OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 329–344

Energy-guided learning approach to compressive FD-OCT

Shimon Schwartz, Chenyi Liu, Alexander Wong, David A. Clausi, Paul Fieguth, and Kostadinka Bizheva  »View Author Affiliations

Optics Express, Vol. 21, Issue 1, pp. 329-344 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (12319 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



High quality, large size volumetric imaging of biological tissue with optical coherence tomography (OCT) requires large number and high density of scans, which results in large data acquisition volume. This may lead to corruption of the data with motion artifacts related to natural motion of biological tissue, and could potentially cause conflicts with the maximum permissible exposure of biological tissue to optical radiation. Therefore, OCT can benefit greatly from different approaches to sparse or compressive sampling of the data where the signal is recovered from its sub-Nyquist measurements. In this paper, a new energy-guided compressive sensing approach is proposed for improving the quality of images acquired with Fourier domain OCT (FD-OCT) and reconstructed from sparse data sets. The proposed algorithm learns an optimized sampling probability density function based on the energy distribution of the training data set, which is then used for sparse sampling instead of the commonly used uniformly random sampling. It was demonstrated that the proposed energy-guided learning approach to compressive FD-OCT of retina images requires 45% fewer samples in comparison with the conventional uniform compressive sensing (CS) approach while achieving similar reconstruction performance. This novel approach to sparse sampling has the potential to significantly reduce data acquisition while maintaining image quality.

© 2013 OSA

OCIS Codes
(100.0100) Image processing : Image processing
(100.3010) Image processing : Image reconstruction techniques
(110.4500) Imaging systems : Optical coherence tomography
(170.4470) Medical optics and biotechnology : Ophthalmology

ToC Category:
Medical Optics and Biotechnology

Original Manuscript: September 26, 2012
Revised Manuscript: November 16, 2012
Manuscript Accepted: December 15, 2012
Published: January 4, 2013

