Abstract

Acquiring three dimensional image volumes with techniques such as Optical Coherence Tomography (OCT) relies on reconstructing the tissue layers based on reflection of light from tissue interfaces. One B-mode scan in an image is acquired by scanning and concatenating several A-mode scans, and several contiguous slices are acquired to assemble a full 3D image volume. In this work, we demonstrate how Compressive Sampling (CS) can be used to accurately reconstruct 3D OCT images with minimal quality degradation from a subset of the original image. The full 3D image is reconstructed from sparsely sampled data by exploiting the sparsity of the image in a carefully chosen transform domain. We use several sub-sampling schemes, recover the full 3D image using CS, and show that there is negligible effect on clinically relevant morphometric measurements of the optic nerve head in the recovered image. The potential outcome of this work is a significant reduction in OCT image acquisition time, with possible extensions to speeding up acquisition in other imaging modalities such as ultrasound and MRI.

© 2010 OSA

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References

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  1. B. Považay, B. Hofer, C. Torti, B. Hermann, A. R. Tumlinson, M. Esmaeelpour, C. A. Egan, A. C. Bird, and W. Drexler, “Impact of enhanced resolution, speed and penetration on three-dimensional retinal optical coherence tomography,” Opt. Express17, 4134–4150 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-5-4134 .
    [Crossref] [PubMed]
  2. T. Schmoll, C. Kolbitsch, and R. A. Leitgeb, “Ultra-high-speed volumetric tomography of human retinal blood flow,”, Opt. Express 17, 4166–4176 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-5-4166 .
  3. M. K. K. Leung, A. Mariampillai, B. A. Standish, K. K. C. Lee, N. R. Munce, A. Vitkin, and V. X. D. Yang, “High-power wavelength-swept laser in Littman telescope-less polygon filter and dual-amplifier configuration for multichannel optical coherence tomography,” Opt. Lett.34, 2814–2816 (2009), http://ol.osa.org/abstract.cfm?URI=ol-34-18-2814
    [Crossref] [PubMed]
  4. S. Mallat, A Wavelet Tour of Signal Processing, Second Edition (Academic Press, New York, 1999).
  5. E. J. Candès and D. L. Donoho, “New tight frames of curvelets and optimal representations of objects with piecewise-C2 singularities,” Comm. Pure Appl. Math.57, 219–266 (2004), http://www.acm.caltech.edu/∼emmanuel/papers/CurveEdges.pdf .
    [Crossref]
  6. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
    [Crossref]
  7. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [Crossref]
  8. E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl.23, 969–985 (2007), http://stacks.iop.org/0266-5611/23/969 .
    [Crossref]
  9. I. Daubechies, M. Defrise, and C. De Mol “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.11, 1413–1457 (2004), http://dx.doi.org/10.1002/cpa.20042 .
    [Crossref]
  10. F. J. Herrmann and G. Hennenfent, “Non-parametric seismic data recovery with curvelet frames,” Geophys. J. Int. 173, 233–248 (2008).
    [Crossref]
  11. M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian, Wavelets, Time-Frequency Methods and Phase Space (Springer-Verlag, Berlin, 1989).
  12. M. Elad, J. L. Starck, P. Querre, and D.L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmon. Anal.19, 340–358 (2005), http://www.sciencedirect.com/science/article/B6WB3-4GWC29F-2/2/61d7afc314d50b27968d84ff4a16acce .
    [Crossref]
  13. M. Young, S. Lee, E. Gibson, K. Hsu, M. F. Beg, P. J. Mackenzie, and M. V. Sarunic, “Morphometric analysis of the optic nerve head with optical coherence tomography.” In proceedings of OCT and Coherence Domain Optical Methods in Biomedicine XIV7554, (2004), http://link.aip.org/link/?PSI/7554/75542L/1 .
  14. B. C. Chauhan, J. W. Blanchard, D. C. Hamilton, and R. P. LeBlanc, “Technique for Detecting Serial Topographic Changes in the Optic Disc and Peripapillary Retina Using Scanning Laser Tomography,”, Invest. Ophthalmol. Vis. Sci. 41, 775–782 (2000).
    [PubMed]

2008 (1)

F. J. Herrmann and G. Hennenfent, “Non-parametric seismic data recovery with curvelet frames,” Geophys. J. Int. 173, 233–248 (2008).
[Crossref]

2006 (2)

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

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

2000 (1)

B. C. Chauhan, J. W. Blanchard, D. C. Hamilton, and R. P. LeBlanc, “Technique for Detecting Serial Topographic Changes in the Optic Disc and Peripapillary Retina Using Scanning Laser Tomography,”, Invest. Ophthalmol. Vis. Sci. 41, 775–782 (2000).
[PubMed]

Blanchard, J. W.

