Abstract

We applied compressed sensing (CS) to spectral domain optical coherence tomography (SD OCT) and studied its effectiveness. We tested the CS reconstruction by randomly undersampling the k-space SD OCT signal. We achieved this by applying pseudo-random masks to sample 62.5%, 50%, and 37.5% of the CCD camera pixels. OCT images are reconstructed by solving an optimization problem that minimizes the l 1 norm of a transformed image to enforce sparsity, subject to data consistency constraints. CS could allow an array detector with fewer pixels to reconstruct high resolution OCT images while reducing the total amount of data required to process the images.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Brezinski, Optical Coherence Tomography: Principles and Applications, (Academic Press, London, 2006).
  2. B. E. Bouma, and G. J. Tearney, Handbook of Optical Coherence Tomography, (Informa Healthcare, New York, 2001).
  3. U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Sel. Top. Quantum Electron. 11(4), 799–805 (2005).
  4. 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. Express 18(11), 11772–11784 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-11-11772 .
    [PubMed]
  5. J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).
  6. R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-8-889 .
    [PubMed]
  7. 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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183 .
    [PubMed]
  8. X. Liu, X. Li, D. Kim, I. Ilev, and J. U. Kang, “Fiber Optic Fourier-domain Common-path OCT,” Chin. Opt. Lett. 6(12), 899–903 (2008).
  9. I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842–4858 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-6-4842 .
    [PubMed]
  10. M. Balicki, J. Han, I. Iordachita, P. Gehlbach, J. Handa, J. U. Kang, and R. Taylor, “Single Fiber Optical Coherence Tomography Microsurgical Instruments for Computer and Robot-Assisted Retinal Surgery,” Proceedings of the MICCAI Conference (2009)
  11. K. Zhang, W. Wang, J. Han, and J. U. Kang, “A surface topology and motion compensation system for microsurgery guidance and intervention based on common-path optical coherence tomography,” IEEE Trans. Biomed. Eng. 56(9), 2318–2321 (2009).
    [PubMed]
  12. D. L. Donoho, “Compressed Sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
  13. E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
  14. M. Lustig, 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).
    [PubMed]
  15. Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15(2), 021311 (2010).
    [PubMed]
  16. N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE 7570, 75700L (2010).
  17. M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
    [PubMed]
  18. Z. Jian, Z. Yu, L. Yu, B. Rao, Z. Chen, and B. J. Tromberg, “Speckle attenuation in optical coherence tomography by curvelet shrinkage,” Opt. Lett. 34(10), 1516–1518 (2009).
    [PubMed]
  19. J. Shewchuk, “An introduction to the conjugate gradient method without the agonizing pain,” Technical Report CMUCS-TR-94–125, Carnegie Mellon University, (1994).
  20. S. M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE 2869, 243–253 (1997).
  21. 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).
  22. D. Donoho and I. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika 81(3), 425–455 (1994).
  23. J. A. Fessler and B. P. Sutton, “Nonuniform fast Fourier transforms using min–max interpolation,” IEEE Trans. Signal Process. 51(2), 560–574 (2003).

2010 (4)

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15(2), 021311 (2010).
[PubMed]

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

J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).

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. Express 18(11), 11772–11784 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-11-11772 .
[PubMed]

2009 (3)

2008 (1)

2007 (2)

M. Lustig, 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).
[PubMed]

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[PubMed]

2006 (2)

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

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

2005 (1)

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Sel. Top. Quantum Electron. 11(4), 799–805 (2005).

2003 (4)

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, 243–253 (1997).

1994 (1)

D. Donoho and I. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika 81(3), 425–455 (1994).

Candes, E.

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

Cense, B.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[PubMed]

Chen, T. C.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[PubMed]

Chen, Z.

Choma, M.

de Boer, J. F.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[PubMed]

Donoho, D.

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

D. Donoho and I. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika 81(3), 425–455 (1994).

Donoho, D. L.

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

Fercher, A.

Fessler, J. A.

