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 Optical Society of America

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. Express 17, 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 XIV 7554, (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]

Appl. Comput. Harmon. Anal.

• 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]

Geophys. J. Int.

• 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

• 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]

Inverse Probl.

• 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]

Invest. Ophthalmol. Vis. Sci.

• 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]

Opt. Express

• 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. Express 17, 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.

Opt. Lett.

• 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]

Other

• 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]
• 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]
• M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian, Wavelets, Time-Frequency Methods and Phase Space (Springer-Verlag, Berlin, 1989).
• 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 XIV 7554, (2004), http://link.aip.org/link/?PSI/7554/75542L/1.

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