Abstract

In this work, we proposed a novel three-dimensional compressive sensing (CS) approach for spectral domain optical coherence tomography (SD OCT) volumetric image acquisition and reconstruction. Instead of taking a spectral volume whose size is the same as that of the volumetric image, our method uses a sub set of the original spectral volume that is under-sampled in all three dimensions, which reduces the amount of spectral measurements to less than 20% of that required by the Shan-non/Nyquist theory. The 3D image is recovered from the under-sampled spectral data dimension-by-dimension using the proposed three-step CS reconstruction strategy. Experimental results show that our method can significantly reduce the sampling rate required for a volumetric SD OCT image while preserving the image quality.

© 2014 Optical Society of America

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References

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  1. D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).
  2. M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
    [Crossref] [PubMed]
  3. T. Schmoll, C. Kolbitsch, and R.A. Leitgeb, “Ultra-high-speed volumetric tomography of human retinal blood flow,” Opt. Express 17(5), 4166–4176 (2009).
    [Crossref] [PubMed]
  4. M. Gargesha, M.W. Jenkins, A.M. Rollins, and D.L. Wilson, “Denoising and 4D visualization of OCT images,” Opt. Express 16(16), 12313–12333 (2008).
    [Crossref] [PubMed]
  5. W. Wieser, B.R. Biedermann, T. Klein, C.M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: high quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express 18(14), 14685–14704 (2010).
    [Crossref] [PubMed]
  6. D.L. Donoho, Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
    [Crossref]
  7. E.J. 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).
    [Crossref]
  8. 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]
  9. 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. Express 3(5), 927–942 (2012).
    [Crossref] [PubMed]
  10. D. Xu, N. Vaswani, Y. Huang, and J.U. Kang, Modified compressive sensing optical coherence tomography with noise reducetion,” Opt. Lett. 37(20), 4209–4211(2012).
    [Crossref] [PubMed]
  11. 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]
  12. C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express 20(9), 10200–10211 (2012).
    [Crossref] [PubMed]
  13. S. Schwartz, C. Liu, A. Wong, D.A. Clausi, P. Fieguth, and K. Bizheva, “Energy-guided learning approach to compressive sensing,” Opt. Express 21(1), 329–344 (2013).
    [Crossref] [PubMed]
  14. D. Xu, Y. Huang, and J.U. Kang, “Compressive sensing with dispersion compensation on non-linear wavenumber sampled spectral domain optical coherence tomography,” Biomed. Opt. Express 4(9), 1519–1532 (2013).
    [Crossref] [PubMed]
  15. 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] [PubMed]
  16. E. Lebed, P.J. Mackenzie, M.V. Sarunic, and M.F. Beg, “Rapid volumetric OCT image acquisition using compressive sampling,” Opt. Express 18(20), 21003–21012 (2010).
    [Crossref] [PubMed]
  17. E. Lebed, S. Lee, M.V. Sarunic, and M.F. Beg, “Rapid radial optical coherence tomography image acquisition,” J. BioMed. Opt. 18(3), 036004 (2013).
    [Crossref] [PubMed]
  18. J. Yang and Y. Zhang, “Alternating direction algorithms for L1-problem in compressive sensing,” SIAM J. on Scientific Computing 33(1–2), 250–278 (2011).
    [Crossref]
  19. D. Xu, Y. Huang, and J.U. Kang, “Assessment of robust reconstruction algorithms for compressive sensing spectral-domain optical coherence tomography,” Proc. SPIE 8589, 85890C (2013).
    [Crossref]
  20. D. Xu, Y. Huang, and J.U. Kang, “Real-time compressive sensing spectral domain optical coherence tomography,” Opt. Lett. 39(1), 76–79 (2014).
    [Crossref]
  21. D. Xu, Y. Huang, and J.U. Kang, “GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography,” Opt. Express 22(12), 14871–14884 (2014).
    [Crossref] [PubMed]
  22. D. Xu, Y. Huang, and J.U. Kang, “Real-time dispersion-compensated image reconstruction for compressive sensing spectral domain optical coherence tomography,” J. Opt. Soc. Am. 31(9), 2064–2069 (2014).
    [Crossref]

2014 (3)

2013 (4)