J. A. Fessler and B. P. Sutton, “Nonuniform fast Fourier transforms using min–max interpolation,” IEEE Trans. Signal Process. 51(2), 560–574 (2003).

Fried, N. M.

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Sel. Top. Quantum Electron. 11(4), 799–805 (2005).

Gehlbach, P.

J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).

Gora, M.

Gorczynska, I.

Grulkowski, I.

Guo, Z.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15(2), 021311 (2010).
[PubMed]

Han, J.

J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).

K. Zhang, W. Wang, J. Han, and J. U. Kang, “A surface topology and motion compensation system for microsurgery guidance and intervention based on common-path optical coherence tomography,” IEEE Trans. Biomed. Eng. 56(9), 2318–2321 (2009).
[PubMed]

Hitzenberger, C.

Ilev, I.

Izatt, J.

Jian, Z.

Johnstone, I.

D. Donoho and I. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika 81(3), 425–455 (1994).

Kang, J. U.

J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).

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. Express 18(11), 11772–11784 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-11-11772 .
[PubMed]

K. Zhang, W. Wang, J. Han, and J. U. Kang, “A surface topology and motion compensation system for microsurgery guidance and intervention based on common-path optical coherence tomography,” IEEE Trans. Biomed. Eng. 56(9), 2318–2321 (2009).
[PubMed]

X. Liu, X. Li, D. Kim, I. Ilev, and J. U. Kang, “Fiber Optic Fourier-domain Common-path OCT,” Chin. Opt. Lett. 6(12), 899–903 (2008).

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Sel. Top. Quantum Electron. 11(4), 799–805 (2005).

Karl, W. C.

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

Kim, D.

Kowalczyk, A.

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).

Leitgeb, R.

Li, C.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15(2), 021311 (2010).
[PubMed]

Li, X.

Liu, X.

J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).

X. Liu, X. Li, D. Kim, I. Ilev, and J. U. Kang, “Fiber Optic Fourier-domain Common-path OCT,” Chin. Opt. Lett. 6(12), 899–903 (2008).

Lustig, M.

M. Lustig, 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).
[PubMed]

Marcos, S.

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, 243–253 (1997).

Mohan, N.

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

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).

Mujat, M.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[PubMed]

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).

Park, B. H.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[PubMed]

Pauly, J. M.

M. Lustig, 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).
[PubMed]

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, 243–253 (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).

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, 243–253 (1997).

Rao, B.

Romberg, J.

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

Saleh, B. E. A.

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

Sarunic, M.

Sharma, U.

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Sel. Top. Quantum Electron. 11(4), 799–805 (2005).

Song, C.

J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).

Song, L.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15(2), 021311 (2010).
[PubMed]

Stojanovic, I.

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

Sutton, B. P.

J. A. Fessler and B. P. Sutton, “Nonuniform fast Fourier transforms using min–max interpolation,” IEEE Trans. Signal Process. 51(2), 560–574 (2003).

Szkulmowski, M.

Szlag, D.

Tao, T.

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

Teich, M. C.

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

Tromberg, B. J.

Wang, L. V.

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15(2), 021311 (2010).
[PubMed]

Wang, W.

K. Zhang, W. Wang, J. Han, and J. U. Kang, “A surface topology and motion compensation system for microsurgery guidance and intervention based on common-path optical coherence tomography,” IEEE Trans. Biomed. Eng. 56(9), 2318–2321 (2009).
[PubMed]

Wojtkowski, M.

Yang, C.

Yu, L.

Yu, Z.

Zhang, K.

J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).

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. Express 18(11), 11772–11784 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-11-11772 .
[PubMed]

K. Zhang, W. Wang, J. Han, and J. U. Kang, “A surface topology and motion compensation system for microsurgery guidance and intervention based on common-path optical coherence tomography,” IEEE Trans. Biomed. Eng. 56(9), 2318–2321 (2009).
[PubMed]

Biometrika (1)

D. Donoho and I. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika 81(3), 425–455 (1994).

Chin. Opt. Lett. (1)

IEEE J. Sel. Top. Quantum Electron. (2)

J. U. Kang, J. Han, X. Liu, K. Zhang, C. Song, and P. Gehlbach, “Endoscopic Functional Fourier Domain Common Path Optical Coherence Tomography for Microsurgery,” IEEE J. Sel. Top. Quantum Electron. 16(4), 781–792 (2010).

