Abstract

High quality, large size volumetric imaging of biological tissue with optical coherence tomography (OCT) requires large number and high density of scans, which results in large data acquisition volume. This may lead to corruption of the data with motion artifacts related to natural motion of biological tissue, and could potentially cause conflicts with the maximum permissible exposure of biological tissue to optical radiation. Therefore, OCT can benefit greatly from different approaches to sparse or compressive sampling of the data where the signal is recovered from its sub-Nyquist measurements. In this paper, a new energy-guided compressive sensing approach is proposed for improving the quality of images acquired with Fourier domain OCT (FD-OCT) and reconstructed from sparse data sets. The proposed algorithm learns an optimized sampling probability density function based on the energy distribution of the training data set, which is then used for sparse sampling instead of the commonly used uniformly random sampling. It was demonstrated that the proposed energy-guided learning approach to compressive FD-OCT of retina images requires 45% fewer samples in comparison with the conventional uniform compressive sensing (CS) approach while achieving similar reconstruction performance. This novel approach to sparse sampling has the potential to significantly reduce data acquisition while maintaining image quality.

© 2013 OSA

Full Article  |  PDF Article
OSA Recommended Articles
Homotopic, non-local sparse reconstruction of optical coherence tomography imagery

Chenyi Liu, Alexander Wong, Kostadinka Bizheva, Paul Fieguth, and Hongxia Bie
Opt. Express 20(9) 10200-10211 (2012)

Dictionary-based light field acquisition using sparse camera array

Xuan Cao, Zheng Geng, and Tuotuo Li
Opt. Express 22(20) 24081-24095 (2014)

Volumetric (3D) compressive sensing spectral domain optical coherence tomography

Daguang Xu, Yong Huang, and Jin U. Kang
Biomed. Opt. Express 5(11) 3921-3934 (2014)

