Abstract

In spectral-domain optical coherence tomography (SD-OCT), data samples are collected nonuniformly in the wavenumber domain, requiring a measurement re-sampling process before a conventional fast Fourier transform can be applied to reconstruct an image. This re-sampling necessitates extra computation and often introduces errors in the data. Instead, we develop an inverse imaging approach to reconstruct an SD-OCT image. We make use of total variation (TV) as a constraint to preserve the image edges, and estimate the two-dimensional cross-section of a sample directly from the SD-OCT measurements rather than processing for each A-line. Experimental results indicate that compared with the conventional method, our technique gives a smaller noise residual. The potential of using the TV constraint to suppress sensitivity falloff in SD-OCT is also demonstrated with experiment data.

© 2012 OSA

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  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,” Science254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  2. W. Drexler and J. G. Fujimoto, Optical Coherence Tomography Technology and Applications (Springer-Verlag, Berlin, 2008).
    [CrossRef]
  3. M. Wojtkowski, “High-speed optical coherence tomography: basics and applications,” Appl. Opt.49, D3–D60 (2010).
    [CrossRef]
  4. D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
    [CrossRef]
  5. R. Zhu, J. Xu, C. Zhang, A. C. Chan, Q. Li, P. Chui, E. Y. Lam, and K. K. Wong, “Dual-band time-multiplexing swept-source OCT based on optical parametric amplification,” to be published in IEEE J. Sel. Top. Quantum Electron.
  6. T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express2, 2438–2448 (2011).
    [CrossRef]
  7. K. H. Y. Cheng, B. A. Standish, V. X. D. Yang, K. K. Y. Cheung, X. Gu, E. Y. Lam, and K. K. Y. Wong, “Wavelength-swept spectral and pulse shaping utilizing hybrid Fourier domain modelocking by fiber optical parametric and erbium-doped fiber amplifiers,” Opt. Express18, 1909–1915 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. K. Zhang and J. U. Kang, “Graphic processing unit accelerated non-uniform fast Fourier transform for ultrahigh-speed, real-time Fourier-domain OCT,” Opt. Express18, 23472–23487 (2010).
    [CrossRef] [PubMed]
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  16. L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev.46, 443–454 (2004).
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  18. E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt.48, H113–H119 (2009).
    [CrossRef] [PubMed]
  19. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D: Nonlinear Phenomena60, 259–268 (1992).
    [CrossRef]
  20. J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniform samples in spectral domain optical coherence tomography,” in Signal Recovery and Synthesis, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SMD2.
  21. J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniformly-spaced samples in Fourier domain optical coherence tomography,” Proc. SPIE8296, 829610 (2012).
    [CrossRef]
  22. Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A27, 1638–1646 (2010).
    [CrossRef]
  23. X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A27, 1630–1637 (2010).
    [CrossRef]
  24. G. H. Golub and C. F. Van Loan, Matrix Computations (The Johns Hopkins University Press, 1996).
  25. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning3, 1–122 (2010).
    [CrossRef]
  26. Y. Huang, M. K. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulat.7, 774–795 (2008).
    [CrossRef] [PubMed]
  27. X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express16, 17215–17226 (2008).
    [CrossRef] [PubMed]
  28. A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision20, 89–97 (2004).
    [CrossRef]
  29. J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt.50, H285–H296 (2011).
    [CrossRef] [PubMed]

2012

J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniformly-spaced samples in Fourier domain optical coherence tomography,” Proc. SPIE8296, 829610 (2012).
[CrossRef]

2011

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express2, 2438–2448 (2011).
[CrossRef]

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]

J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt.50, H285–H296 (2011).
[CrossRef] [PubMed]

2010

M. Wojtkowski, “High-speed optical coherence tomography: basics and applications,” Appl. Opt.49, D3–D60 (2010).
[CrossRef]

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning3, 1–122 (2010).
[CrossRef]

K. H. Y. Cheng, B. A. Standish, V. X. D. Yang, K. K. Y. Cheung, X. Gu, E. Y. Lam, and K. K. Y. Wong, “Wavelength-swept spectral and pulse shaping utilizing hybrid Fourier domain modelocking by fiber optical parametric and erbium-doped fiber amplifiers,” Opt. Express18, 1909–1915 (2010).
[CrossRef] [PubMed]

X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A27, 1630–1637 (2010).
[CrossRef]

Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A27, 1638–1646 (2010).
[CrossRef]

Y. Watanabe, S. Maeno, K. Aoshima, H. Hasegawa, and H. Koseki, “Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units,” Appl. Opt.49, 4756–4762 (2010).
[CrossRef] [PubMed]

K. Zhang and J. U. Kang, “Graphic processing unit accelerated non-uniform fast Fourier transform for ultrahigh-speed, real-time Fourier-domain OCT,” Opt. Express18, 23472–23487 (2010).
[CrossRef] [PubMed]

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]

2009

2008

Y. Huang, M. K. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulat.7, 774–795 (2008).
[CrossRef] [PubMed]

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express16, 17215–17226 (2008).
[CrossRef] [PubMed]

2004

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision20, 89–97 (2004).
[CrossRef]

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev.46, 443–454 (2004).
[CrossRef]

2003

1998

L. I. Rudin, S. Osher, and E. Fatemi, “An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs),” IEEE Microwave Guided Wave Lett. 8, 18–20 (1998).
[CrossRef]

1992

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D: Nonlinear Phenomena60, 259–268 (1992).
[CrossRef]

1991

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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Aoshima, K.