Virtual Issues
Vol. 8, Iss. 2 Virtual Journal for Biomedical Optics

Shimon Schwartz, Chenyi Liu, Alexander Wong, David A. Clausi, Paul Fieguth, and Kostadinka Bizheva, "Energy-guided learning approach to compressive FD-OCT," Opt. Express 21, 329-344 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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,” Science254, 1178–1181 (1991). [CrossRef] [PubMed]
  2. W. Drexler and J. G. Fujimoto, “Optical coherence tomography,” Springer BerlinHeidelberg (2008).
  3. ML Gabriele, G Wollstein, H Ishikawa, L Kagemann, J Xu, LS Folio, and JS Schuman, “Optical coherence tomography: history, current status, and laboratory work,” Invest Ophthalmol Vis Sci52, 2425–2436 (2011). [CrossRef] [PubMed]
  4. W. Geitzenauer, C. K. Hitzenberger, and U. M. Schmidt-Erfurth, “Retinal optical coherence tomography: past, present and future perspectives,” Br. J. Ophthalmol95(2), 171–177 (2010). [CrossRef] [PubMed]
  5. J. Wang, M. A. Shousha, V. L. Perez, C. L. Karp, S. H. Yoo, M. Shen, L. Cui, V. Hurmeriz, C. Du, D. Zhu, Q. Chen, and M. Li, “Ultra-high resolution optical coherence tomography for imaging the anterior segment of the eye,” Ophthalmic Surg Lasers Imaging42(4), 15–27 (2011). [CrossRef]
  6. S. Martinez-Conde, S. L. Macknik, and D. H. Hubel, “The role of fixational eye movements in visual perception,” Nat. Rev. Neurosci5(3), 229–240 (2004). [CrossRef] [PubMed]
  7. M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “The role of fixational eye movements in visual perception,” Biomed. Opt. Express2(9), 2690–2697 (2011). [CrossRef] [PubMed]
  8. T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express19(4), 3044–3062 (2011). [CrossRef] [PubMed]
  9. R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolutionFourier domain optical coherence tomography,” Opt. Express12, 2156–2165 (2004). [CrossRef] [PubMed]
  10. M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express11(18), 2183 (2003). [CrossRef] [PubMed]
  11. E. Candës, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory52, 489–509 (2006). [CrossRef]
  12. D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006). [CrossRef]
  13. D. Donoho and J. Tanner, “Counting faces of randomly-projected polytopes when the projection radically lowers dimension,” J. AMS22, 1–5 (2009).
  14. E.J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory52, 5406–5425 (2004). [CrossRef]
  15. M. Lustig, D. Donoho, and J. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med.58, 1182–1195 (2007). [CrossRef] [PubMed]
  16. J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Image28, 106–121 (2009). [CrossRef]
  17. A. Wong, A. Mishra, D. Clausi, and P. Fieguth, “Sparse reconstruction of breast MRI using homotopic L0 minimization in a regional sparsified domain,” Biomed. Eng. IEEE Trans, 1–10 (2010).
  18. D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc.1032–1035 (2009).
  19. N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE7570, 75700L–75700L-5 (2010). [CrossRef]
  20. X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express18, 22010–22019 (2010). [CrossRef] [PubMed]
  21. 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,” Opt. Express2, 2690–2697 (2011) [CrossRef]
  22. C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, “Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express20, 10200–10211 (2012). [CrossRef] [PubMed]
  23. B. Wu, E. Lebed, M. Sarunic, and M. Beg, “Quantitative evaluation of transform domains for compressive sampling-based recovery of sparsely sampled volumetric OCT images,” IEEE Trans. Bio. Eng.1–9 (2012). [CrossRef]
  24. D.L. Donoho and X. Huo, “Uncertainty principles and ideal atom decomposition,” IEEE Trans. Inf. Theory47, 2845–2862 (2001). [CrossRef]
  25. M. Elad and A.M. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of bases,” IEEE Trans. Inf. Theory48, 2558–2567 (2002). [CrossRef]
  26. R. Gribonval and M. Nielsen, “Sparse representations in unions of bases,” IEEE Trans. Inf. Theory49, 3320–3325 (2003). [CrossRef]
  27. E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,”Communications on Pure and Applied Mathematics59, 1207–1221 (2006). [CrossRef]
  28. J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory50, 2231–2242 (2004). [CrossRef]
  29. J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory51, 1030–1051 (2006). [CrossRef]
  30. L. He, T. Chang, S. Osher, T. Fang, and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Reports6–35, 2006.
  31. S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale L1-regularized least squares problems with applications in signal processing and statistics,” Manuscript, (2007).
  32. E. J. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl23, 969–985 (2007). [CrossRef]
  33. S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation28, 277–289 (2008). [CrossRef]
  34. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation28, 253–263 (2008). [CrossRef]
  35. E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique386, 589–592 (2008). [CrossRef]
  36. M. Rudelson and R. Vershynin, “Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements,” 40th An. Conf. Inf. Sc. Sys.207–210 (2009).
  37. Z. Wang and G. Arce, “Variable density compressed image sampling,”IEEE Tran. on Image Proc.19, 264–270 (2010). [CrossRef]
  38. G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett18, 595–598 (2011). [CrossRef]
  39. X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE7904, 79041C (2011). [CrossRef]
  40. M.F. Duarte and Y.C. Elda, “Structured compressed sensing from theory to applications,” IEEE Tran. Sig. Proc. Lett59, 4053–4085 (2011). [CrossRef]
  41. R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,”IEEE Int. Conf. Ac. Speech Sig. Proc.5125–5128 (2008). [CrossRef]
  42. S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” Journal of Visual Communication and Image Representation (2012). [CrossRef]
  43. S. Schwartz, A. Wong, and D. A. Clausi, “Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion,” Opt. Express20, 17281–17296 (2012). [CrossRef] [PubMed]
  44. S.M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE2869, 243253 (1997).
  45. S.P. Monacos, R.K. Lam, A.A. Portillo, and G.G. Ortiz, “Design of an event-driven random-access-windowing CCD-based camera,” Proc. SPIE4975, 115 (2003). [CrossRef]
  46. B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE2950, 2–7 (1996). [CrossRef]
  47. P. Fieguth, Statistical image processing and multidimensional modeling (SpringerNew York, 2010).
  48. B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput.24, 227–234 (1995). [CrossRef]
  49. G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” Tech. Rep. CAM Report 07–23, Univ. California, Los Angeles, 2007.
  50. W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag101–104 (2009).
  51. C. P. Robert and G. Casella, “Stable signal recovery from incomplete and inaccurate measurements,”Monte Carlo Statistical Methods, New York: Springer-Verlag (1999).
  52. H. Chen, Tutorial on monte carlo sampling (The Ohio state university, department of chemcal and biomolecular engineering, technical report, 2005).
  53. P. Puvanathasan, P. Forbes, Z. Ren, D. Malchow, S. Boyd, and K. Bizheva, “High-speed, high-resolution Fourier-domain optical coherence tomography system for retinal imaging in the 1060 nm wavelength region,” Opt. Lett33, 2479–2481 (2008). [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited