## Image reconstruction from nonuniformly spaced samples in spectral-domain optical coherence tomography |

Biomedical Optics Express, Vol. 3, Issue 4, pp. 741-752 (2012)

http://dx.doi.org/10.1364/BOE.3.000741

Acrobat PDF (8384 KB)

### Abstract

In spectral-domain optical coherence tomography (SD-OCT), data samples are collected nonuniformly in the wavenumber domain, requiring a measurement re-sampling process before a conventional fast Fourier transform can be applied to reconstruct an image. This re-sampling necessitates extra computation and often introduces errors in the data. Instead, we develop an inverse imaging approach to reconstruct an SD-OCT image. We make use of total variation (TV) as a constraint to preserve the image edges, and estimate the two-dimensional cross-section of a sample directly from the SD-OCT measurements rather than processing for each A-line. Experimental results indicate that compared with the conventional method, our technique gives a smaller noise residual. The potential of using the TV constraint to suppress sensitivity falloff in SD-OCT is also demonstrated with experiment data.

© 2012 OSA

## 1. Introduction

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,” Science **254**, 1178–1181 (1991). [CrossRef] [PubMed]

2. W. Drexler and J. G. Fujimoto, *Optical Coherence Tomography Technology and Applications* (Springer-Verlag, Berlin, 2008). [CrossRef]

3. M. Wojtkowski, “High-speed optical coherence tomography: basics and applications,” Appl. Opt. **49**, D3–D60 (2010). [CrossRef]

4. D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev. **3**, 155–169 (2011). [CrossRef]

*μ*m to several

*μ*m. Data acquisition speed has also increased from 2 A-lines per second in 1991 to 480,000 A-lines per second in 2011 [6

6. T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express **2**, 2438–2448 (2011). [CrossRef]

2. W. Drexler and J. G. Fujimoto, *Optical Coherence Tomography Technology and Applications* (Springer-Verlag, Berlin, 2008). [CrossRef]

7. K. H. Y. Cheng, B. A. Standish, V. X. D. Yang, K. K. Y. Cheung, X. Gu, E. Y. Lam, and K. K. Y. Wong, “Wavelength-swept spectral and pulse shaping utilizing hybrid Fourier domain modelocking by fiber optical parametric and erbium-doped fiber amplifiers,” Opt. Express **18**, 1909–1915 (2010). [CrossRef] [PubMed]

8. R. A. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express **11**, 889–893 (2003). [CrossRef] [PubMed]

9. S.-H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, “High-speed spectral-domain optical coherence tomography at 1.3*μ*m wavelength,” Opt. Express **11**, 3598–3604 (2003). [CrossRef] [PubMed]

*λ*. This is because the measurement device, a spectrometer, operates by tuning to different wavelengths. On the other hand, in reconstructing the image, we use a Fourier transform of the measurement with respect to the wavenumber

*k*, where

*k*= 2

*π*/

*λ*. Therefore, the measurements are in fact nonuniform samples in

*k*-space [10]. Customarily, the SD-OCT measurements undergo a resampling process to generate a uniformly-spaced data in

*k*-space, where the resampling is achieved through linear, or cubic, interpolations [10, 11

11. Y. Watanabe, S. Maeno, K. Aoshima, H. Hasegawa, and H. Koseki, “Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units,” Appl. Opt. **49**, 4756–4762 (2010). [CrossRef] [PubMed]

12. K. Zhang and J. U. Kang, “Graphic processing unit accelerated non-uniform fast Fourier transform for ultrahigh-speed, real-time Fourier-domain OCT,” Opt. Express **18**, 23472–23487 (2010). [CrossRef] [PubMed]

13. K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express **17**, 12121–12131 (2009). [CrossRef] [PubMed]

12. K. Zhang and J. U. Kang, “Graphic processing unit accelerated non-uniform fast Fourier transform for ultrahigh-speed, real-time Fourier-domain OCT,” Opt. Express **18**, 23472–23487 (2010). [CrossRef] [PubMed]

13. K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express **17**, 12121–12131 (2009). [CrossRef] [PubMed]

14. H. K. Chan and S. Tang, “High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform,” Biomed. Opt. Express **1**, 1309–1319 (2010). [CrossRef]

15. L. I. Rudin, S. Osher, and E. Fatemi, “An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs),” IEEE Microwave Guided Wave Lett . **8**, 18–20 (1998). [CrossRef]

16. L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. **46**, 443–454 (2004). [CrossRef]

13. K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express **17**, 12121–12131 (2009). [CrossRef] [PubMed]

12. K. Zhang and J. U. Kang, “Graphic processing unit accelerated non-uniform fast Fourier transform for ultrahigh-speed, real-time Fourier-domain OCT,” Opt. Express **18**, 23472–23487 (2010). [CrossRef] [PubMed]

*k*) spectrometer [17

17. M. Jeon, J. Kim, U. Jung, C. Lee, W. Jung, and S. A. Boppart, “Full-range k-domain linearization in spectral-domain optical coherence tomography,” Appl. Opt. **50**, 1158–1162 (2011). [CrossRef] [PubMed]