D. Xu, Y. Huang, and J.U. Kang, “Assessment of robust reconstruction algorithms for compressive sensing spectral-domain optical coherence tomography,” Proc. SPIE 8589, 85890C (2013).
[Crossref]

S. Schwartz, C. Liu, A. Wong, D.A. Clausi, P. Fieguth, and K. Bizheva, “Energy-guided learning approach to compressive sensing,” Opt. Express 21(1), 329–344 (2013).
[Crossref] [PubMed]

D. Xu, Y. Huang, and J.U. Kang, “Compressive sensing with dispersion compensation on non-linear wavenumber sampled spectral domain optical coherence tomography,” Biomed. Opt. Express 4(9), 1519–1532 (2013).
[Crossref] [PubMed]

E. Lebed, S. Lee, M.V. Sarunic, and M.F. Beg, “Rapid radial optical coherence tomography image acquisition,” J. BioMed. Opt. 18(3), 036004 (2013).
[Crossref] [PubMed]

2012 (4)

2011 (2)

2010 (3)

2009 (1)

2008 (1)

2007 (1)

D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).

2006 (2)

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,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

2005 (1)

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Adler, D.C.

D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).

Beg, M.F.

Bie, H.

Biedermann, B.R.

Bizheva, K.

Candes, E.J.

E.J. 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).
[Crossref]

Chen, T.

Chen, Y.

D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).

Clausi, D.A.

Connolly, J.

D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).

Donoho, D.L.

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

Duker, J.S.

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Eigenwillig, C.M.

Fang, L.

Farsiu, S.

Fieguth, P.

Fujimoto, J.G.

D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Gargesha, M.

Huang, Y.

Huber, R.

W. Wieser, B.R. Biedermann, T. Klein, C.M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: high quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express 18(14), 14685–14704 (2010).
[Crossref] [PubMed]

D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).

Huo, T.

Izatt, J.A.

Jenkins, M.W.

Jian, Y.

Kang, J.U.

Klein, T.

Ko, T.

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Kolbitsch, C.

Kowalczyk, A.

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Lebed, E.

Lee, S.

E. Lebed, S. Lee, M.V. Sarunic, and M.F. Beg, “Rapid radial optical coherence tomography image acquisition,” J. BioMed. Opt. 18(3), 036004 (2013).
[Crossref] [PubMed]

Leitgeb, R.A.

Li, S.

Liu, C.

Liu, X.

Mackenzie, P.J.

Nie, Q.

Rollins, A.M.

Romberg, J.

E.J. 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).
[Crossref]

Sarunic, M.V.

Schmitt, J.

D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).

Schmoll, T.

Schuman, J.S.

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Schwartz, S.

Srinivasan, V.

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Tao, T.

E.J. 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).
[Crossref]

Toth, C.A.

Vaswani, N.

Wang, C.

Wieser, W.

Wilson, D.L.

Wojtkowski, M.

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Wong, A.

Xu, D.

Xue, P.

Yang, J.

J. Yang and Y. Zhang, “Alternating direction algorithms for L1-problem in compressive sensing,” SIAM J. on Scientific Computing 33(1–2), 250–278 (2011).
[Crossref]

Young, M.

Zhang, N.

Zhang, Y.

J. Yang and Y. Zhang, “Alternating direction algorithms for L1-problem in compressive sensing,” SIAM J. on Scientific Computing 33(1–2), 250–278 (2011).
[Crossref]

Zheng, J.

Biomed. Opt. Express (3)

IEEE Trans. Inf. Theory (2)

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,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

J. BioMed. Opt. (1)

E. Lebed, S. Lee, M.V. Sarunic, and M.F. Beg, “Rapid radial optical coherence tomography image acquisition,” J. BioMed. Opt. 18(3), 036004 (2013).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

D. Xu, Y. Huang, and J.U. Kang, “Real-time dispersion-compensated image reconstruction for compressive sensing spectral domain optical coherence tomography,” J. Opt. Soc. Am. 31(9), 2064–2069 (2014).
[Crossref]

Nat. Med. (1)

D.C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J.G. Fujimoto, “Three-dimensional endomiscroscopy using optical coherence tomography,” Nat. Med. 12(12), 1429–1433 (2007).

