Abstract

Optical coherence tomography is an emerging non-invasive technology that provides high resolution, cross-sectional tomographic images of internal structures of specimens. OCT images, however, are usually degraded by significant speckle noise. Here we introduce to our knowledge the first 3D approach to attenuating speckle noise in OCT images. Unlike 2D approaches which only consider information in individual images, 3D processing, by analyzing all images in a volume simultaneously, has the advantage of also taking the information between images into account. This, coupled with the curvelet transform’s nearly optimal sparse representation of curved edges that are common in OCT images, provides a simple yet powerful platform for speckle attenuation. We show the approach suppresses a significant amount of speckle noise, while in the mean time preserves and thus reveals many subtle features that could get attenuated in other approaches.

© 2010 OSA

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References

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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,” Science 254(5035), 1178–1181 (1991).
    [CrossRef] [PubMed]
  2. J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42(7), 1427–1439 (1997).
    [CrossRef] [PubMed]
  3. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in Optical Coherence Tomography,” J. Biomed. Opt. 4(1), 95 (1999).
    [CrossRef]
  4. A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography images using digital filtering,” J. Opt. Soc. Am. A 24(7), 1901 (2007).
    [CrossRef]
  5. D. L. Marks, T. S. Ralston, and S. A. Boppart, “Speckle reduction by I-divergence regularization in optical coherence tomography,” J. Opt. Soc. Am. A 22(11), 2366 (2005).
    [CrossRef]
  6. D. C. Adler, T. H. Ko, and J. G. Fujimoto, “Speckle reduction in optical coherence tomography images by use of a spatially adaptive wavelet filter,” Opt. Lett. 29(24), 2878–2880 (2004).
    [CrossRef]
  7. 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]
  8. P. Puvanathasan and K. Bizheva, “Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set,” Opt. Express 15(24), 15747–15758 (2007).
    [CrossRef] [PubMed]
  9. S. H. Xiang, L. Zhou, and J. M. Schmitt, “Speckle Noise Reduction for Optical Coherence Tomography,” Proc. SPIE 3196, 79 (1997).
    [CrossRef]
  10. Z. Jian, Z. Yu, L. Yu, B. Rao, Z. Chen, and B. J. Tromberg, “Speckle Attenuation by Curvelet Shrinkage in Optical Coherence Tomography,” Opt. Lett. 34, 1516 (2009).
    [CrossRef] [PubMed]
  11. E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” SIAM Multiscale Model. Simul. 5(3), 861 (2006).
    [CrossRef]
  12. E. J. Candès, and D. L. Donoho, “Curvelets–a surprisingly effective nonadaptive representation for objects with edges,” in Curves and Surface Fitting, C. Rabut, A. Cohen, and L. L. Schumaker, eds. (Vanderbilt University Press, Nashville, TN., 2000).
  13. E. J. Candès and D. L. Donoho, “New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities,” Commun. Pure Appl. Math. 57, 219 (2003).
    [CrossRef]
  14. J.-L. Starck, E. J. Candès, and D. L. Donoho, “The Curvelet Transform for Image Denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
    [CrossRef]
  15. B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
    [CrossRef] [PubMed]
  16. S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
    [CrossRef]

2009 (1)

2008 (2)

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]

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (1)

E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” SIAM Multiscale Model. Simul. 5(3), 861 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (1)

E. J. Candès and D. L. Donoho, “New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities,” Commun. Pure Appl. Math. 57, 219 (2003).
[CrossRef]

2002 (1)

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The Curvelet Transform for Image Denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[CrossRef]

2000 (1)

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[CrossRef]

1999 (1)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in Optical Coherence Tomography,” J. Biomed. Opt. 4(1), 95 (1999).
[CrossRef]

1997 (2)

S. H. Xiang, L. Zhou, and J. M. Schmitt, “Speckle Noise Reduction for Optical Coherence Tomography,” Proc. SPIE 3196, 79 (1997).
[CrossRef]

J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42(7), 1427–1439 (1997).
[CrossRef] [PubMed]

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, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Adler, D. C.

