Abstract

We propose a novel compressive sensing (CS) method on spectral domain optical coherence tomography (SDOCT). By replacing the widely used uniform discrete Fourier transform (UDFT) matrix with a new sensing matrix which is a modification of the non-uniform discrete Fourier transform (NUDFT) matrix, it is shown that undersampled non-linear wavenumber spectral data can be used directly in the CS reconstruction. Thus k-space grid filling and k-linear mask calibration which were proposed to obtain linear wavenumber sampling from the non-linear wavenumber interferometric spectra in previous studies of CS in SDOCT (CS-SDOCT) are no longer needed. The NUDFT matrix is modified to promote the sparsity of reconstructed A-scans by making them symmetric while preserving the value of the desired half. In addition, we show that dispersion compensation can be implemented by multiplying the frequency-dependent correcting phase directly to the real spectra, eliminating the need for constructing complex component of the real spectra. This enables the incorporation of dispersion compensation into the CS reconstruction by adding the correcting term to the modified NUDFT matrix. With this new sensing matrix, A-scan with dispersion compensation can be reconstructed from undersampled non-linear wavenumber spectral data by CS reconstruction. Experimental results show that proposed method can achieve high quality imaging with dispersion compensation.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Drexler and J. G. Fujimoto, Optical coherence tomography: Technology and Applications (Springer, Berlin, Germany, 2008).
    [CrossRef]
  2. A.F. Fercher, W. Drexler, C.K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys., 66(2), 239–303 (2003).
    [CrossRef]
  3. R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express, 11(8), 889–894 (2003).
    [CrossRef]
  4. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express, 11(18), 2183–2189 (2003).
    [CrossRef] [PubMed]
  5. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, 52(4), 1289–1306 (2006).
    [CrossRef]
  6. E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory, 52(2), 489–509 (2006).
    [CrossRef]
  7. E. J. Candes and T. Tao, “Near-optical signal recovery from random projection: universal encoding strategies?” IEEE Trans. Inf. Theory, 52(12), 5406–5425 (2006).
    [CrossRef]
  8. N. Mohan, I. Stojanovic, W.C. Karl, B.E.A. Saleh, and M.C. Teich, “Compressed sensing in optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7570, 75700L (2010).
    [CrossRef]
  9. X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express, 18(21), 22010–22019 (2010).
    [CrossRef] [PubMed]
  10. E. Lebed, P. J. Mackenzie, M. V. Sarunic, and F. M. Beg, “Rapid volumetric OCT image acquisition using compressive sampling,” Opt. Express, 18(29), 21003–21012 (2010).
    [CrossRef] [PubMed]
  11. 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,” Biomed. Opt. Express, 2(9), 2690–2697 (2011).
    [CrossRef]
  12. X. Liu and J. U. Kang, “Sparse OCT: Optimizing compressed sensing in spectral domain optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7904, 79041CL (2011).
  13. L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express3(5), 927–942 (2012).
    [CrossRef] [PubMed]
  14. N. Zhang, T. Huo, C. Wang, T. Chen, J. Zheng, and P. Xue, “Compressed sensing with linear-in-wavenumber sampling in spectral-domain optical coherence tomography,” Opt. Lett.37(15), 3075–3077 (2012).
    [CrossRef] [PubMed]
  15. D. Xu, N. Vaswani, Y. Huang, and J. U. Kang, “Modified compressive sensing optical coherence tomography with noise reduction,” Opt. Lett.37(20), 4209–4211 (2012).
    [CrossRef] [PubMed]
  16. S. Schwartz, C. Liu, A. Wong, D. A. Clausi, P. Fieguth, and K. Bizheva, “Energy-guided learning approach to compressive sensing,” Opt. Express21(1), 329–344 (2013).