Ophthalmology (1)

M. Wojtkowski, V. Srinivasan, J.G. Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and J.S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005).
[Crossref] [PubMed]

Opt. Express (8)

T. Schmoll, C. Kolbitsch, and R.A. Leitgeb, “Ultra-high-speed volumetric tomography of human retinal blood flow,” Opt. Express 17(5), 4166–4176 (2009).
[Crossref] [PubMed]

M. Gargesha, M.W. Jenkins, A.M. Rollins, and D.L. Wilson, “Denoising and 4D visualization of OCT images,” Opt. Express 16(16), 12313–12333 (2008).
[Crossref] [PubMed]

W. Wieser, B.R. Biedermann, T. Klein, C.M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: high quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express 18(14), 14685–14704 (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]

E. Lebed, P.J. Mackenzie, M.V. Sarunic, and M.F. Beg, “Rapid volumetric OCT image acquisition using compressive sampling,” Opt. Express 18(20), 21003–21012 (2010).
[Crossref] [PubMed]

C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express 20(9), 10200–10211 (2012).
[Crossref] [PubMed]

S. Schwartz, C. Liu, A. Wong, D.A. Clausi, P. Fieguth, and K. Bizheva, “Energy-guided learning approach to compressive sensing,” Opt. Express 21(1), 329–344 (2013).
[Crossref] [PubMed]

D. Xu, Y. Huang, and J.U. Kang, “GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography,” Opt. Express 22(12), 14871–14884 (2014).
[Crossref] [PubMed]

Opt. Lett. (3)

Proc. SPIE (1)

D. Xu, Y. Huang, and J.U. Kang, “Assessment of robust reconstruction algorithms for compressive sensing spectral-domain optical coherence tomography,” Proc. SPIE 8589, 85890C (2013).
[Crossref]

SIAM J. on Scientific Computing (1)

J. Yang and Y. Zhang, “Alternating direction algorithms for L1-problem in compressive sensing,” SIAM J. on Scientific Computing 33(1–2), 250–278 (2011).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic demonstration of the proposed sampling pattern which under-samples the original spectral volume in all three dimensions.
Fig. 2
Fig. 2 Schematic demonstration of the proposed three-step CS reconstruction strategy.
Fig. 3
Fig. 3 (a) relative error vs. axial sampling rate. The overall sampling rate is fixed; (b) relative error vs. lateral sampling rate. The axial sampling rate is fixed.
Fig. 4
Fig. 4 Reconstruction results of human skin. (a) is obtained using 100% spectral data. (b) is obtained using 25% spectral data for each A-scan and no under-sampling is applied in the fast-scanning direction. (c) and (d) are obtained using the proposed method, with the wavelet transformation and Fourier transformation as sparsifying operators, respectively. The under-sampling rates for the axial direction and fast-scanning direction are both 50%. The scale bars represent 100 μm. The image size in pixel is 900×925.
Fig. 5
Fig. 5 First row: volumetric visualization by ray-casting; second row: orthogonal cross-sectional display; first column: image obtained with 100% spectral data; second column: image obtained using the proposed method with the wavelet transformation; third column: image obtained using the proposed method with the Fourier transformation.
Fig. 6
Fig. 6 Recovered slices in the reconstructed volumetric images. Rows (a) and (b) are two en-face slices at the position of 160 μm and 800 μm below the surface, respectively. The image size in pixel is 925×250. Rows (c) and (d) are slices in the slow-scanning direction. The image size in pixel is 900×250. Rows (e) and (f) are B-scans in the fast-scanning direction. The image size in pixel is 900×925. The first column is the image obtained using 100% data. The second and third columns are images obtained using the proposed method with the wavelet and the Fourier transformation, respectively.
Fig. 7
Fig. 7 First row: representative slices obtained using 100% spectral measurements (first column) and under-sampled spectral volume using the wavelet transformation (second column) and the Fourier transformation (third column). Second row: zoom-in of the green rectangle areas in the first row.

Equations (3)

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min x | Ψ x 1 s . t . MFx y u 2 2 ε
e = f CS f ref 2 / f ref 2
PSNR = 10 log 10 ( max 2 ( f ( x ) ) / var )

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