B. C. Chauhan, J. W. Blanchard, D. C. Hamilton, and R. P. LeBlanc, “Technique for Detecting Serial Topographic Changes in the Optic Disc and Peripapillary Retina Using Scanning Laser Tomography,”, Invest. Ophthalmol. Vis. Sci. 41, 775–782 (2000).
[PubMed]

Candès, E. J.

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

Chauhan, B. C.

B. C. Chauhan, J. W. Blanchard, D. C. Hamilton, and R. P. LeBlanc, “Technique for Detecting Serial Topographic Changes in the Optic Disc and Peripapillary Retina Using Scanning Laser Tomography,”, Invest. Ophthalmol. Vis. Sci. 41, 775–782 (2000).
[PubMed]

Donoho, D. L.

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

Hamilton, D. C.

B. C. Chauhan, J. W. Blanchard, D. C. Hamilton, and R. P. LeBlanc, “Technique for Detecting Serial Topographic Changes in the Optic Disc and Peripapillary Retina Using Scanning Laser Tomography,”, Invest. Ophthalmol. Vis. Sci. 41, 775–782 (2000).
[PubMed]

Hennenfent, G.

F. J. Herrmann and G. Hennenfent, “Non-parametric seismic data recovery with curvelet frames,” Geophys. J. Int. 173, 233–248 (2008).
[Crossref]

Herrmann, F. J.

F. J. Herrmann and G. Hennenfent, “Non-parametric seismic data recovery with curvelet frames,” Geophys. J. Int. 173, 233–248 (2008).
[Crossref]

Holschneider, M.

M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian, Wavelets, Time-Frequency Methods and Phase Space (Springer-Verlag, Berlin, 1989).

Kronland-Martinet, R.

M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian, Wavelets, Time-Frequency Methods and Phase Space (Springer-Verlag, Berlin, 1989).

LeBlanc, R. P.

B. C. Chauhan, J. W. Blanchard, D. C. Hamilton, and R. P. LeBlanc, “Technique for Detecting Serial Topographic Changes in the Optic Disc and Peripapillary Retina Using Scanning Laser Tomography,”, Invest. Ophthalmol. Vis. Sci. 41, 775–782 (2000).
[PubMed]

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing, Second Edition (Academic Press, New York, 1999).

Morlet, J.

M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian, Wavelets, Time-Frequency Methods and Phase Space (Springer-Verlag, Berlin, 1989).

Romberg, J.

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

Tao, T.

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

Tchamitchian, P.

M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian, Wavelets, Time-Frequency Methods and Phase Space (Springer-Verlag, Berlin, 1989).

Geophys. J. Int. (1)

F. J. Herrmann and G. Hennenfent, “Non-parametric seismic data recovery with curvelet frames,” Geophys. J. Int. 173, 233–248 (2008).
[Crossref]

IEEE Trans. Inf. Theory (2)

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

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

Invest. Ophthalmol. Vis. Sci. (1)

B. C. Chauhan, J. W. Blanchard, D. C. Hamilton, and R. P. LeBlanc, “Technique for Detecting Serial Topographic Changes in the Optic Disc and Peripapillary Retina Using Scanning Laser Tomography,”, Invest. Ophthalmol. Vis. Sci. 41, 775–782 (2000).
[PubMed]

Other (10)

M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian, Wavelets, Time-Frequency Methods and Phase Space (Springer-Verlag, Berlin, 1989).

M. Elad, J. L. Starck, P. Querre, and D.L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmon. Anal.19, 340–358 (2005), http://www.sciencedirect.com/science/article/B6WB3-4GWC29F-2/2/61d7afc314d50b27968d84ff4a16acce .
[Crossref]

M. Young, S. Lee, E. Gibson, K. Hsu, M. F. Beg, P. J. Mackenzie, and M. V. Sarunic, “Morphometric analysis of the optic nerve head with optical coherence tomography.” In proceedings of OCT and Coherence Domain Optical Methods in Biomedicine XIV7554, (2004), http://link.aip.org/link/?PSI/7554/75542L/1 .

