Abstract

We propose a novel method called compressed sensing with linear-in-wavenumber sampling (k-linear CS) to retrieve an image for spectral-domain optical coherence tomography (SD-OCT). An array of points that is evenly spaced in wavenumber domain is sampled from an original interferogram by a preset k-linear mask. Then the compressed sensing based on l1 norm minimization is applied on these points to reconstruct an A-scan data. To get an OCT image, this method uses less than 20% of the total data as required in the typical process and gets rid of the spectral calibration with numerical interpolation in traditional CS-OCT. Therefore k-linear CS is favorable for high speed imaging. It is demonstrated that the k-linear CS has the same axial resolution performance with 30dB higher signal-to-noise ratio (SNR) as compared with the numerical interpolation. Imaging of bio-tissue by SD-OCT with k-linear CS is also demonstrated.

© 2012 Optical Society of America

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2012 (1)

2010 (5)

2009 (1)

2008 (1)

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, IEEE Signal Process. Mag. 25 (2), 72 (2008).
[CrossRef]

2007 (2)

M. Lustig, D. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[CrossRef]

Z. Hu and A. M. Rollins, Opt. Lett. 32, 3525 (2007).
[CrossRef]

2005 (1)

2004 (1)

2003 (1)

2002 (1)

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, J. Biomed. Opt. 7, 457 (2002).
[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, Science 254, 1178 (1991).
[CrossRef]

Bajraszewski, T.

R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, Opt. Express 12, 2156 (2004).
[CrossRef]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

Balicki, M.

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, Science 254, 1178 (1991).
[CrossRef]

Chen, M.

Chen, T.

Ding, Z.

Donoho, D.

M. Lustig, D. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[CrossRef]

Donoho, D. L.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, IEEE Signal Process. Mag. 25 (2), 72 (2008).
[CrossRef]

Drexler, W.

Faisal Beg, M.

Fercher, A.

Fercher, A. F.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

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, Science 254, 1178 (1991).
[CrossRef]

Fujimoto, J. G.

R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, Opt. Express 13, 3513 (2005).
[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, Science 254, 1178 (1991).
[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, Science 254, 1178 (1991).
[CrossRef]

Guo, Z.

Z. Guo, C. Li, L. Song, and L. V. Wang, J. Biomed. Opt. 15, 021311 (2010).
[CrossRef]

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, Science 254, 1178 (1991).
[CrossRef]

Hermann, B.

Hitzenberger, C.

Hsu, K.

Hu, Z.

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, Science 254, 1178 (1991).
[CrossRef]

Huber, R.

Huo, L.

Huo, T.

Kang, J. U.

Kowalczyk, A.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

Le, T.

Lebed, E.

Leitgeb, R.

Li, C.

Z. Guo, C. Li, L. Song, and L. V. Wang, J. Biomed. Opt. 15, 021311 (2010).
[CrossRef]

Li, J.

Li, X.

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, Science 254, 1178 (1991).
[CrossRef]

Liu, X.

Lustig, M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, IEEE Signal Process. Mag. 25 (2), 72 (2008).
[CrossRef]

M. Lustig, D. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[CrossRef]

Mackenzie, P. J.

Meng, J.

Pauly, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, IEEE Signal Process. Mag. 25 (2), 72 (2008).
[CrossRef]

M. Lustig, D. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[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, Science 254, 1178 (1991).
[CrossRef]

Rollins, A. M.

Santos, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, IEEE Signal Process. Mag. 25 (2), 72 (2008).
[CrossRef]

Sarunic, M. V.

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, Science 254, 1178 (1991).
[CrossRef]

Song, L.

Z. Guo, C. Li, L. Song, and L. V. Wang, J. Biomed. Opt. 15, 021311 (2010).
[CrossRef]

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, Science 254, 1178 (1991).
[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, Science 254, 1178 (1991).
[CrossRef]

Taira, K.

Taylor, R. H.

Unterhuber, A.

Wang, C.

Wang, K.

Wang, L. V.

Z. Guo, C. Li, L. Song, and L. V. Wang, J. Biomed. Opt. 15, 021311 (2010).
[CrossRef]

Wojtkowski, M.

R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, Opt. Express 13, 3513 (2005).
[CrossRef]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

Wu, T.

Xi, J.

Xu, L.

Xue, P.

Zhang, J.

Zhang, N.

Zheng, J.

IEEE Signal Process. Mag. (1)

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, IEEE Signal Process. Mag. 25 (2), 72 (2008).
[CrossRef]

J. Biomed. Opt. (2)

Z. Guo, C. Li, L. Song, and L. V. Wang, J. Biomed. Opt. 15, 021311 (2010).
[CrossRef]

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

Magn. Reson. Med. (1)

M. Lustig, D. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[CrossRef]

Opt. Express (8)

Opt. Lett. (2)

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, Science 254, 1178 (1991).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Interferograms at (a) 700 μm and (c) 200 μm and the corresponding A-scans at (b) 700 μm and (d) 200 μm. The red circles represent k-linear sampling points. (e) A-scans at different depths. The blue dotted lines represent original A-scans. The black dashed, interpolation. The red solid, k-linear CS.

Fig. 2.
Fig. 2.

A-scans at 700 μm on logarithm scale. Blue dashed, original A-scan; purple, direct FFT to the k-linear points; green, direct CS to the original data; red, k-linear CS.; black, after interpolation.

Fig. 3.
Fig. 3.

Onion cell images. (a) Original image; (b) interpolation; (c) k-linear CS. The scale bars represent 100 μm.

Fig. 4.
Fig. 4.

Skin images. (a) Original image; (b) interpolation; (c) k-linear CS. The scale bars represent 100 μm.

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MinimizeΨm1subject toFumMx2<ε.
Minimizef(m)=λ1Ψm1+λ2TV(m)+FumMx22

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