Bilenca, A.

Bizheva, K.

Boppart, S. A.

Bouma, B. E.

Candès, E. J.

E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” SIAM Multiscale Model. Simul. 5(3), 861 (2006).
[CrossRef]

E. J. Candès and D. L. Donoho, “New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities,” Commun. Pure Appl. Math. 57, 219 (2003).
[CrossRef]

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The Curvelet Transform for Image Denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[CrossRef]

Chang, S. G.

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, Z.

Z. Jian, Z. Yu, L. Yu, B. Rao, Z. Chen, and B. J. Tromberg, “Speckle Attenuation by Curvelet Shrinkage in Optical Coherence Tomography,” Opt. Lett. 34, 1516 (2009).
[CrossRef] [PubMed]

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

Chiang, H. K.

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

Demanet, L.

E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” SIAM Multiscale Model. Simul. 5(3), 861 (2006).
[CrossRef]

Desjardins, A. E.

Donoho, D. L.

E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” SIAM Multiscale Model. Simul. 5(3), 861 (2006).
[CrossRef]

E. J. Candès and D. L. Donoho, “New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities,” Commun. Pure Appl. Math. 57, 219 (2003).
[CrossRef]

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The Curvelet Transform for Image Denoising,” IEEE Trans. Image Process. 11(6), 670–684 (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, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. C. Adler, T. H. Ko, and J. G. Fujimoto, “Speckle reduction in optical coherence tomography images by use of a spatially adaptive wavelet filter,” Opt. Lett. 29(24), 2878–2880 (2004).
[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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Gargesha, M.

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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Jenkins, M. W.

Jian, Z.

Ko, T. H.

Kuppermann, B. D.

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

Kurtz, R. M.

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Marks, D. L.

Ozcan, A.

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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Puvanathasan, P.

Ralston, T. S.

Rao, B.

Z. Jian, Z. Yu, L. Yu, B. Rao, Z. Chen, and B. J. Tromberg, “Speckle Attenuation by Curvelet Shrinkage in Optical Coherence Tomography,” Opt. Lett. 34, 1516 (2009).
[CrossRef] [PubMed]

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

Rollins, A. M.

Schmitt, J. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in Optical Coherence Tomography,” J. Biomed. Opt. 4(1), 95 (1999).
[CrossRef]

S. H. Xiang, L. Zhou, and J. M. Schmitt, “Speckle Noise Reduction for Optical Coherence Tomography,” Proc. SPIE 3196, 79 (1997).
[CrossRef]

J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42(7), 1427–1439 (1997).
[CrossRef] [PubMed]

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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Starck, J.-L.

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The Curvelet Transform for Image Denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[CrossRef]

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,” Science 254(5035), 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,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

Tromberg, B. J.

Vetterli, M.

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[CrossRef]

Wilson, D. L.

Xiang, S. H.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in Optical Coherence Tomography,” J. Biomed. Opt. 4(1), 95 (1999).
[CrossRef]

S. H. Xiang, L. Zhou, and J. M. Schmitt, “Speckle Noise Reduction for Optical Coherence Tomography,” Proc. SPIE 3196, 79 (1997).
[CrossRef]

Ying, L.

E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” SIAM Multiscale Model. Simul. 5(3), 861 (2006).
[CrossRef]

Yu, B.

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[CrossRef]

Yu, L.

Z. Jian, Z. Yu, L. Yu, B. Rao, Z. Chen, and B. J. Tromberg, “Speckle Attenuation by Curvelet Shrinkage in Optical Coherence Tomography,” Opt. Lett. 34, 1516 (2009).
[CrossRef] [PubMed]

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

Yu, Z.

Yung, K. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in Optical Coherence Tomography,” J. Biomed. Opt. 4(1), 95 (1999).
[CrossRef]

Zacharias, L. C.

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

Zhou, L.