    [CrossRef] [PubMed]
  17. J. Ke and E. Lam, “Image reconstruction from nonuniformly spaced samples in spectral-domain optical coherence tomography,” Biomed. Opt. Express3, 741–752 (2012).
    [CrossRef] [PubMed]
  18. M. Jeon, J. Kim, U. Jung, C. Lee, W. Jung, and S. A. Boppart, “Full-range k-domain linearization in spectral-domain optical coherence tomography, Appl. Opt.50, 1158–1162 (2011).
    [CrossRef] [PubMed]
  19. H. K. Chan and S. Tang, High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform, Biomed. Opt. Express1, 1309–1319 (2010).
    [CrossRef]
  20. K. Zhang and J. U. Kang, “Real-time 4D signal processing and visualization using graphics processing unit on a regular nonlinear-k Fourier-domain OCT system,” Opt. Express18(11), 11772–11784 (2010).
    [CrossRef] [PubMed]
  21. S.S. Sherif, C. Flueraru, Y. Mao, and S. Change, “Swept source optical coherence tomography with nonuniform frequency domain sampling,” Biomedical Optics, OSA, Technical Digest (CD)(Optical Society of America, 2008), paper BMD86.
    [CrossRef]
  22. K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express17(14), 12121–12131 (2009).
    [CrossRef] [PubMed]
  23. S. Vergnole, D. Levesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express18(12), 10446–10461 (2010).
    [CrossRef] [PubMed]
  24. M. Lustig and J. M. Pauly, “SPIRiT: iterative self-consistent parallel imaging reconstruction from arbitrary k-space,” Magn. Reson. Med., 64, 457–471 (2010).
    [PubMed]
  25. F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).
  26. E. Aboussouan, L. Marinelli, and E. Tan, “Non-cartesian compressed sensing for diffusion spectrum imaging,” Proc. Intl. Soc. Mag. Recon. Med., 19, 1919 (2011).
  27. X. Chen, M. Salerno, F. H. Epstein, and C. H. Meyer, “Accelerated multi-TI spiral MRI using compressed sensing with temporal constraints,” Proc. Intl. Soc. Mag. Recon. Med.19, 4369 (2011).
  28. M. Wojtkowski, V.J. Srinivasan, T.H. Ko, J.G. Fujimoto, A. Kowalczyk, and J.S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express12(11), 2404–2422 (2004).
    [CrossRef] [PubMed]
  29. Y. Chen and X. Li, “Dispersion management up to the third order for real-time optical coherence tomography involving a phase or frequency modulator,” Opt. Express12(24), 5968–5978 (2004).
    [CrossRef] [PubMed]
  30. D.L. Marks, A.L. Oldenburg, J.J. Reynolds, and S.A. Boppart, “Digital algorithm for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt.42(2), 204–217 (2003).
    [CrossRef] [PubMed]
  31. K. Zhang and J. U. Kang, “Real-time numerical dispersion compensation using graphics processing unit for Fourier-domain optical coherence tomography,” Electron. Lett., 47(5), 309–310 (2011).
    [CrossRef]
  32. E. van den Berg and M.P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM Journal on Scientific Computing, 31(2), 890–912 (2008).
    [CrossRef]
  33. E. van den Berg and M.P. Friedlander, “SPGL1: a solver for large-scale sparse reconstruction”, http://www.cs.ubc.ca/labs/scl/spgl1 (2007).
  34. S. M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE2869, 243253 (1997).
  35. S. P. Monacos, R. K. Lam, A. A. Portillo, and G. G. Ortiz, “Design of an event-driven random-assess-windowing CCD-based camera,” Proc. SPIE4975, 115 (2003).
    [CrossRef]
  36. B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996).
    [CrossRef]
  37. M. lusting, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med.58(6), 1182–1195 (2007).
    [CrossRef]
  38. S. Becker, J. O. Robin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” Technical report, California Institute of Technology (2009).
  39. M. Afonso, J. Bioucas-Dias, and M. Figueiredo, “An augmented Lagrangian approach to the constraint optimization formulation of imaging inverse problems,” IEEE Trans. on Image Proc.20(3), 681–695 (2009).
    [CrossRef]