Boppart, S. A.

Bouma, B. E.

Boyd, S.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning3, 1–122 (2010).
[CrossRef]

Brezinski, M.

M. Brezinski, Optical Coherence Tomography: Principles and Applications (Elsevier, 2006).

Chambolle, A.

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision20, 89–97 (2004).
[CrossRef]

Chan, A. C.

R. Zhu, J. Xu, C. Zhang, A. C. Chan, Q. Li, P. Chui, E. Y. Lam, and K. K. Wong, “Dual-band time-multiplexing swept-source OCT based on optical parametric amplification,” to be published in IEEE J. Sel. Top. Quantum Electron.

Chan, H. K.

Chang, S.

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, M.

Cheng, K. H. Y.

Cheung, K. K. Y.

Choo-Smith, L.-P.

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

Chu, E.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning3, 1–122 (2010).
[CrossRef]

Chui, P.

R. Zhu, J. Xu, C. Zhang, A. C. Chan, Q. Li, P. Chui, E. Y. Lam, and K. K. Wong, “Dual-band time-multiplexing swept-source OCT based on optical parametric amplification,” to be published in IEEE J. Sel. Top. Quantum Electron.

de Boer, J. F.

Ding, Z.

Disano, J.

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

Drexler, W.

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography Technology and Applications (Springer-Verlag, Berlin, 2008).
[CrossRef]

Eckstein, J.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning3, 1–122 (2010).
[CrossRef]

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs),” IEEE Microwave Guided Wave Lett. 8, 18–20 (1998).
[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D: Nonlinear Phenomena60, 259–268 (1992).
[CrossRef]

Fercher, A. F.

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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Flueraru, C.

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

Fujimoto, J. G.

T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express2, 2438–2448 (2011).
[CrossRef]

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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

W. Drexler and J. G. Fujimoto, Optical Coherence Tomography Technology and Applications (Springer-Verlag, Berlin, 2008).
[CrossRef]

Golub, G. H.

G. H. Golub and C. F. Van Loan, Matrix Computations (The Johns Hopkins University Press, 1996).

Greengard, L.

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev.46, 443–454 (2004).
[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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gu, X.

Hasegawa, H.

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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hitzenberger, C. K.

Hornegger, J.

T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express2, 2438–2448 (2011).
[CrossRef]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, Y.

Y. Huang, M. K. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulat.7, 774–795 (2008).
[CrossRef] [PubMed]

Indebetouw, G.

Jeon, M.

Jung, U.

Jung, W.

Kang, J. U.

Ke, J.

J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniformly-spaced samples in Fourier domain optical coherence tomography,” Proc. SPIE8296, 829610 (2012).
[CrossRef]

J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt.50, H285–H296 (2011).
[CrossRef] [PubMed]

J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniform samples in spectral domain optical coherence tomography,” in Signal Recovery and Synthesis, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SMD2.

Kim, J.

Koseki, H.

Kraus, M. F.

T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express2, 2438–2448 (2011).
[CrossRef]

Lam, E. Y.

J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniformly-spaced samples in Fourier domain optical coherence tomography,” Proc. SPIE8296, 829610 (2012).
[CrossRef]

J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt.50, H285–H296 (2011).
[CrossRef] [PubMed]

K. H. Y. Cheng, B. A. Standish, V. X. D. Yang, K. K. Y. Cheung, X. Gu, E. Y. Lam, and K. K. Y. Wong, “Wavelength-swept spectral and pulse shaping utilizing hybrid Fourier domain modelocking by fiber optical parametric and erbium-doped fiber amplifiers,” Opt. Express18, 1909–1915 (2010).
[CrossRef] [PubMed]

X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A27, 1630–1637 (2010).
[CrossRef]

Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A27, 1638–1646 (2010).
[CrossRef]

E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt.48, H113–H119 (2009).
[CrossRef] [PubMed]

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express16, 17215–17226 (2008).
[CrossRef] [PubMed]

J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniform samples in spectral domain optical coherence tomography,” in Signal Recovery and Synthesis, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SMD2.

