. Bizheva, “High-speed, high-resolution Fourier-domain optical coherence tomography system for retinal imaging in the 1060 nm wavelength region,” Opt. Lett. 33, 2479–2481 (2008).
    [PubMed]

2010 (2)

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
[CrossRef]

X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express 18, 22010–22019 (2010).
[CrossRef] [PubMed]

2009 (2)

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Imag. 28, 106–121 (2009).
[CrossRef]

W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag, 101–104 (2009).

2008 (1)

2007 (1)

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

2006 (2)

E. Candës, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

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

2005 (1)

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (3)

R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express 11, 889–894 (2003).
[CrossRef] [PubMed]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

S. A. Boppart, “Optical coherence tomography: technology and applications for neuroimaging,” Psychophysiology 40, 529–541 (2003).
[CrossRef] [PubMed]

2002 (1)

1995 (1)

B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. 24, 227–234 (1995).
[CrossRef]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Bajraszewski, T.

Bizheva, K.

Boppart, S. A.

S. A. Boppart, “Optical coherence tomography: technology and applications for neuroimaging,” Psychophysiology 40, 529–541 (2003).
[CrossRef] [PubMed]

Bouma, B. E.

B. E. Bouma and G. J. Tearney, Handbook of Optical Coherence Tomography (Informa Healthcare, 2001).

Boyd, S.

Candës, E.

E. Candës, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Clausi, D.

A. Wong, A. Mishra, D. Clausi, and P. Fieguth, “Sparse reconstruction of breast MRI using homotopic L0 minimization in a regional sparsified domain,” Biomed. Eng. IEEE Trans, 1–10 (2010).

Donoho, D.

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

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

Drexler, W.

R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express 12, 2156–2165 (2004).
[CrossRef] [PubMed]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer, 2008).
[CrossRef]

Duker, J. S.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

Fercher, A.

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
[CrossRef]

Fieguth, P.

P. Fieguth, Statistical Image Processing and Multidimensional Modeling (Springer, 2010).

A. Wong, A. Mishra, D. Clausi, and P. Fieguth, “Sparse reconstruction of breast MRI using homotopic L0 minimization in a regional sparsified domain,” Biomed. Eng. IEEE Trans, 1–10 (2010).

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Forbes, P.

Fujimoto, J. G.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer, 2008).
[CrossRef]

Gilboa, G.

G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” Tech. Rep. CAM Report 07-23, Univ. California, Los Angeles, 2007.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Guo, W.

W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag, 101–104 (2009).

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hermann, B.

Hitzenberger, C.

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, F.

W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag, 101–104 (2009).

Kang, J. U.

Karl, W. C.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Ko, T.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

Kowalczyk, A.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
[CrossRef]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Le, T.

Leitgeb, R.

Liang, D.

D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc., 1032–1035 (2009).

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Liu, X.

Lustig, M.

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

Malchow, D.

Manduca, A.

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Imag. 28, 106–121 (2009).
[CrossRef]

Mishra, A.

A. Wong, A. Mishra, D. Clausi, and P. Fieguth, “Sparse reconstruction of breast MRI using homotopic L0 minimization in a regional sparsified domain,” Biomed. Eng. IEEE Trans, 1–10 (2010).

Mohan, N.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Natarajan, B. K.

B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. 24, 227–234 (1995).
[CrossRef]

Osher, S.

G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” Tech. Rep. CAM Report 07-23, Univ. California, Los Angeles, 2007.

Pauly, J.

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

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Puvanathasan, P.

Ren, Z.

Romberg, J.

E. Candës, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Saleh, B. E. A.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Schuman, J. S.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Srinivasan, V.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

Stingl, A.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Stojanovic, I.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tao, T.

E. Candës, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Tearney, G. J.

B. E. Bouma and G. J. Tearney, Handbook of Optical Coherence Tomography (Informa Healthcare, 2001).

Teich, M. C.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Trzasko, J.

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Imag. 28, 106–121 (2009).
[CrossRef]

Unterhuber, A.

Wang, H.

D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc., 1032–1035 (2009).

Wojtkowski, M.

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
[CrossRef]

Wong, A.

A. Wong, A. Mishra, D. Clausi, and P. Fieguth, “Sparse reconstruction of breast MRI using homotopic L0 minimization in a regional sparsified domain,” Biomed. Eng. IEEE Trans, 1–10 (2010).

Ying, L.

D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc., 1032–1035 (2009).