2013 (1)

2012 (5)

2011 (5)

K. Zhang and J. U. Kang, “Real-time numerical dispersion compensation using graphics processing unit for Fourier-domain optical coherence tomography,” Electron. Lett., 47(5), 309–310 (2011).
[CrossRef]

X. Chen, M. Salerno, F. H. Epstein, and C. H. Meyer, “Accelerated multi-TI spiral MRI using compressed sensing with temporal constraints,” Proc. Intl. Soc. Mag. Recon. Med.19, 4369 (2011).

M. Jeon, J. Kim, U. Jung, C. Lee, W. Jung, and S. A. Boppart, “Full-range k-domain linearization in spectral-domain optical coherence tomography, Appl. Opt.50, 1158–1162 (2011).
[CrossRef] [PubMed]

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,” Biomed. Opt. Express, 2(9), 2690–2697 (2011).
[CrossRef]

X. Liu and J. U. Kang, “Sparse OCT: Optimizing compressed sensing in spectral domain optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7904, 79041CL (2011).

2010 (7)

2009 (2)

K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express17(14), 12121–12131 (2009).
[CrossRef] [PubMed]

M. Afonso, J. Bioucas-Dias, and M. Figueiredo, “An augmented Lagrangian approach to the constraint optimization formulation of imaging inverse problems,” IEEE Trans. on Image Proc.20(3), 681–695 (2009).
[CrossRef]

2008 (1)

E. van den Berg and M.P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM Journal on Scientific Computing, 31(2), 890–912 (2008).
[CrossRef]

2007 (1)

M. lusting, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med.58(6), 1182–1195 (2007).
[CrossRef]

2006 (3)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, 52(4), 1289–1306 (2006).
[CrossRef]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory, 52(2), 489–509 (2006).
[CrossRef]

E. J. Candes and T. Tao, “Near-optical signal recovery from random projection: universal encoding strategies?” IEEE Trans. Inf. Theory, 52(12), 5406–5425 (2006).
[CrossRef]

2004 (2)

2003 (5)

1997 (1)

S. M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE2869, 243253 (1997).

1996 (1)

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996).
[CrossRef]

1919 (1)

E. Aboussouan, L. Marinelli, and E. Tan, “Non-cartesian compressed sensing for diffusion spectrum imaging,” Proc. Intl. Soc. Mag. Recon. Med., 19, 1919 (2011).

Aboussouan, E.

E. Aboussouan, L. Marinelli, and E. Tan, “Non-cartesian compressed sensing for diffusion spectrum imaging,” Proc. Intl. Soc. Mag. Recon. Med., 19, 1919 (2011).

Afonso, M.

M. Afonso, J. Bioucas-Dias, and M. Figueiredo, “An augmented Lagrangian approach to the constraint optimization formulation of imaging inverse problems,” IEEE Trans. on Image Proc.20(3), 681–695 (2009).
[CrossRef]

Becker, S.

S. Becker, J. O. Robin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” Technical report, California Institute of Technology (2009).

Beg, F. M.

Beg, M. F.

Bioucas-Dias, J.

M. Afonso, J. Bioucas-Dias, and M. Figueiredo, “An augmented Lagrangian approach to the constraint optimization formulation of imaging inverse problems,” IEEE Trans. on Image Proc.20(3), 681–695 (2009).
[CrossRef]

Bizheva, K.

Boppart, S. A.

Boppart, S.A.

Bredies, K.

F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).

Candes, E. J.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory, 52(2), 489–509 (2006).
[CrossRef]

E. J. Candes and T. Tao, “Near-optical signal recovery from random projection: universal encoding strategies?” IEEE Trans. Inf. Theory, 52(12), 5406–5425 (2006).
[CrossRef]

S. Becker, J. O. Robin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” Technical report, California Institute of Technology (2009).

Chan, H. K.

Change, S.

S.S. Sherif, C. Flueraru, Y. Mao, and S. Change, “Swept source optical coherence tomography with nonuniform frequency domain sampling,” Biomedical Optics, OSA, Technical Digest (CD)(Optical Society of America, 2008), paper BMD86.
[CrossRef]

Chen, M.

Chen, T.

Chen, X.

X. Chen, M. Salerno, F. H. Epstein, and C. H. Meyer, “Accelerated multi-TI spiral MRI using compressed sensing with temporal constraints,” Proc. Intl. Soc. Mag. Recon. Med.19, 4369 (2011).

Chen, Y.

Choma, M.

Clausi, D. A.

Dierickx, B.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996).
[CrossRef]

Ding, Z.

Donoho, D.

M. lusting, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med.58(6), 1182–1195 (2007).
[CrossRef]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, 52(4), 1289–1306 (2006).
[CrossRef]

Drexler, W.

A.F. Fercher, W. Drexler, C.K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys., 66(2), 239–303 (2003).
[CrossRef]

W. Drexler and J. G. Fujimoto, Optical coherence tomography: Technology and Applications (Springer, Berlin, Germany, 2008).
[CrossRef]

Duker, J.S.

Epstein, F. H.

X. Chen, M. Salerno, F. H. Epstein, and C. H. Meyer, “Accelerated multi-TI spiral MRI using compressed sensing with temporal constraints,” Proc. Intl. Soc. Mag. Recon. Med.19, 4369 (2011).

Fang, L.

Farsiu, S.

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(2), 239–303 (2003).
[CrossRef]

Fieguth, P.

Figueiredo, M.

M. Afonso, J. Bioucas-Dias, and M. Figueiredo, “An augmented Lagrangian approach to the constraint optimization formulation of imaging inverse problems,” IEEE Trans. on Image Proc.20(3), 681–695 (2009).
[CrossRef]

Flueraru, C.