18. E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. **48**, H113–H119 (2009). [CrossRef] [PubMed]

19. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D: Nonlinear Phenomena **60**, 259–268 (1992). [CrossRef]

21. J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniformly-spaced samples in Fourier domain optical coherence tomography,” Proc. SPIE **8296**, 829610 (2012). [CrossRef]

22. Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A **27**, 1638–1646 (2010). [CrossRef]

23. X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A **27**, 1630–1637 (2010). [CrossRef]

## 2. SD-OCT system modeling

*Ĩ*(

*k*) be the system measurement as a function of the wavenumber

*k*, and

*G*(

*k*) the source power spectrum. The SD-OCT system measurements for one A-line is [10] where

*p*is the reflective ratio of the reference mirror (normally we take

_{r}*p*= 1),

_{r}*p*(

_{s}*z*) is the reflective ratio of the sample varying with depth value

*z*,

*a*is the sample refractive index (also assumed to be unity), and

_{s}*p*(

_{s}*z*).

*p*(

_{s}*z*) is further assumed to be symmetric with respect to

*z*= 0, and therefore it can be estimated from measurements

*Ĩ*(

*k*) using the fast Fourier transform (FFT) [13

**17**, 12121–12131 (2009). [CrossRef] [PubMed]

*G*(

*k*) can be estimated independently, we can substract

*p*= 1) from Eq. (1) and represent the last term as an error

_{r}*e*(

*k*), which is usually small compared with the other two terms. Thus, the SD-OCT measurement is simplified to In the discrete domain, this measurement can be written as where we have discretized to

*N*sections in the axial direction, and

*m*∈ {0

*,*1

*,...,M*– 1} denotes the

*m*th pixel of the line-scan CCD camera. The value of

*N*is not required to be the same as

*M*, which is different from the FFT or NUDFT methods. However, the largest

*N*should be limited by the largest detectable depth, which is determined by the spectrometer’s spectral resolution. Writing Eq. (3) into a matrix formulation, we have

*H*

_{m}_{,}

*= 2*

_{n}*G*(

*k*) cos (2

_{m}*k*).

_{m}z_{n}**y**= [

*I*(

*k*

_{0})

*I*(

*k*

_{1}) ...

*I*(

*k*

_{M}_{−1})]

*,*

^{T}**x**= [

*p*(

_{s}*z*

_{0})

*p*(

_{s}*z*

_{1}) ...

*p*(

_{s}*z*

_{N}_{−1})]

*, and*

^{T}**e**= [

*e*(

*k*

_{0})

*e*(

*k*

_{1}) ···

*e*(

*k*

_{M}_{−1})]

*to represent the SD-OCT measurement vector, one A-line sample signal, and the detection error vector, respectively. Matrix H is defined as the SD-OCT system impulse response matrix with*

^{T}*H*in the (

_{m,n}*m*,

*n*)th position. Using these notations, we can write the measurement process as

**y**= H

**x**+

**e**. This formulation represents the basic idea for the FFT and NUDFT methods as well. Furthermore, the SD-OCT measurements for

*L*number of A-lines can be represented as where matrices Y and E are of size

*M*×

*L*, and X is of size

*N*×

*L*. Each column of these quantities represents the measurement for one A-line.

## 3. Signal reconstruction using TV regularization

*ℓ*

_{2}norm for a vector) for signal fidelity together with a total variation regularization, i.e. where

*α*> 0 is a penalty parameter, and ||X||

_{TV}is the total variation of X defined as with (∇

*X)*

_{n}

_{n}_{,}

*= X*

_{l}

_{n}_{+1,}

*− X*

_{l}

_{n}_{,}

*if*

_{l}*n*<

*N*− 1 and is zero when

*n*=

*N*− 1, and (∇

*X)*

_{l}

_{n}_{,}

*= X*

_{l}

_{n}_{,}

_{l}_{+1}− X

_{n}_{,}

*if*

_{l}*l*<

*L*− 1 and is zero when

*l*=

*L*− 1.

25. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning **3**, 1–122 (2010). [CrossRef]

26. Y. Huang, M. K. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulat. **7**, 774–795 (2008). [CrossRef] [PubMed]

*α*

_{1}> 0 and

*α*

_{2}> 0 are two predefined positive penalty parameters. We then use an alternating minimization algorithm where each iteration consists of the following two steps: (using the superscript (

*i*) to denote the

*i*th step) Conjugate gradient (CG) and Chambolle’s projection algorithms are used to search for X

^{(i)}and U

^{(i)}, respectively. Details about these two algorithms can be found in [26

26. Y. Huang, M. K. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulat. **7**, 774–795 (2008). [CrossRef] [PubMed]

27. X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express **16**, 17215–17226 (2008). [CrossRef] [PubMed]

28. A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision **20**, 89–97 (2004). [CrossRef]

29. J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. **50**, H285–H296 (2011). [CrossRef] [PubMed]

^{(i)}and U

^{(i)}as a stop criteria for the iterative algorithm. The parameters

*α*

_{1}and

*α*

_{2}are used to balance the measurement error and the TV regularization penalty in Eq. (8). Large

*α*

_{1}and

*α*

_{2}values are for the case of a high measurement error. However, if they are set at very big values, the images will be significantly smoothed in the reconstruction process.