References

  • View by:
  • |
  • |
  • |

  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]
  2. W. Drexler and J. G. Fujimoto, “Optical coherence tomography,” Springer BerlinHeidelberg (2008).
  3. ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
    [Crossref] [PubMed]
  4. W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol 95(2), 171–177 (2010).
    [Crossref] [PubMed]
  5. J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
    [Crossref]
  6. S. Martinez-Conde, S. L. Macknik, and D. H. Hubel, “The role of fixational eye movements in visual perception,” Nat. Rev. Neurosci 5(3), 229–240 (2004).
    [Crossref] [PubMed]
  7. M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “The role of fixational eye movements in visual perception,” Biomed. Opt. Express 2(9), 2690–2697 (2011).
    [Crossref] [PubMed]
  8. T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
    [Crossref] [PubMed]
  9. R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolutionFourier domain optical coherence tomography,” Opt. Express 12, 2156–2165 (2004).
    [Crossref] [PubMed]
  10. M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183 (2003).
    [Crossref] [PubMed]
  11. 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]
  12. D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [Crossref]
  13. D. Donoho and J. Tanner, “Counting faces of randomly-projected polytopes when the projection radically lowers dimension,” J. AMS 22, 1–5 (2009).
  14. E.J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2004).
    [Crossref]
  15. M. Lustig, D. Donoho, and J. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
    [Crossref] [PubMed]
  16. J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Image 28, 106–121 (2009).
    [Crossref]
  17. 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).
  18. D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc.1032–1035 (2009).
  19. 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–75700L-5 (2010).
    [Crossref]
  20. 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]
  21. M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “Real-time high-speed volumetric imaging using compressive sampling optical coherence tomography,” Opt. Express 2, 2690–2697 (2011)
    [Crossref]
  22. C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, “Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express 20, 10200–10211 (2012).
    [Crossref] [PubMed]
  23. B. Wu, E. Lebed, M. Sarunic, and M. Beg, “Quantitative evaluation of transform domains for compressive sampling-based recovery of sparsely sampled volumetric OCT images,” IEEE Trans. Bio. Eng.1–9 (2012).
    [Crossref]
  24. D.L. Donoho and X. Huo, “Uncertainty principles and ideal atom decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
    [Crossref]
  25. M. Elad and A.M. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of bases,” IEEE Trans. Inf. Theory 48, 2558–2567 (2002).
    [Crossref]
  26. R. Gribonval and M. Nielsen, “Sparse representations in unions of bases,” IEEE Trans. Inf. Theory 49, 3320–3325 (2003).
    [Crossref]
  27. E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,”Communications on Pure and Applied Mathematics 59, 1207–1221 (2006).
    [Crossref]
  28. J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50, 2231–2242 (2004).
    [Crossref]
  29. J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory 51, 1030–1051 (2006).
    [Crossref]
  30. L. He, T. Chang, S. Osher, T. Fang, and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Reports6–35, 2006.
  31. S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale L1-regularized least squares problems with applications in signal processing and statistics,” Manuscript, (2007).
  32. E. J. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl 23, 969–985 (2007).
    [Crossref]
  33. S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation 28, 277–289 (2008).
    [Crossref]
  34. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28, 253–263 (2008).
    [Crossref]
  35. E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique 386, 589–592 (2008).
    [Crossref]
  36. M. Rudelson and R. Vershynin, “Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements,” 40th An. Conf. Inf. Sc. Sys.207–210 (2009).
  37. Z. Wang and G. Arce, “Variable density compressed image sampling,”IEEE Tran. on Image Proc. 19, 264–270 (2010).
    [Crossref]
  38. G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett 18, 595–598 (2011).
    [Crossref]
  39. X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE 7904, 79041C (2011).
    [Crossref]
  40. M.F. Duarte and Y.C. Elda, “Structured compressed sensing from theory to applications,” IEEE Tran. Sig. Proc. Lett 59, 4053–4085 (2011).
    [Crossref]
  41. R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
    [Crossref]
  42. S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” Journal of Visual Communication and Image Representation (2012).
    [Crossref]
  43. S. Schwartz, A. Wong, and D. A. Clausi, “Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion,” Opt. Express 20, 17281–17296 (2012).
    [Crossref] [PubMed]
  44. S.M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE 2869, 243253 (1997).
  45. S.P. Monacos, R.K. Lam, A.A. Portillo, and G.G. Ortiz, “Design of an event-driven random-access-windowing CCD-based camera,” Proc. SPIE 4975, 115 (2003).
    [Crossref]
  46. B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE 2950, 2–7 (1996).
    [Crossref]
  47. P. Fieguth, Statistical image processing and multidimensional modeling (SpringerNew York, 2010).
  48. B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. 24, 227–234 (1995).
    [Crossref]
  49. G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” Tech. Rep. CAM Report 07–23, Univ. California, Los Angeles, 2007.
  50. W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag101–104 (2009).
  51. C. P. Robert and G. Casella, “Stable signal recovery from incomplete and inaccurate measurements,”Monte Carlo Statistical Methods, New York: Springer-Verlag (1999).
  52. H. Chen, Tutorial on monte carlo sampling (The Ohio state university, department of chemcal and biomolecular engineering, technical report, 2005).
  53. 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]

2012 (3)

2011 (8)

G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett 18, 595–598 (2011).
[Crossref]

X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE 7904, 79041C (2011).
[Crossref]

M.F. Duarte and Y.C. Elda, “Structured compressed sensing from theory to applications,” IEEE Tran. Sig. Proc. Lett 59, 4053–4085 (2011).
[Crossref]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “Real-time high-speed volumetric imaging using compressive sampling optical coherence tomography,” Opt. Express 2, 2690–2697 (2011)
[Crossref]

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “The role of fixational eye movements in visual perception,” Biomed. Opt. Express 2(9), 2690–2697 (2011).
[Crossref] [PubMed]

T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011).
[Crossref] [PubMed]

2010 (5)

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol 95(2), 171–177 (2010).
[Crossref] [PubMed]

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).