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl.23, 969–985 (2007), http://stacks.iop.org/0266-5611/23/969 .
[Crossref]

I. Daubechies, M. Defrise, and C. De Mol “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.11, 1413–1457 (2004), http://dx.doi.org/10.1002/cpa.20042 .
[Crossref]

B. Považay, B. Hofer, C. Torti, B. Hermann, A. R. Tumlinson, M. Esmaeelpour, C. A. Egan, A. C. Bird, and W. Drexler, “Impact of enhanced resolution, speed and penetration on three-dimensional retinal optical coherence tomography,” Opt. Express17, 4134–4150 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-5-4134 .
[Crossref] [PubMed]

T. Schmoll, C. Kolbitsch, and R. A. Leitgeb, “Ultra-high-speed volumetric tomography of human retinal blood flow,”, Opt. Express 17, 4166–4176 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-5-4166 .

M. K. K. Leung, A. Mariampillai, B. A. Standish, K. K. C. Lee, N. R. Munce, A. Vitkin, and V. X. D. Yang, “High-power wavelength-swept laser in Littman telescope-less polygon filter and dual-amplifier configuration for multichannel optical coherence tomography,” Opt. Lett.34, 2814–2816 (2009), http://ol.osa.org/abstract.cfm?URI=ol-34-18-2814
[Crossref] [PubMed]

S. Mallat, A Wavelet Tour of Signal Processing, Second Edition (Academic Press, New York, 1999).

E. J. Candès and D. L. Donoho, “New tight frames of curvelets and optimal representations of objects with piecewise-C2 singularities,” Comm. Pure Appl. Math.57, 219–266 (2004), http://www.acm.caltech.edu/∼emmanuel/papers/CurveEdges.pdf .
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Proposed scan pattern consisting of randomly spaced horizontal B-scans and randomly spaced vertical B-scans. The doted lines represent the fly-back trajectory of the galvonometer mirrors.

Fig. 2
Fig. 2

(a) One en-face slice of an optic nerve head volume. (b) The data as it would appear if acquired with the proposed sampling scheme (53% of the data missing). The red portions in the image indicate regions where no data was acquired. The four green lines represent recovered B-scans shown in Fig. 3. (c) En-face image generated from the CS recovered volume with 53% missing data. (d) Contrast-enhanced difference between (a) and (c).

Fig. 3
Fig. 3

The B-scans in the first row are two typical vertical and two horizontal slices taken from the model, at locations shown by the green lines in Fig. 2(b). The images in the second row are the same slices taken from a volume with 53% missing data at locations corresponding to missing B-scans. The third row represents the slices that were recovered from the data by the CS interpolation method, while the fourth row represents B-scans that are the recovered by bilinear interpolation. The fifth row contains several zoomed sections of the CS-based and bilinear-based recovery. Note the presence of artifacts in recovered images with bilinear interpolation, and the standard good quality of CS-recovery compared to the original images.

Fig. 4
Fig. 4

Representative typical slices recovered with CS in volumes with 23%, 35%, 61% and 75% missing data. Note that even at 75% missing data the image quality remains comparable to the original B-scan.

Fig. 5
Fig. 5

(a) Extracted internal limiting membrane (ILM) of the optic nerve head from the original image. Color map represents the height function. (b) Extracted ILM from the recovered volume with 53% missing data. (c) Standard deviation of distance of the three segmentations of the original image volume, computed to measure the natural variability in segmentation of ILM from original image.

Fig. 6
Fig. 6

Topographical Change Analysis (TCA) maps showing position of ILM surface overlaid on top of summed-voxels-projection images of recovered volumes at (a) 23%, (b) 35%, (c)53%, (d) 61% and (e) 75% missing data, respectively. The relative surface position relative to standard deviation is shown with red representing posterior surface location, and green representing anterior surface location in the recovered image.

Fig. 7
Fig. 7

Percent reduction in scan time by the proposed scanning pattern, as a function of the percent of missing data. The diagonal line shows the asymptotic behavior of the percentage of reduction in scan time as a function of percentage of missing data.

Tables (1)

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Table 1 Relative change in surface area (ΔS.A.) and volume (ΔVOL) in CS-based recovery

Equations (2)

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x ˜ = arg min x x 1 subject to y RS H x 2 ε .
x ˜ = arg min x x 1 + λ y RS H x 2 ,

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