S.S. Sherif, C. Flueraru, Y. Mao, and S. Change, “Swept source optical coherence tomography with nonuniform frequency domain sampling,” Biomedical Optics, OSA, Technical Digest (CD)(Optical Society of America, 2008), paper BMD86.
[CrossRef]

Friedlander, M.P.

E. van den Berg and M.P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM Journal on Scientific Computing, 31(2), 890–912 (2008).
[CrossRef]

Fujimoto, J. G.

W. Drexler and J. G. Fujimoto, Optical coherence tomography: Technology and Applications (Springer, Berlin, Germany, 2008).
[CrossRef]

Fujimoto, J.G.

Gallichan, D.

F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).

Hennig, J.

F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).

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(2), 239–303 (2003).
[CrossRef]

Huang, Y.

Huo, T.

Izatt, J.

Izatt, J. A.

Jeon, M.

Jian, Y.

Jung, U.

Jung, W.

Kang, J. U.

D. Xu, N. Vaswani, Y. Huang, and J. U. Kang, “Modified compressive sensing optical coherence tomography with noise reduction,” Opt. Lett.37(20), 4209–4211 (2012).
[CrossRef] [PubMed]

X. Liu and J. U. Kang, “Sparse OCT: Optimizing compressed sensing in spectral domain optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7904, 79041CL (2011).

K. Zhang and J. U. Kang, “Real-time numerical dispersion compensation using graphics processing unit for Fourier-domain optical coherence tomography,” Electron. Lett., 47(5), 309–310 (2011).
[CrossRef]

K. Zhang and J. U. Kang, “Real-time 4D signal processing and visualization using graphics processing unit on a regular nonlinear-k Fourier-domain OCT system,” Opt. Express18(11), 11772–11784 (2010).
[CrossRef] [PubMed]

X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express, 18(21), 22010–22019 (2010).
[CrossRef] [PubMed]

Karl, W.C.

N. Mohan, I. Stojanovic, W.C. Karl, B.E.A. Saleh, and M.C. Teich, “Compressed sensing in optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7570, 75700L (2010).
[CrossRef]

Ke, J.

Kim, J.

Knoll, F.

F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).

Ko, T.H.

Kowalczyk, A.

Lam, E.

Lam, R. K.

S. P. Monacos, R. K. Lam, A. A. Portillo, and G. G. Ortiz, “Design of an event-driven random-assess-windowing CCD-based camera,” Proc. SPIE4975, 115 (2003).
[CrossRef]

Lamouche, G.

Lasser, T.

A.F. Fercher, W. Drexler, C.K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys., 66(2), 239–303 (2003).
[CrossRef]

Lebed, E.

Lee, C.

Leitgeb, R.

Levesque, D.

Li, S.

Li, X.

Liu, C.

Liu, X.

X. Liu and J. U. Kang, “Sparse OCT: Optimizing compressed sensing in spectral domain optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7904, 79041CL (2011).

X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express, 18(21), 22010–22019 (2010).
[CrossRef] [PubMed]

Lustig, M.

M. Lustig and J. M. Pauly, “SPIRiT: iterative self-consistent parallel imaging reconstruction from arbitrary k-space,” Magn. Reson. Med., 64, 457–471 (2010).
[PubMed]

lusting, M.

M. lusting, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med.58(6), 1182–1195 (2007).
[CrossRef]

Mackenzie, P. J.

Mao, Y.

S.S. Sherif, C. Flueraru, Y. Mao, and S. Change, “Swept source optical coherence tomography with nonuniform frequency domain sampling,” Biomedical Optics, OSA, Technical Digest (CD)(Optical Society of America, 2008), paper BMD86.
[CrossRef]

Marinelli, L.

E. Aboussouan, L. Marinelli, and E. Tan, “Non-cartesian compressed sensing for diffusion spectrum imaging,” Proc. Intl. Soc. Mag. Recon. Med., 19, 1919 (2011).

Marks, D.L.

Mart, A.

S. M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE2869, 243253 (1997).

Meng, J.

Meyer, C. H.

X. Chen, M. Salerno, F. H. Epstein, and C. H. Meyer, “Accelerated multi-TI spiral MRI using compressed sensing with temporal constraints,” Proc. Intl. Soc. Mag. Recon. Med.19, 4369 (2011).

Meynants, G.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996).
[CrossRef]

Mohan, N.

N. Mohan, I. Stojanovic, W.C. Karl, B.E.A. Saleh, and M.C. Teich, “Compressed sensing in optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7570, 75700L (2010).
[CrossRef]

Monacos, S. P.