IEEE Trans. Inf. Theory (2)

E. Candës, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

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

IEEE Trans. Med. Imag. (1)

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Imag. 28, 106–121 (2009).
[CrossRef]

Int. Sym. Biomed Imag (1)

W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag, 101–104 (2009).

Magn. Reson. Med. (1)

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

Ophthalmology (1)

M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Proc. SPIE (1)

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Psychophysiology (1)

S. A. Boppart, “Optical coherence tomography: technology and applications for neuroimaging,” Psychophysiology 40, 529–541 (2003).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

SIAM J. Comput. (1)

B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. 24, 227–234 (1995).
[CrossRef]

Other (6)

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer, 2008).
[CrossRef]

G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” Tech. Rep. CAM Report 07-23, Univ. California, Los Angeles, 2007.

P. Fieguth, Statistical Image Processing and Multidimensional Modeling (Springer, 2010).

B. E. Bouma and G. J. Tearney, Handbook of Optical Coherence Tomography (Informa Healthcare, 2001).

A. Wong, A. Mishra, D. Clausi, and P. Fieguth, “Sparse reconstruction of breast MRI using homotopic L0 minimization in a regional sparsified domain,” Biomed. Eng. IEEE Trans, 1–10 (2010).

D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc., 1032–1035 (2009).

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Figures (7)

Fig. 1
Fig. 1

Reconstruction results from 50% of the acquired human retinal fovea data. The colored boxes mark sections that are enlarged in Fig. 2. The reconstruction results using 100% of the samples are provided as a reference.

Fig. 2
Fig. 2

Zoomed-in regions from Fig. 1. The fine details and the structural detail of the individual layers are better maintained in the reconstructed results produced using NLR compared to L2 and L1.

Fig. 3
Fig. 3

Reconstruction results from 50% of the acquired human corneal data. The colored boxes mark sections that are enlarged in Fig. 4.

Fig. 4
Fig. 4

Zoomed-in regions from Fig. 3. The structural detail of the individual layers as well as the keratocyte cells are better maintained in the reconstructed results produced using NLR compared to L2 and L1.

Fig. 5
Fig. 5

Reconstruction results from 50% of the acquired human limbus data. The colored boxes mark sections that are enlarged in Fig. 6.

Fig. 6
Fig. 6

Zoomed-in regions from Fig. 5. The structural detail of the individual layers as well as the fine structural details are better maintained in the reconstructed results produced using NLR compared to L2 and L1.

Fig. 7
Fig. 7

SNR of the reconstructed retinal, corneal and limbus data as a function of the percentage of camera pixels used for sparse reconstruction. Observe the substantial improvement in all cases of the proposed NLR method over the L2 and L1 reconstruction methods.

Tables (1)

Tables Icon

Algorithm 1 Homotopic, non-local sparse reconstruction for OCT imagery

Equations (14)

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f ( x ) = 𝔽 1 { F ( k ) }
K 2 x max Δ k / π ,
f u ( x ) = 𝔽 1 { Φ F ( k ) }
f ^ ( x ) = argmin f ( x ) f ( x ) 2 s . t . Φ F ^ ( k ) = Φ F ( k )
f ^ ( x ) = argmin f ( x ) Ψ f ( x ) 0 s . t . Φ F ^ ( k ) = Φ F ( k )
f ^ ( x ) = argmin f ( x ) Ψ f ( x ) 1 s . t . Φ F ^ ( k ) = Φ F ( k )
f ^ ( x ) = argmin f ( x ) Ψ f ( x ) 1 + T V ( f ( x ) ) s . t . Φ F ^ ( k ) = Φ F ( k )
f ^ ( x ) = lim σ 0 argmin f ( x ) ρ ( | Ψ f ( x ) | , σ ) s . t . Φ F ^ ( k ) = Φ F ( k )
f ^ ( x ) = lim σ 0 argmin f ( x ) ρ ( | Ψ f ( x ) | , σ ) s . t . Φ F ^ ( k ) Φ F ( k ) 2 < ε
f ^ ( x ) = lim σ 0 argmin f ( x ) η ( | Ψ f ( x ) | , σ ) s . t . Φ F ^ ( k ) Φ F ( k ) 2 < ε
η ( | Φ f ( x ) | , σ ) = [ x Ω y 𝒩 ( x ) w ( x , y , σ ) ( N ( x ) N ( y ) ) 2 ]
w [ x , y , σ ] = exp { ( N ( x ) ) N ( y ) 2 σ 2 }
SNR = 10 log 10 ( max ( x ) 2 MSE )
MSE = 1 N x Ω ( f ( x ) f ^ ( x ) ) 2

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