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–75700L-5 (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]

Z. Wang and G. Arce, “Variable density compressed image sampling,”IEEE Tran. on Image Proc. 19, 264–270 (2010).
[Crossref]

2009 (5)

M. Rudelson and R. Vershynin, “Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements,” 40th An. Conf. Inf. Sc. Sys.207–210 (2009).

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

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

D. Donoho and J. Tanner, “Counting faces of randomly-projected polytopes when the projection radically lowers dimension,” J. AMS 22, 1–5 (2009).

W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag101–104 (2009).

2008 (5)

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]

R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
[Crossref]

S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation 28, 277–289 (2008).
[Crossref]

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28, 253–263 (2008).
[Crossref]

E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique 386, 589–592 (2008).
[Crossref]

2007 (2)

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

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

2006 (4)

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]

J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory 51, 1030–1051 (2006).
[Crossref]

E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,”Communications on Pure and Applied Mathematics 59, 1207–1221 (2006).
[Crossref]

2004 (4)

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

E.J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2004).
[Crossref]

S. Martinez-Conde, S. L. Macknik, and D. H. Hubel, “The role of fixational eye movements in visual perception,” Nat. Rev. Neurosci 5(3), 229–240 (2004).
[Crossref] [PubMed]

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

2003 (3)

M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183 (2003).
[Crossref] [PubMed]

R. Gribonval and M. Nielsen, “Sparse representations in unions of bases,” IEEE Trans. Inf. Theory 49, 3320–3325 (2003).
[Crossref]

S.P. Monacos, R.K. Lam, A.A. Portillo, and G.G. Ortiz, “Design of an event-driven random-access-windowing CCD-based camera,” Proc. SPIE 4975, 115 (2003).
[Crossref]

2002 (1)

M. Elad and A.M. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of bases,” IEEE Trans. Inf. Theory 48, 2558–2567 (2002).
[Crossref]

2001 (1)

D.L. Donoho and X. Huo, “Uncertainty principles and ideal atom decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[Crossref]

1997 (1)

S.M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE 2869, 243253 (1997).

1996 (1)

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE 2950, 2–7 (1996).
[Crossref]

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]

Anderson, D.

R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
[Crossref]

Arce, G.

Z. Wang and G. Arce, “Variable density compressed image sampling,”IEEE Tran. on Image Proc. 19, 264–270 (2010).
[Crossref]

Bajraszewski, T.

Baraniuk, R.

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28, 253–263 (2008).
[Crossref]

Beg, M.

B. Wu, E. Lebed, M. Sarunic, and M. Beg, “Quantitative evaluation of transform domains for compressive sampling-based recovery of sparsely sampled volumetric OCT images,” IEEE Trans. Bio. Eng.1–9 (2012).
[Crossref]

Beg, M. F.

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “Real-time high-speed volumetric imaging using compressive sampling optical coherence tomography,” Opt. Express 2, 2690–2697 (2011)
[Crossref]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “The role of fixational eye movements in visual perception,” Biomed. Opt. Express 2(9), 2690–2697 (2011).
[Crossref] [PubMed]

Bie, H.

Biedermann, B. R.

Bizheva, K.

C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, “Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express 20, 10200–10211 (2012).
[Crossref] [PubMed]

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]

Boyd, S.

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]

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale L1-regularized least squares problems with applications in signal processing and statistics,” Manuscript, (2007).

Bruckstein, A.M.

M. Elad and A.M. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of bases,” IEEE Trans. Inf. Theory 48, 2558–2567 (2002).
[Crossref]

Candes, E.

E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,”Communications on Pure and Applied Mathematics 59, 1207–1221 (2006).
[Crossref]

Candes, E. J.

E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique 386, 589–592 (2008).
[Crossref]

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

Candes, E.J.

E.J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2004).
[Crossref]

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]

Casella, G.

C. P. Robert and G. Casella, “Stable signal recovery from incomplete and inaccurate measurements,”Monte Carlo Statistical Methods, New York: Springer-Verlag (1999).

Chang, T.

L. He, T. Chang, S. Osher, T. Fang, and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Reports6–35, 2006.

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]

Chen, H.