S. P. Monacos, R. K. Lam, A. A. Portillo, and G. G. Ortiz, “Design of an event-driven random-assess-windowing CCD-based camera,” Proc. SPIE4975, 115 (2003).
[CrossRef]

Nie, Q.

Ogiers, W.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996).
[CrossRef]

Oldenburg, A.L.

Ortiz, G. G.

S. P. Monacos, R. K. Lam, A. A. Portillo, and G. G. Ortiz, “Design of an event-driven random-assess-windowing CCD-based camera,” Proc. SPIE4975, 115 (2003).
[CrossRef]

Pauly, J. M.

M. Lustig and J. M. Pauly, “SPIRiT: iterative self-consistent parallel imaging reconstruction from arbitrary k-space,” Magn. Reson. Med., 64, 457–471 (2010).
[PubMed]

M. lusting, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med.58(6), 1182–1195 (2007).
[CrossRef]

Pine, J.

S. M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE2869, 243253 (1997).

Portillo, A. A.

S. P. Monacos, R. K. Lam, A. A. Portillo, and G. G. Ortiz, “Design of an event-driven random-assess-windowing CCD-based camera,” Proc. SPIE4975, 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. SPIE2869, 243253 (1997).

Reynolds, J.J.

Robin, J. O.

S. Becker, J. O. Robin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” Technical report, California Institute of Technology (2009).

Romberg, J.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory, 52(2), 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,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7570, 75700L (2010).
[CrossRef]

Salerno, M.

X. Chen, M. Salerno, F. H. Epstein, and C. H. Meyer, “Accelerated multi-TI spiral MRI using compressed sensing with temporal constraints,” Proc. Intl. Soc. Mag. Recon. Med.19, 4369 (2011).

Sarunic, M.

Sarunic, M. V.

Scheffer, D.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996).
[CrossRef]

Schultz, G.

F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).

Schwartz, S.

Sherif, S.S.

S.S. Sherif, C. Flueraru, Y. Mao, and S. Change, “Swept source optical coherence tomography with nonuniform frequency domain sampling,” Biomedical Optics, OSA, Technical Digest (CD)(Optical Society of America, 2008), paper BMD86.
[CrossRef]

Srinivasan, V.J.

Stojanovic, I.

N. Mohan, I. Stojanovic, W.C. Karl, B.E.A. Saleh, and M.C. Teich, “Compressed sensing in optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7570, 75700L (2010).
[CrossRef]

Stollberger, R.

F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).

Tan, E.

E. Aboussouan, L. Marinelli, and E. Tan, “Non-cartesian compressed sensing for diffusion spectrum imaging,” Proc. Intl. Soc. Mag. Recon. Med., 19, 1919 (2011).

Tang, S.

Tao, T.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory, 52(2), 489–509 (2006).
[CrossRef]

E. J. Candes and T. Tao, “Near-optical signal recovery from random projection: universal encoding strategies?” IEEE Trans. Inf. Theory, 52(12), 5406–5425 (2006).
[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,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7570, 75700L (2010).
[CrossRef]

Toth, C. A.

van den Berg, E.

E. van den Berg and M.P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM Journal on Scientific Computing, 31(2), 890–912 (2008).
[CrossRef]

Vaswani, N.

Vergnole, S.

Vlummens, J.

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996).
[CrossRef]

Wang, C.

Wang, K.

Wojtkowski, M.

Wong, A.

Wu, T.

Xu, D.

Xu, L.

Xue, P.

Yang, C.

Young, M.

Zaitsev, M.

F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).

Zhang, K.

K. Zhang and J. U. Kang, “Real-time numerical dispersion compensation using graphics processing unit for Fourier-domain optical coherence tomography,” Electron. Lett., 47(5), 309–310 (2011).
[CrossRef]

K. Zhang and J. U. Kang, “Real-time 4D signal processing and visualization using graphics processing unit on a regular nonlinear-k Fourier-domain OCT system,” Opt. Express18(11), 11772–11784 (2010).
[CrossRef] [PubMed]

Zhang, N.

Zheng, J.