R. Zhu, J. Xu, C. Zhang, A. C. Chan, Q. Li, P. Chui, E. Y. Lam, and K. K. Wong, “Dual-band time-multiplexing swept-source OCT based on optical parametric amplification,” to be published in IEEE J. Sel. Top. Quantum Electron.

Lee, C.

Lee, J.-Y.

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev.46, 443–454 (2004).
[CrossRef]

Leitgeb, R. A.

Li, Q.

R. Zhu, J. Xu, C. Zhang, A. C. Chan, Q. Li, P. Chui, E. Y. Lam, and K. K. Wong, “Dual-band time-multiplexing swept-source OCT based on optical parametric amplification,” to be published in IEEE J. Sel. Top. Quantum Electron.

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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Maeno, S.

Mao, Y.

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

Meng, J.

Ng, M. K.

Y. Huang, M. K. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulat.7, 774–795 (2008).
[CrossRef] [PubMed]

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs),” IEEE Microwave Guided Wave Lett. 8, 18–20 (1998).
[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D: Nonlinear Phenomena60, 259–268 (1992).
[CrossRef]

Parikh, N.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning3, 1–122 (2010).
[CrossRef]

Park, B. H.

Peleato, B.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning3, 1–122 (2010).
[CrossRef]

Poon, T.-C.

Popescu, D. P.

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

Potsaid, B.

T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express2, 2438–2448 (2011).
[CrossRef]

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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs),” IEEE Microwave Guided Wave Lett. 8, 18–20 (1998).
[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D: Nonlinear Phenomena60, 259–268 (1992).
[CrossRef]

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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sherif, S.

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

Sowa, M. G.

D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011).
[CrossRef]

Standish, B. 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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

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,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tang, S.

Tao, Y. K.

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Figures (8)

Fig. 1
Fig. 1

The SD-OCT system diagram.

Fig. 2
Fig. 2

(a) Raw measurements Ĩl (km), where each A-line is represented by a different color. (b) The averaged Fourier transform of Ĩl(km). (c) The estimated source power spectrum. (d) I(km) after adjustment.

Fig. 3
Fig. 3

Reconstruction using (a) the FFT, (b) the NUDFT, and (c) the TV regularization.

Fig. 4
Fig. 4

One line of the reconstructed signals using FFT, NUDFT, and TV along (a) the axial direction and (b) the transversal directions.

Fig. 5
Fig. 5

Reconstructions using (a) the FFT, (c) the NUDFT, and (e) the TV regularization. Zoomed-in views of the reconstructions using (b) the FFT, (d) the NUDFT, and (f) the TV regularization.

Fig. 6
Fig. 6

Zoom-in reconstructed signals at l = 9, 601, and 930 using (a) the FFT, (b) the NUDFT, (c) the TV regularization.

Fig. 7
Fig. 7

Reconstructions for an orange flesh and a pearl using (a–b) the FFT, (c–d) the NUDFT, and (e–f) the TV regularization.

Fig. 8
Fig. 8

Reconstructions for a fingernail sample using (a–b) the FFT, (c–d) the NUDFT, and (e–f) the TV regularization.

Tables (1)

Tables Icon

Table 1 Normalized peak values (dB) of the reconstructed signal in Fig. 6.

Equations (10)

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I ˜ ( k ) = G ( k ) { p r 2 + 2 0 p r p s ( z ) cos ( 2 a s k z ) d z + 0 0 p s ( z ) p s ( z ) e j 2 k a s ( z z ) d z d z } ,
I ( k ) = 2 G ( k ) 0 p s ( z ) cos ( 2 k z ) d z + e ( k ) .
I ( k m ) = 2 G ( k m ) n = 0 N 1 p s ( z n ) cos ( 2 k m z n ) + e ( k m ) ,
[ I ( k 0 ) I ( k 1 ) I ( k M 1 ) ] = [ H 0 , 0 H 0 , 1 H 0 , N 1 H 1 , 0 H 1 , 1 H 1 , N 1 H M 1 , 0 H M 1 , 1 H M 1 , N 1 ] [ p s ( z 0 ) p s ( z 1 ) p s ( z N 1 ) ] + [ e ( k 0 ) e ( k 1 ) e ( k M 1 ) ] ,
Y = HX + E ,
X min = arg min X HX Y F 2 + α X TV ,
X TV = n = 0 N 1 l = 0 L 1 | ( n X ) n , l ) | 2 + | ( l X ) n , l ) | 2 ,
( X min , U min ) = arg min X , U HX Y F 2 + α 1 X U F 2 + α 2 U TV ,
{ X ( i ) = arg min X HX Y F 2 + α 1 X U ( i 1 ) F 2 U ( i ) = arg min U α 1 X ( i ) U F 2 + α 2 U TV .
( 0 p s ( z ) e j 2 k a s z d z ) ( 0 p s ( z ) e j 2 k a s z d z ) = | 0 p s ( z ) e j 2 k a s z d z | 2 ,

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