H. Chen, Tutorial on monte carlo sampling (The Ohio state university, department of chemcal and biomolecular engineering, technical report, 2005).

Chen, Q.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Chiu, L.K.

R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
[Crossref]

Choma, M. A.

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).

Clausi, D. A.

S. Schwartz, A. Wong, and D. A. Clausi, “Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion,” Opt. Express 20, 17281–17296 (2012).
[Crossref] [PubMed]

S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” Journal of Visual Communication and Image Representation (2012).
[Crossref]

Cui, L.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Davenport, M.

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28, 253–263 (2008).
[Crossref]

DeVore, R.

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28, 253–263 (2008).
[Crossref]

Dierickx, B.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE 2950, 2–7 (1996).
[Crossref]

Donoho, D.

D. Donoho and J. Tanner, “Counting faces of randomly-projected polytopes when the projection radically lowers dimension,” J. AMS 22, 1–5 (2009).

M. Lustig, D. Donoho, and J. Pauly, “Sparse MRI: The application of compressed sensing 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]

Donoho, D.L.

D.L. Donoho and X. Huo, “Uncertainty principles and ideal atom decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[Crossref]

Drexler, W.

Du, C.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Duarte, M.F.

M.F. Duarte and Y.C. Elda, “Structured compressed sensing from theory to applications,” IEEE Tran. Sig. Proc. Lett 59, 4053–4085 (2011).
[Crossref]

Eigenwillig, C. M.

Elad, M.

M. Elad and A.M. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of bases,” IEEE Trans. Inf. Theory 48, 2558–2567 (2002).
[Crossref]

Elda, Y.C.

M.F. Duarte and Y.C. Elda, “Structured compressed sensing from theory to applications,” IEEE Tran. Sig. Proc. Lett 59, 4053–4085 (2011).
[Crossref]

Fang, T.

L. He, T. Chang, S. Osher, T. Fang, and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Reports6–35, 2006.

Fercher, A.

Fieguth, P.

C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, “Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express 20, 10200–10211 (2012).
[Crossref] [PubMed]

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).

P. Fieguth, Statistical image processing and multidimensional modeling (SpringerNew York, 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]

Folio, LS

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

Forbes, P.

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]

Fujimoto, J. 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]

W. Drexler and J. G. Fujimoto, “Optical coherence tomography,” Springer BerlinHeidelberg (2008).

Gabriele, ML

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

Geitzenauer, W.

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol 95(2), 171–177 (2010).
[Crossref] [PubMed]

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.

Gorinevsky, D.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale L1-regularized least squares problems with applications in signal processing and statistics,” Manuscript, (2007).

Gray, J.

R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
[Crossref]

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]

Gribonval, R.

R. Gribonval and M. Nielsen, “Sparse representations in unions of bases,” IEEE Trans. Inf. Theory 49, 3320–3325 (2003).
[Crossref]

Guo, W.

W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag101–104 (2009).

Hasler, P.

R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
[Crossref]

He, L.

L. He, T. Chang, S. Osher, T. Fang, and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Reports6–35, 2006.

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. K.

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol 95(2), 171–177 (2010).
[Crossref] [PubMed]

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 Imag101–104 (2009).

Hubel, D. H.

S. Martinez-Conde, S. L. Macknik, and D. H. Hubel, “The role of fixational eye movements in visual perception,” Nat. Rev. Neurosci 5(3), 229–240 (2004).
[Crossref] [PubMed]

Huber, R.

Huo, X.

D.L. Donoho and X. Huo, “Uncertainty principles and ideal atom decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[Crossref]

Hurmeriz, V.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Ishikawa, H

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

Izatt, J. A.

Jian, Y.

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “Real-time high-speed volumetric imaging using compressive sampling optical coherence tomography,” Opt. Express 2, 2690–2697 (2011)
[Crossref]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “The role of fixational eye movements in visual perception,” Biomed. Opt. Express 2(9), 2690–2697 (2011).
[Crossref] [PubMed]

Kagemann, L

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

Kang, J. U.