Appl. Opt. (2)

Biomed. Opt. Express (4)

Electron. Lett. (1)

K. Zhang and J. U. Kang, “Real-time numerical dispersion compensation using graphics processing unit for Fourier-domain optical coherence tomography,” Electron. Lett., 47(5), 309–310 (2011).
[CrossRef]

IEEE Trans. Inf. Theory (2)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, 52(4), 1289–1306 (2006).
[CrossRef]

E. J. Candes and T. Tao, “Near-optical signal recovery from random projection: universal encoding strategies?” IEEE Trans. Inf. Theory, 52(12), 5406–5425 (2006).
[CrossRef]

IEEE Trans. on Image Proc. (1)

M. Afonso, J. Bioucas-Dias, and M. Figueiredo, “An augmented Lagrangian approach to the constraint optimization formulation of imaging inverse problems,” IEEE Trans. on Image Proc.20(3), 681–695 (2009).
[CrossRef]

Inf. Theory (1)

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory, 52(2), 489–509 (2006).
[CrossRef]

Magn. Reson. Med. (3)

M. Lustig and J. M. Pauly, “SPIRiT: iterative self-consistent parallel imaging reconstruction from arbitrary k-space,” Magn. Reson. Med., 64, 457–471 (2010).
[PubMed]

F. Knoll, G. Schultz, K. Bredies, D. Gallichan, M. Zaitsev, J. Hennig, and R. Stollberger, “Reconstruction of undersampled radial PatLoc imaging using total generalized variation,” Magn. Reson. Med.37(15), in Press (2012).

M. lusting, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med.58(6), 1182–1195 (2007).
[CrossRef]

Opt. Express (10)

K. Zhang and J. U. Kang, “Real-time 4D signal processing and visualization using graphics processing unit on a regular nonlinear-k Fourier-domain OCT system,” Opt. Express18(11), 11772–11784 (2010).
[CrossRef] [PubMed]

K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express17(14), 12121–12131 (2009).
[CrossRef] [PubMed]

S. Vergnole, D. Levesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express18(12), 10446–10461 (2010).
[CrossRef] [PubMed]

M. Wojtkowski, V.J. Srinivasan, T.H. Ko, J.G. Fujimoto, A. Kowalczyk, and J.S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express12(11), 2404–2422 (2004).
[CrossRef] [PubMed]

Y. Chen and X. Li, “Dispersion management up to the third order for real-time optical coherence tomography involving a phase or frequency modulator,” Opt. Express12(24), 5968–5978 (2004).
[CrossRef] [PubMed]

R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express, 11(8), 889–894 (2003).
[CrossRef]

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express, 11(18), 2183–2189 (2003).
[CrossRef] [PubMed]

S. Schwartz, C. Liu, A. Wong, D. A. Clausi, P. Fieguth, and K. Bizheva, “Energy-guided learning approach to compressive sensing,” Opt. Express21(1), 329–344 (2013).
[CrossRef] [PubMed]

X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express, 18(21), 22010–22019 (2010).
[CrossRef] [PubMed]

E. Lebed, P. J. Mackenzie, M. V. Sarunic, and F. M. Beg, “Rapid volumetric OCT image acquisition using compressive sampling,” Opt. Express, 18(29), 21003–21012 (2010).
[CrossRef] [PubMed]

Opt. Lett. (2)

Proc. Intl. Soc. Mag. Recon. Med. (2)

E. Aboussouan, L. Marinelli, and E. Tan, “Non-cartesian compressed sensing for diffusion spectrum imaging,” Proc. Intl. Soc. Mag. Recon. Med., 19, 1919 (2011).

X. Chen, M. Salerno, F. H. Epstein, and C. H. Meyer, “Accelerated multi-TI spiral MRI using compressed sensing with temporal constraints,” Proc. Intl. Soc. Mag. Recon. Med.19, 4369 (2011).

Proc. SPIE (3)

S. M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE2869, 243253 (1997).

S. P. Monacos, R. K. Lam, A. A. Portillo, and G. G. Ortiz, “Design of an event-driven random-assess-windowing CCD-based camera,” Proc. SPIE4975, 115 (2003).
[CrossRef]

B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996).
[CrossRef]

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(2), 239–303 (2003).
[CrossRef]

SIAM Journal on Scientific Computing (1)

E. van den Berg and M.P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM Journal on Scientific Computing, 31(2), 890–912 (2008).
[CrossRef]

Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE (2)

N. Mohan, I. Stojanovic, W.C. Karl, B.E.A. Saleh, and M.C. Teich, “Compressed sensing in optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7570, 75700L (2010).
[CrossRef]

X. Liu and J. U. Kang, “Sparse OCT: Optimizing compressed sensing in spectral domain optical coherence tomography,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, SPIE, 7904, 79041CL (2011).

Other (4)

W. Drexler and J. G. Fujimoto, Optical coherence tomography: Technology and Applications (Springer, Berlin, Germany, 2008).
[CrossRef]

E. van den Berg and M.P. Friedlander, “SPGL1: a solver for large-scale sparse reconstruction”, http://www.cs.ubc.ca/labs/scl/spgl1 (2007).