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Sel. Top. Quantum Electron. 11(4), 799–805 (2005).

IEEE Trans. Biomed. Eng. (1)

K. Zhang, W. Wang, J. Han, and J. U. Kang, “A surface topology and motion compensation system for microsurgery guidance and intervention based on common-path optical coherence tomography,” IEEE Trans. Biomed. Eng. 56(9), 2318–2321 (2009).
[PubMed]

IEEE Trans. Inf. Theory (2)

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

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

IEEE Trans. Signal Process. (1)

J. A. Fessler and B. P. Sutton, “Nonuniform fast Fourier transforms using min–max interpolation,” IEEE Trans. Signal Process. 51(2), 560–574 (2003).

J. Biomed. Opt. (2)

Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. 15(2), 021311 (2010).
[PubMed]

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[PubMed]

Magn. Reson. Med. (1)

M. Lustig, 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).
[PubMed]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (3)

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

S. M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE 2869, 243–253 (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).

Other (4)

J. Shewchuk, “An introduction to the conjugate gradient method without the agonizing pain,” Technical Report CMUCS-TR-94–125, Carnegie Mellon University, (1994).

M. Balicki, J. Han, I. Iordachita, P. Gehlbach, J. Handa, J. U. Kang, and R. Taylor, “Single Fiber Optical Coherence Tomography Microsurgical Instruments for Computer and Robot-Assisted Retinal Surgery,” Proceedings of the MICCAI Conference (2009)

M. Brezinski, Optical Coherence Tomography: Principles and Applications, (Academic Press, London, 2006).

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

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 (8)

Fig. 1
Fig. 1

Schematic of CP SD OCT.

Fig. 2
Fig. 2

Illustration of random undersampling.

Fig. 3
Fig. 3

Simulated PSF (1,j) when randomly undersampling 20% of CCD pixels.

Fig. 4
Fig. 4

(a) Spectral interferogram obtained by using a mirror as sample; (b) illustration of different sampling schemes (red circles = random undersampling; green squares = uniform undersampling; blue stars = complete sampling).

Fig. 5
Fig. 5

M-scans obtained by standard SD OCT image reconstruction algorithms using different sampling schemes: (a) complete sampling, (b) uniform density undersampling, (c) random undersampling.

Fig. 6
Fig. 6

(a) A-scan obtained from random undersampled spectrum after the 1st CG iteration, (b) A-scan obtained from random undersampled spectrum after the 11th CG iteration, (c) blue curve: A-scan which is the solution of Eq. (2), red curve: A-scan obtained with complete spectral data; (d) M-scan obtained by CS.

Fig. 7
Fig. 7

OCT image of onion cells: (a) obtained using complete spectral data; (b), (c), and (d) obtained by sampling 62.5%, 50%, 37.5% of the pixels and pursuing sparsity in pixel domain; (e), (f), and (g) obtained by sampling 62.5%, 50%, 37.5% of the pixels and pursuing sparsity in wavelet domain.

Fig. 8
Fig. 8

(a) Profile of sample surface obtained from Fig. 7(a); (b) histogram of Δ(P) when sampling 62.5%, 50% and 37.5% of the pixels.

Equations (9)

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

y k = Re ( a 0 n x n e -i nk δ k δ x )
K =2x max Δ k/ π
y=Fx
x=F -1 y
y u =F u x
K > G δ T l o g ( N )
TPSF ( i , j ) = e j W F u F u W e i
m i n i m i z e   | | Wx | | 1 s . t . | | F u x - y u | | 2 < ε    
m i n i m i z e   f ( x ) = λ | | Wx | | 1 + | | F u x - y u | | 2

Metrics