Kang, J.U.

X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE 7904, 79041C (2011).
[Crossref]

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–75700L-5 (2010).
[Crossref]

Karp, C. L.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Kim, S.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale L1-regularized least squares problems with applications in signal processing and statistics,” Manuscript, (2007).

Klein, T.

Koh, K.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale L1-regularized least squares problems with applications in signal processing and statistics,” Manuscript, (2007).

Lam, R.K.

S.P. Monacos, R.K. Lam, A.A. Portillo, and G.G. Ortiz, “Design of an event-driven random-access-windowing CCD-based camera,” Proc. SPIE 4975, 115 (2003).
[Crossref]

Le, T.

Lebed, E.

B. Wu, E. Lebed, M. Sarunic, and M. Beg, “Quantitative evaluation of transform domains for compressive sampling-based recovery of sparsely sampled volumetric OCT images,” IEEE Trans. Bio. Eng.1–9 (2012).
[Crossref]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “Real-time high-speed volumetric imaging using compressive sampling optical coherence tomography,” Opt. Express 2, 2690–2697 (2011)
[Crossref]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “The role of fixational eye movements in visual perception,” Biomed. Opt. Express 2(9), 2690–2697 (2011).
[Crossref] [PubMed]

Leitgeb, R.

Li, M.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

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, C.

Liu, X.

X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE 7904, 79041C (2011).
[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]

Lustig, M.

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

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale L1-regularized least squares problems with applications in signal processing and statistics,” Manuscript, (2007).

Mackenzie, P. J.

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “Real-time high-speed volumetric imaging using compressive sampling optical coherence tomography,” Opt. Express 2, 2690–2697 (2011)
[Crossref]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “The role of fixational eye movements in visual perception,” Biomed. Opt. Express 2(9), 2690–2697 (2011).
[Crossref] [PubMed]

Macknik, S. L.

S. Martinez-Conde, S. L. Macknik, and D. H. Hubel, “The role of fixational eye movements in visual perception,” Nat. Rev. Neurosci 5(3), 229–240 (2004).
[Crossref] [PubMed]

Malchow, D.

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]

Manduca, A.

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

Mart, A.

S.M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE 2869, 243253 (1997).

Martinez-Conde, S.

S. Martinez-Conde, S. L. Macknik, and D. H. Hubel, “The role of fixational eye movements in visual perception,” Nat. Rev. Neurosci 5(3), 229–240 (2004).
[Crossref] [PubMed]

Mendelson, S.

S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation 28, 277–289 (2008).
[Crossref]

Meynants, G.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE 2950, 2–7 (1996).
[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–75700L-5 (2010).
[Crossref]

Monacos, S.P.

S.P. Monacos, R.K. Lam, A.A. Portillo, and G.G. Ortiz, “Design of an event-driven random-access-windowing CCD-based camera,” Proc. SPIE 4975, 115 (2003).
[Crossref]

Natarajan, B. K.

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

Nielsen, M.

R. Gribonval and M. Nielsen, “Sparse representations in unions of bases,” IEEE Trans. Inf. Theory 49, 3320–3325 (2003).
[Crossref]

Ogiers, W.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE 2950, 2–7 (1996).
[Crossref]

Ortiz, G.G.

S.P. Monacos, R.K. Lam, A.A. Portillo, and G.G. Ortiz, “Design of an event-driven random-access-windowing CCD-based camera,” Proc. SPIE 4975, 115 (2003).
[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.

L. He, T. Chang, S. Osher, T. Fang, and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Reports6–35, 2006.

Pajor, A.

S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation 28, 277–289 (2008).
[Crossref]

Pauly, J.

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

Perez, V. L.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Pine, J.

S.M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE 2869, 243253 (1997).

Portillo, A.A.

S.P. Monacos, R.K. Lam, A.A. Portillo, and G.G. Ortiz, “Design of an event-driven random-access-windowing CCD-based camera,” Proc. SPIE 4975, 115 (2003).
[Crossref]

Potter, S.M.