S. H. Xiang, L. Zhou, and J. M. Schmitt, “Speckle Noise Reduction for Optical Coherence Tomography,” Proc. SPIE 3196, 79 (1997).
[CrossRef]

Commun. Pure Appl. Math. (1)

E. J. Candès and D. L. Donoho, “New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities,” Commun. Pure Appl. Math. 57, 219 (2003).
[CrossRef]

IEEE Trans. Image Process. (2)

J.-L. Starck, E. J. Candès, and D. L. Donoho, “The Curvelet Transform for Image Denoising,” IEEE Trans. Image Process. 11(6), 670–684 (2002).
[CrossRef]

S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[CrossRef]

J. Biomed. Opt. (2)

B. Rao, L. Yu, H. K. Chiang, L. C. Zacharias, R. M. Kurtz, B. D. Kuppermann, and Z. Chen, “Imaging pulsatile retinal blood flow in human eye,” J. Biomed. Opt. 13(4), 040505 (2008).
[CrossRef] [PubMed]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in Optical Coherence Tomography,” J. Biomed. Opt. 4(1), 95 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (2)

Opt. Lett. (2)

Phys. Med. Biol. (1)

J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42(7), 1427–1439 (1997).
[CrossRef] [PubMed]

Proc. SPIE (1)

S. H. Xiang, L. Zhou, and J. M. Schmitt, “Speckle Noise Reduction for Optical Coherence Tomography,” Proc. SPIE 3196, 79 (1997).
[CrossRef]

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, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

SIAM Multiscale Model. Simul. (1)

E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” SIAM Multiscale Model. Simul. 5(3), 861 (2006).
[CrossRef]

Other (1)

E. J. Candès, and D. L. Donoho, “Curvelets–a surprisingly effective nonadaptive representation for objects with edges,” in Curves and Surface Fitting, C. Rabut, A. Cohen, and L. L. Schumaker, eds. (Vanderbilt University Press, Nashville, TN., 2000).

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Figures (6)

Fig. 1
Fig. 1

Left: A schematic of the curvelet partitioning of fx-fy domain. The number of scales is 6, and the number of orientations at the second scale is 8. Right: two example curvelets, shown for the scale and orientation A and B, respectively. The curvelet A is along horizontal direction, while B is along a dipping direction.

Fig. 2
Fig. 2

(color online) acquired cross-sectional retina images before denoising at different planes: (a) x-y plane (B-scan plane), (b) x-z plane along the vertical solid white line in (a), and (c) the cross-section image in the y-z plane along the horizontal solid white line in (a). The white dotted lines in the figure indicate where the signals in Fig. 5 are shown.

Fig. 3
Fig. 3

(color online) the same images shown in Fig. 2, but after denoising, and shown on the same color scale. The black arrow in (b) indicates the photoreceptor inner and outer segment junction that is preserved and made more distinct by the despeckling process. The two black arrows in (c) indicate two yellow features that are preserved and made more distinct by the despeckling process.

Fig. 4
Fig. 4

(color online) the cross section signals along the three white dot lines in Fig. 2, before (blue dotted) and after (red solid) denoising. The edge sharpness of the original image is well preserved in the denoising process. The denoising process also makes clearer the layered structure of the retina, as indicated by the more distinct peak values in the denoised signals.

Fig. 5
Fig. 5

(color online) the same images shown in Fig. 2, but after denoising by the 2D curvelet algorithm. The features indicated by the black arrows are preserved and made more distinct by the despeckling process, but to a less degree than the 3D algorithm. The layers of tissue where the white arrows reside are significantly attenuated, while those in 3D are largely preserved.

Fig. 6
Fig. 6

SNR and Crosscorrelation as a function of different threshold k in the 3D despeckling algorithm. The algorithm improves the most SNR of 32.59 dB at k=0.5, and the crosscorrelation between the original image and the despeckled image is 0.914. The crosscorrelation does not change much between k=0.6 and k=1.0, which demonstrates the curvelet transform’s advantage in despeckling, as further explained in the text.

Tables (1)

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