S.S. Sherif, C. Flueraru, Y. Mao, and S. Change, “Swept source optical coherence tomography with nonuniform frequency domain sampling,” Biomedical Optics, OSA, Technical Digest (CD)(Optical Society of America, 2008), paper BMD86.
[CrossRef]

S. Becker, J. O. Robin, and E. J. Candes, “NESTA: a fast and accurate first-order method for sparse recovery,” Technical report, California Institute of Technology (2009).

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 (6)

Fig. 1
Fig. 1

Sparsity comparison of A-scans by applying (a) inverse UDFT to the linear wavenumber whole spectra (ŷ), (b) inverse NUDFT to the non-linear wavenumber whole spectra (y), (c) modified inverse NUDFT to the non-linear wavenumber whole spectra (y)

Fig. 2
Fig. 2

Plot of |T1(τ1)|/|T2(τ1)| versus different reflector position τ1. Simulation is done with different level of dispersion (a2 ∈ {−500, −250, −100, 0, 100, 250, 500} fs2; a3 = 0).

Fig. 3
Fig. 3

Sensitivity roll-off of systems applying (a) inverse UDFT to the linear wavenumber real spectra without dispersion compensation, (b) inverse NUDFT to the non-linear wavenumber real spectra without dispersion compensation, (c) dispersion compensation method in [28], (d) proposed dispersion compensation method on the non-linear wavenumber real spectra. A 2cm water cell is inserted to introduce large dispersion mismatch.

Fig. 4
Fig. 4

B-scans of a mouse paw. (a) original image obtained by applying NUDFT to 100% of the acquired non-linear wavenumber spectra; (b) CS reconstruction result with the NUDFT matrix from 40% of the acquired non-linear wavenumber spectra; (c) CS reconstruction result with the MNUDFT matrix from 40% of the acquired non-linear wavenumber spectra; The scale bars represent 100μm. Image size in pixel is 450 × 1000

Fig. 5
Fig. 5

B-scans of a mouse cornea; (a) original image obtained by applying NUDFT to 100% of the acquired non-linear wavenumber spectra; (b) CS reconstruction result with the NUDFT matrix from 37.5% of the acquired non-linear wavenumber spectra; (c) CS reconstruction result with the MNUDFT matrix from 37.5% of the acquired non-linear wavenumber spectra; (d), (e) and (f) are zoom in of the cyan rectangle areas in (a), (b) and (c) respectively. The scale bars represent 100μm. Image size in pixel is 700 × 1000.

Fig. 6
Fig. 6

B-scans of a polymer-layered phantom with 2.4cm water induced dispersion; (a) original image obtained by applying NUDFT to 100% of the acquired non-linear wavenumber spectra; (b) CS reconstruction result with the NUDFT matrix from 50% of the acquired non-linear wavenumber spectra; (c) CS reconstruction result with the MNUDFT matrix from 50% of the acquired non-linear wavenumber spectra; (d) image obtained by applying the forward MNUDFT matrix to 100% of the acquired non-linear wavenumber spectra. The scale bars represent 100μm. Image size in pixel is 450 × 1000.

Tables (3)

Tables Icon

Table 1 Local contrast and SNR of the B-scans of mouse paw in Fig. 4

Tables Icon

Table 2 Local contrast and SNR of the B-scans of mouse cornea in Fig. 5

Tables Icon

Table 3 Local contrast and SNR of the B-scans of polymer-layered phantom in Fig. 6

Equations (15)

