Abstract

We address the reconstruction problem in frequency-domain optical-coherence tomography (FDOCT) from undersampled measurements within the framework of compressed sensing (CS). Specifically, we propose optimal sparsifying bases for accurate reconstruction by analyzing the backscattered signal model. Although one might expect Fourier bases to be optimal for the FDOCT reconstruction problem, it turns out that the optimal sparsifying bases are windowed cosine functions where the window is the magnitude spectrum of the laser source. Further, the windowed cosine bases can be phase locked, which allows one to obtain higher accuracy in reconstruction. We present experimental validations on real data. The findings reported in this Letter are useful for optimal dictionary design within the framework of CS-FDOCT.

© 2012 Optical Society of America

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References

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2012 (1)

2011 (1)

2010 (2)

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, Proc. SPIE 7570, 75700L (2010).
[CrossRef]

X. Liu and J. U. Kang, Opt. Express 18, 22010 (2010).
[CrossRef]

2008 (1)

2007 (2)

S. Mallat and Z. Zhang, IEEE Trans. Signal Process. 41, 3397 (2007).
[CrossRef]

J. A. Tropp and A. C. Gilbert, IEEE Trans. Inf. Theory 53, 4655 (2007).
[CrossRef]

2005 (1)

P. H. Tomlins and R. K. Wang, J. Phys. D 38, 2519 (2005).
[CrossRef]

2003 (1)

2002 (1)

M. Wojtkowski, T. Bajraszewski, and A. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

Bajraszewski, T.

M. Wojtkowski, T. Bajraszewski, and A. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

Chen, T.

Fercher, A.

M. Wojtkowski, T. Bajraszewski, and A. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

Fercher, A. F.

Gilbert, A. C.

J. A. Tropp and A. C. Gilbert, IEEE Trans. Inf. Theory 53, 4655 (2007).
[CrossRef]

Hitzenberger, C. K.

Huo, T.

Kang, J. U.

Karl, W. C.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Leitgeb, R. A.

Liu, X.

Mallat, S.

S. Mallat and Z. Zhang, IEEE Trans. Signal Process. 41, 3397 (2007).
[CrossRef]

Mohan, N.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Saleh, B. E. A.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Seck, H.

Seelamantula, C. S.

Soh, Y.

Stojanovic, I.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Teich, M. C.

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, Proc. SPIE 7570, 75700L (2010).
[CrossRef]

Tomlins, P. H.

P. H. Tomlins and R. K. Wang, J. Phys. D 38, 2519 (2005).
[CrossRef]

Tropp, J. A.

J. A. Tropp and A. C. Gilbert, IEEE Trans. Inf. Theory 53, 4655 (2007).
[CrossRef]

Unser, M.

Villiger, M. L.

Wang, C.

Wang, R. K.

P. H. Tomlins and R. K. Wang, J. Phys. D 38, 2519 (2005).
[CrossRef]

Wojtkowski, M.

M. Wojtkowski, T. Bajraszewski, and A. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

Xue, P.

Zhang, N.

Zhang, Y.

Zhang, Z.

S. Mallat and Z. Zhang, IEEE Trans. Signal Process. 41, 3397 (2007).
[CrossRef]

Zheng, J.

IEEE Trans. Inf. Theory (1)

J. A. Tropp and A. C. Gilbert, IEEE Trans. Inf. Theory 53, 4655 (2007).
[CrossRef]

IEEE Trans. Signal Process. (1)

S. Mallat and Z. Zhang, IEEE Trans. Signal Process. 41, 3397 (2007).
[CrossRef]

J. Biomed. Opt. (1)

M. Wojtkowski, T. Bajraszewski, and A. Fercher, J. Biomed. Opt. 7, 457 (2002).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. D (1)

P. H. Tomlins and R. K. Wang, J. Phys. D 38, 2519 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (1)

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, Proc. SPIE 7570, 75700L (2010).
[CrossRef]

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Figures (1)

Fig. 1.
Fig. 1.

Comparison of the quality of reconstruction with windowed Fourier bases and windowed cosine bases. The experimental data is courtesy of R. A. Leitgeb, Medical University of Vienna, Austria.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

I(k)=|R(k)|2(1+=1Lrejωk+=1Lr*ejωk+p=1Lq=1Lrprq*ej(ωpωq)kAutocorrelation terms).
y(k)=|R(k)|2(2=1Lrcos(ωk)),

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