Homotopic, non-local sparse reconstruction of optical coherence tomography imagery

doi:10.1364/OE.20.010200

Homotopic, non-local sparse reconstruction of optical coherence tomography imagery

Chenyi Liu, Alexander Wong, Kostadinka Bizheva, Paul Fieguth, and Hongxia Bie »View Author Affiliations

Optics Express, Vol. 20, Issue 9, pp. 10200-10211 (2012)
http://dx.doi.org/10.1364/OE.20.010200

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Abstract

The resolution in optical coherence tomography imaging is an important parameter which determines the size of the smallest features that can be visualized. Sparse sampling approaches have shown considerable promise in producing high resolution OCT images with fewer camera pixels, reducing both the cost and the complexity of an imaging system. In this paper, we propose a non-local approach to the reconstruction of high resolution OCT images from sparsely sampled measurements. An iterative strategy is introduced for minimizing a homotopic, non-local regularized functional in the spatial domain, subject to data fidelity constraints in the k-space domain. The novel algorithm was tested on human retinal, corneal, and limbus images, acquired in-vivo, demonstrating the effectiveness of the proposed approach in generating high resolution reconstructions from a limited number of camera pixels.

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:
Image Processing

History
Original Manuscript: March 1, 2012
Revised Manuscript: April 5, 2012
Manuscript Accepted: April 11, 2012
Published: April 19, 2012

Virtual Issues
Vol. 7, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Chenyi Liu, Alexander Wong, Kostadinka Bizheva, Paul Fieguth, and Hongxia Bie, "Homotopic, non-local sparse reconstruction of optical coherence tomography imagery," Opt. Express 20, 10200-10211 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-10200

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References

S. A. Boppart, “Optical coherence tomography: technology and applications for neuroimaging,” Psychophysiology40, 529–541 (2003). [CrossRef] [PubMed]
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]
B. E. Bouma and G. J. Tearney, Handbook of Optical Coherence Tomography (Informa Healthcare, 2001).
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,” Ophthalmology112, 1734–1746 (2005). [CrossRef] [PubMed]
W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer, 2008). [CrossRef]
M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett.27, 1415–1417 (2002). [CrossRef]
R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express12, 2156–2165 (2004). [CrossRef] [PubMed]
R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express11, 889–894 (2003). [CrossRef] [PubMed]
A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys.66, 239–303 (2003). [CrossRef]
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]
D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006). [CrossRef]
M. Lustig, D. Donoho, and J. Pauly, “Sparse MRI: the application of compressed sesing for rapid MR imaging,” Magn. Reson. Med.58, 1182–1195 (2007). [CrossRef] [PubMed]
J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Imag.28, 106–121 (2009). [CrossRef]
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).
D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc., 1032–1035 (2009).
N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE7570, 75700L (2010). [CrossRef]
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]
G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” Tech. Rep. CAM Report 07-23, Univ. California, Los Angeles, 2007.
P. Fieguth, Statistical Image Processing and Multidimensional Modeling (Springer, 2010).
B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput.24, 227–234 (1995). [CrossRef]
W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag, 101–104 (2009).
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. Lett.33, 2479–2481 (2008). [PubMed]

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[1] S. A. Boppart, “Optical coherence tomography: technology and applications for neuroimaging,” Psychophysiology40, 529–541 (2003). [CrossRef] [PubMed]

[2] 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]

[3] B. E. Bouma and G. J. Tearney, Handbook of Optical Coherence Tomography (Informa Healthcare, 2001).

[4] 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,” Ophthalmology112, 1734–1746 (2005). [CrossRef] [PubMed]

[5] W. Drexler and J. G. Fujimoto, Optical Coherence Tomography (Springer, 2008). [CrossRef]

[6] M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett.27, 1415–1417 (2002). [CrossRef]

[7] R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express12, 2156–2165 (2004). [CrossRef] [PubMed]

[8] R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express11, 889–894 (2003). [CrossRef] [PubMed]

[9] A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys.66, 239–303 (2003). [CrossRef]

[10] 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]

[11] D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory52, 1289–1306 (2006). [CrossRef]

[12] M. Lustig, D. Donoho, and J. Pauly, “Sparse MRI: the application of compressed sesing for rapid MR imaging,” Magn. Reson. Med.58, 1182–1195 (2007). [CrossRef] [PubMed]

[13] J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization,” IEEE Trans. Med. Imag.28, 106–121 (2009). [CrossRef]

[14] 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).

[15] D. Liang, H. Wang, and L. Ying, “SENSE reconstruction with nonlocal TV regularization,” Proc. IEEE Eng. Med. Biol. Soc., 1032–1035 (2009).

[16] N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE7570, 75700L (2010). [CrossRef]

[17] 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]

[18] G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” Tech. Rep. CAM Report 07-23, Univ. California, Los Angeles, 2007.

[19] P. Fieguth, Statistical Image Processing and Multidimensional Modeling (Springer, 2010).

[20] B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput.24, 227–234 (1995). [CrossRef]

[21] W. Guo and F. Huang, “Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts,” Int. Sym. Biomed Imag, 101–104 (2009).

[22] 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. Lett.33, 2479–2481 (2008). [PubMed]

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Homotopic, non-local sparse reconstruction of optical coherence tomography imagery