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

x ^ n = 1 N m = 0 N 1 y ^ m exp ( i 2 π Δ k ^ ( k ^ m k ^ 0 ) × n ) = 1 N m = 0 N 1 y ^ m exp ( i ω ^ m × n )
x n = 1 N m = 0 N 1 y m exp ( i 2 π Δ k ( k m k 0 ) × n ) = 1 N m = 0 N 1 y m exp ( i ω m × n )
minimize g W g 1 , s . t . F u g z u 2 ε
x ^ N n = 1 N m = 0 N 1 y ^ m exp ( i 2 π N m × ( N n ) ) = 1 N m = 0 N 1 y ^ m exp ( i 2 π N m × n ) = ( x ^ n ) *
x N n = 1 N m = 0 N 1 y m exp ( i ω m × ( N n ) ) = 1 N m = 0 N 1 y m exp ( i ω m × n ) × exp ( i ω m N ) ( x n ) *
[ x 0 x 1 x N ] = [ h ( 0 , 0 ) h ( 1 , 0 ) h ( N 1 , 0 ) h ( 0 , N / 2 ) h ( 1 , N / 2 ) h ( N 1 , N / 2 ) h ( 0 , N 1 ) h ( 1 , N 1 ) h ( N 1 , N 1 ) ] [ y 0 y 1 y N 1 ]
[ x 0 x 1 x N 1 ] = [ h ( 0 , 0 ) h ( 1 , 0 ) h ( N 1 , 0 ) h ( 0 , 1 ) h ( 1 , 1 ) h ( N 1 , 1 ) h ( 0 , N / 2 1 ) h ( 1 , N / 2 1 ) h ( N 1 , N / 2 1 ) h ( 0 , N / 2 ) h ( 1 , N / 2 ) h ( N 1 , N / 2 ) h ( 0 , N / 2 1 ) * h ( 1 , N / 2 1 ) * h ( N 1 , N / 2 1 ) * h ( 0 , 1 ) * h ( 1 , 1 ) * h ( N 1 , 1 ) * ] [ y 0 y 1 y N 1 ]
x N n = 1 N m = 0 N 1 y m h ( m , n ) * = ( 1 N m = 0 N 1 y m h ( m , n ) ) * = ( x n ) *
I comp ( ω m ) = Re { 2 × Σ n S n ( ω m ) S r ( ω m ) exp ( i [ ω m τ n + Φ ( ω m ) ] ) } × exp ( i Φ ( ω m ) ) = ( Σ n A n ( ω m ) ( exp ( i [ ω m τ n + Φ ( ω m ) ] + exp ( i [ ω m τ n + Φ ( ω m ) ] ) ) ) exp ( i Φ ( ω m ) ) = n A n ( ω m ) exp ( i [ ω m τ n ] ) A 1 + n A n ( ω m ) exp ( i [ ω m τ n + 2 Φ ( ω m ) ] ) A 2
[ x 0 c x 1 c x N 1 c ] = [ h ( 0 , 0 ) h ( 1 , 0 ) h ( N 1 , 0 ) h ( 0 , N / 2 ) h ( 1 , N / 2 ) h ( N 1 , N / 2 ) h ( 0 , N 1 ) h ( 1 , N 1 ) h ( N 1 , N 1 ) ] ( [ y 0 y 1 y N 1 ] . * [ e i Φ ( ω 0 ) e i Φ ( ω 1 ) e i Φ ( ω N 1 ) ] )
[ x 0 c x 1 c x N 1 c ] = [ h ( 0 , 0 ) Φ 0 h ( 1 , 0 ) Φ 1 h ( N 1 , 0 ) Φ N 1 h ( 0 , N / 2 ) Φ 0 h ( 1 , N / 2 ) Φ 1 h ( N 1 , N / 2 ) Φ N 1 h ( 0 , N 1 ) Φ 0 h ( 1 , N 1 ) Φ 1 h ( N 1 , N 1 ) Φ N 1 ] [ y 0 y 1 y N 1 ]
[ x 0 c x 1 c x N 1 c ] = [ h ( 0 , 0 ) Φ 0 h ( 1 , 0 ) Φ 1 h ( N 1 , 0 ) Φ N 1 h ( 0 , 1 ) Φ 0 h ( 1 , 1 ) Φ 1 h ( N 1 , 1 ) Φ N 1 h ( 0 , N / 2 1 ) Φ 0 h ( 1 , N / 2 1 ) Φ 1 h ( N 1 , N / 2 1 ) Φ N 1 h ( 0 , N / 2 ) Φ 0 h ( 1 , N / 2 ) Φ 1 h ( N 1 , N / 2 ) Φ N 1 ( h ( 0 , N / 2 1 ) Φ 0 ) * ( h ( 1 , N / 2 1 ) Φ 1 ) * ( h ( N 1 , N / 2 1 ) Φ N 1 ) * ( h ( 0 , 1 ) Φ 0 ) * ( h ( 1 , 1 ) Φ 1 ) * ( h ( N 1 , 1 ) Φ N 1 ) * ] [ y 0 y 1 y N 1 ]
[ ( h ( 0 , 0 ) Φ 0 ) * ( h ( 0 , N / 2 1 ) Φ 0 ) * h ( 0 , N / 2 1 ) Φ 0 h ( 0 , 1 ) Φ 0 ( h ( N 1 , 0 ) Φ N 1 ) * ( h ( N 1 , N / 2 1 ) Φ N 1 ) * h ( N 1 , N / 2 1 ) Φ N 1 h ( N 1 , 1 ) Φ N 1 ]
local contrast = μ o μ b
SNR = 20 × log 10 ( 1 N o ( i , j ) object I ( i , j ) 2 1 N b ( i , j ) background I ( i , j ) 2 )

Metrics