S.M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE 2869, 243253 (1997).

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.

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]

Puy, G.

G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett 18, 595–598 (2011).
[Crossref]

Ren, Z.

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]

Robert, C. P.

C. P. Robert and G. Casella, “Stable signal recovery from incomplete and inaccurate measurements,”Monte Carlo Statistical Methods, New York: Springer-Verlag (1999).

Robucci, R.

R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
[Crossref]

Romberg, J.

R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
[Crossref]

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

E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,”Communications on Pure and Applied Mathematics 59, 1207–1221 (2006).
[Crossref]

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]

Rudelson, M.

M. Rudelson and R. Vershynin, “Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements,” 40th An. Conf. Inf. Sc. Sys.207–210 (2009).

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–75700L-5 (2010).
[Crossref]

Sarunic, M.

B. Wu, E. Lebed, M. Sarunic, and M. Beg, “Quantitative evaluation of transform domains for compressive sampling-based recovery of sparsely sampled volumetric OCT images,” IEEE Trans. Bio. Eng.1–9 (2012).
[Crossref]

Sarunic, M. V.

Scheffer, D.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE 2950, 2–7 (1996).
[Crossref]

Schmidt-Erfurth, U. M.

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol 95(2), 171–177 (2010).
[Crossref] [PubMed]

Schuman, J. S.

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]

Schuman, JS

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

Schwartz, S.

S. Schwartz, A. Wong, and D. A. Clausi, “Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion,” Opt. Express 20, 17281–17296 (2012).
[Crossref] [PubMed]

S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” Journal of Visual Communication and Image Representation (2012).
[Crossref]

Shen, M.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Shousha, M. A.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Speier, P.

L. He, T. Chang, S. Osher, T. Fang, and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Reports6–35, 2006.

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–75700L-5 (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]

Tanner, J.

D. Donoho and J. Tanner, “Counting faces of randomly-projected polytopes when the projection radically lowers dimension,” J. AMS 22, 1–5 (2009).

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]

E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,”Communications on Pure and Applied Mathematics 59, 1207–1221 (2006).
[Crossref]

E.J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2004).
[Crossref]

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–75700L-5 (2010).
[Crossref]

Tomczak-Jaegermann, N.

S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation 28, 277–289 (2008).
[Crossref]

Tropp, J. A.

J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory 51, 1030–1051 (2006).
[Crossref]

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

Trzasko, J.

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

Unterhuber, A.

Vandergheynst, P.

G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett 18, 595–598 (2011).
[Crossref]

Vershynin, R.

M. Rudelson and R. Vershynin, “Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements,” 40th An. Conf. Inf. Sc. Sys.207–210 (2009).

Vlummens, J.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE 2950, 2–7 (1996).
[Crossref]

Wakin, M.

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28, 253–263 (2008).
[Crossref]

Wang, H.

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

Wang, J.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Wang, Z.

Z. Wang and G. Arce, “Variable density compressed image sampling,”IEEE Tran. on Image Proc. 19, 264–270 (2010).
[Crossref]

Wiaux, Y.

G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett 18, 595–598 (2011).
[Crossref]

Wieser, W.

Wollstein, G

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

Wong, A.

S. Schwartz, A. Wong, and D. A. Clausi, “Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion,” Opt. Express 20, 17281–17296 (2012).
[Crossref] [PubMed]

C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, “Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express 20, 10200–10211 (2012).
[Crossref] [PubMed]

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).

S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” Journal of Visual Communication and Image Representation (2012).
[Crossref]

Wu, B.

B. Wu, E. Lebed, M. Sarunic, and M. Beg, “Quantitative evaluation of transform domains for compressive sampling-based recovery of sparsely sampled volumetric OCT images,” IEEE Trans. Bio. Eng.1–9 (2012).
[Crossref]

Xu, J

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

Yang, C.

Ying, L.

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

Yoo, S. H.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Young, M.

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “Real-time high-speed volumetric imaging using compressive sampling optical coherence tomography,” Opt. Express 2, 2690–2697 (2011)
[Crossref]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “The role of fixational eye movements in visual perception,” Biomed. Opt. Express 2(9), 2690–2697 (2011).
[Crossref] [PubMed]

Zhu, D.

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

40th An. Conf. Inf. Sc. Sys. (1)

M. Rudelson and R. Vershynin, “Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements,” 40th An. Conf. Inf. Sc. Sys.207–210 (2009).

Biomed. Eng. IEEE Trans (1)

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).

Biomed. Opt. Express (1)

Br. J. Ophthalmol (1)

W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol 95(2), 171–177 (2010).
[Crossref] [PubMed]

Communications on Pure and Applied Mathematics (1)

E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,”Communications on Pure and Applied Mathematics 59, 1207–1221 (2006).
[Crossref]

Comptes rendus - Mathematique (1)

E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique 386, 589–592 (2008).
[Crossref]

Constructive Approximation (2)

S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation 28, 277–289 (2008).
[Crossref]

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28, 253–263 (2008).
[Crossref]

IEEE Int. Conf. Ac. Speech Sig. Proc. (1)

R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008).
[Crossref]

IEEE Sig. Proc. Lett (1)

G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett 18, 595–598 (2011).
[Crossref]

IEEE Tran. on Image Proc. (1)

Z. Wang and G. Arce, “Variable density compressed image sampling,”IEEE Tran. on Image Proc. 19, 264–270 (2010).
[Crossref]

IEEE Tran. Sig. Proc. Lett (1)

M.F. Duarte and Y.C. Elda, “Structured compressed sensing from theory to applications,” IEEE Tran. Sig. Proc. Lett 59, 4053–4085 (2011).
[Crossref]

IEEE Trans. Bio. Eng. (1)

B. Wu, E. Lebed, M. Sarunic, and M. Beg, “Quantitative evaluation of transform domains for compressive sampling-based recovery of sparsely sampled volumetric OCT images,” IEEE Trans. Bio. Eng.1–9 (2012).
[Crossref]

IEEE Trans. Inf. Theory (8)

D.L. Donoho and X. Huo, “Uncertainty principles and ideal atom decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[Crossref]

M. Elad and A.M. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of bases,” IEEE Trans. Inf. Theory 48, 2558–2567 (2002).
[Crossref]

R. Gribonval and M. Nielsen, “Sparse representations in unions of bases,” IEEE Trans. Inf. Theory 49, 3320–3325 (2003).
[Crossref]

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]

E.J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2004).
[Crossref]

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

J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory 51, 1030–1051 (2006).
[Crossref]

IEEE Trans. Med. Image (1)

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Image 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 Imag101–104 (2009).

Inverse Probl (1)

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

Invest Ophthalmol Vis Sci (1)

ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci 52, 2425–2436 (2011).
[Crossref] [PubMed]

J. AMS (1)

D. Donoho and J. Tanner, “Counting faces of randomly-projected polytopes when the projection radically lowers dimension,” J. AMS 22, 1–5 (2009).

Magn. Reson. Med. (1)

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

Nat. Rev. Neurosci (1)

S. Martinez-Conde, S. L. Macknik, and D. H. Hubel, “The role of fixational eye movements in visual perception,” Nat. Rev. Neurosci 5(3), 229–240 (2004).
[Crossref] [PubMed]

Ophthalmic Surg Lasers Imaging (1)

J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging 42(4), 15–27 (2011).
[Crossref]

Opt. Express (7)

Opt. Lett (1)

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]

Proc. IEEE Eng. Med. Biol. Soc. (1)

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

Proc. SPIE (5)

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–75700L-5 (2010).
[Crossref]

X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE 7904, 79041C (2011).
[Crossref]

S.M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE 2869, 243253 (1997).

S.P. Monacos, R.K. Lam, A.A. Portillo, and G.G. Ortiz, “Design of an event-driven random-access-windowing CCD-based camera,” Proc. SPIE 4975, 115 (2003).
[Crossref]

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE 2950, 2–7 (1996).
[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 (8)

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

C. P. Robert and G. Casella, “Stable signal recovery from incomplete and inaccurate measurements,”Monte Carlo Statistical Methods, New York: Springer-Verlag (1999).

H. Chen, Tutorial on monte carlo sampling (The Ohio state university, department of chemcal and biomolecular engineering, technical report, 2005).

P. Fieguth, Statistical image processing and multidimensional modeling (SpringerNew York, 2010).

W. Drexler and J. G. Fujimoto, “Optical coherence tomography,” Springer BerlinHeidelberg (2008).

S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” Journal of Visual Communication and Image Representation (2012).
[Crossref]

L. He, T. Chang, S. Osher, T. Fang, and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Reports6–35, 2006.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale L1-regularized least squares problems with applications in signal processing and statistics,” Manuscript, (2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Energy-guided compressive sensing implementation.

Fig. 2
Fig. 2

Sampling data PDF obtained from energy-guided learning approach based on different type of tissues and background. All the PDF plots comply with the basic shape of background PDF, and have different characteristics according to different kind of tissues. For illustration purposes only, the function presented in Fig. 2 were smoothened. No filtering was used for smoothing Ps(k) (Eq. (12)) in the implementation.

Fig. 3
Fig. 3

Reconstruction results from 50% of the acquired human retinal fovea data. The colored boxes mark sections that are enlarged in Fig. 4. The reconstruction results using 100% of the samples are provided as a reference.

Fig. 4
Fig. 4

Zoomed-in regions from Fig. 3. The fine details and the structural detail of the individual layers are better maintained in the reconstructed results produced using EGCS compared to CS.

Fig. 5
Fig. 5

Reconstruction results from 50% of the acquired human corneal data. The colored boxes mark sections that are enlarged in Fig. 6. The reconstruction results using 100% of the samples are provided as a reference.

Fig. 6
Fig. 6

Zoomed-in regions from Fig. 5. The fine details and the structural detail of the individual layers are better maintained in the reconstructed results produced using EGCS compared to CS.

Fig. 7
Fig. 7

Reconstruction results from 50% of the acquired human fingertip data. The colored boxes mark sections that are enlarged in Fig. 8. The reconstruction results using 100% of the samples are provided as a reference.

Fig. 8
Fig. 8

Zoomed-in regions from Fig. 7. The fine details and the structural detail of the individual layers are better maintained in the reconstructed results produced using EGCS compared to CS.

Fig. 9
Fig. 9

PSNR vs. sampling rate for cornea, retina and fingertip measurements.

Fig. 10
Fig. 10

Effect on point-spread functions of the system through cornea measurements at 40% sampling rate.

Equations (17)

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

f ( x ) = 𝔽 1 { F ( k ) }
K 2 x max Δ k / π ,
f u ( x ) = 𝔽 1 { Φ F ( k ) }
Ω K = { k | k = 1 , , K } ,
Ω K = Ω T Ω T c , with Ω T Ω T c ,
p S ( k ) [ 0 , 1 ] k
y m = F , φ m + ε m = k = 1 K φ m ( k ) + ε m
y ¯ = Φ T F + ε ¯
φ T , m ( k ) = { φ m ( k ) , if ( k ) Ω T , 0 , if ( k ) Ω T c .
y m = F , φ T , m + ε m , m = 1 , 2 , , M
p T ( k | π ) = ( 1 π p S ( k ) ) δ ( k ) + π p S ( k )
p S ( k ) = i | F i ( k ) | k i | F i ( k ) |
I ( k ) = P ( ω k )
f ^ ( x ) = lim σ 0 argmin f ( x ) η ( | Ψ f ( x ) | , σ ) s . t . Φ F ^ ( k ) Φ F ( k ) 2 < ε
p T C S ( k | π ) = ( 1 π p S C S ( k ) ) δ ( k ) + π p S C S ( k )
P S N R = 10 log 10 ( max 2 ( f ( x ) ) M S E )
M S E = 1 N x Ω ( f ( x ) f ^ ( x ) ) 2

Metrics