## 4. Experimental results

*μ*m, and a maximum detectable depth of 2.42 mm. The mirror in the reference arm is silver-coated with a two-inch diameter. System measurements are collected using a customized spectrometer consisting of a one-inch volume-phase holographic (VPH) grating and a line-scan camera. As depicted in Fig. 1, the camera and the galvano mirrors are controlled by a computer.

*G*(

*k*) from the raw data. We note that the raw measurements, denoted

_{m}*Ĩ*(

_{l}*k*), resemble a Gaussian-shaped low-frequency signal modulated by high-frequency components. The former originates from the SLD source power spectrum

_{m}*G*(

*k*), while the high-frequency components are the interference signals represented by the second and third terms in Eq. (1), together with detector noise. These can be suppressed by a lowpass filter when our objective is to estimate

_{m}*G*(

*k*).

_{m}*G*

_{est}(

*k*), from the inverse Fourier transform of the filtered signal. Fig. 2(b) and (c) present the averaged transformation and the spectrum estimation, respectively. Subtracting the latter from the system raw measurements, we have the 800 “adjusted” A-line measurements

_{m}*I*(

*k*) as plotted in Fig. 2(d). For each A-line,

_{m}*I*(

*k*) can now be deemed a linear combination of

_{m}*p*(

_{s}*z*) using Eq. (3).

_{n}*I*(

*k*) also has an envelope of a Gaussian function due to

_{m}*G*(

*k*). However, the envelope is not symmetric with respect to zero, which seems to contradict the symmetry of the cosine function in H of Eq. (5). In fact, this is caused by several factors. Chief among them is the interference between different sample layers

_{m}*p*(

_{s}*z*), represented by the third term of Eq. (1). We can re-write this term as where the values of

_{n}*p*(

_{s}*z*) are real. This nonnegative term shifts the measurement envelope towards the positive side with respect to zero. Other factors causing the asymmetric envelope include the detector noise, quantization error in data acquisition, and detector nonlinear responsivity. All of these limit the reconstruction performance of the TV regularization.

**y**with a matrix Ĥ, with elements

*Ĥ*

_{m}_{,}

*= exp (−*

_{n}*jk*

_{m}*z*) [12

_{n}**18**, 23472–23487 (2010). [CrossRef] [PubMed]

**17**, 12121–12131 (2009). [CrossRef] [PubMed]

14. H. K. Chan and S. Tang, “High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform,” Biomed. Opt. Express **1**, 1309–1319 (2010). [CrossRef]

*α*

_{1}= 20 and

*α*

_{2}= 100. Totally 80 iterations are used for the algorithm defined in Eq. (9). The cross-sectional sample reconstructions using these three methods are presented in Fig. 3. The horizontal and vertical directions are the A-line (

*l*) and the index of the depth (

*n*), respectively.

*p*(

_{s}*z*) and any remaining error in the reconstruction. Because

*Ĩ*(

*k*), this SNR is different from the value obtained by comparing the reconstruction using a mirror sample and the signal by simply detecting the reflection from the reference arm [9

_{m}9. S.-H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, “High-speed spectral-domain optical coherence tomography at 1.3*μ*m wavelength,” Opt. Express **11**, 3598–3604 (2003). [CrossRef] [PubMed]

*l*= 150 in Fig. 4(a), and at the depth position

*n*= 425 in (b). The smoothness of the results corresponding to the TV regularization suggests that it minimizes fluctuations in the signal.

*α*

_{1}and

*α*

_{2}for the TV regularization are still

*α*

_{1}= 20 and

*α*

_{2}= 100. We use 100 iterations to obtain the reconstruction result. Fig. 5 presents the reconstructed signals and their zoomed-in views.

*z*increases, as evident from the slanted lines approaching the left, errors such as the vertical line segment indicated by the arrows in Fig. 5(b) appear in the reconstruction. This is because the wavenumber

_{n}*k*is inversely proportional to the wavelength

*λ*, and therefore a uniformly-spaced

*λ*corresponds to fewer measurements in the region where

*k*is large. As a result, more reconstruction error exists in a larger depth. The situation is considerably better with NUDFT and TV. If we compare Fig. 5(c) with (e), we see that the reconstruction using the TV regularization presents much less noise residue than using NUDFT, consistent with the earlier experiment.

*l*= 9 (for deep in the sample),

*l*= 601 (intermediate), and

*l*= 930 (shallow). Notice that in these images, we masked out the places far from the two slanted lines. For example, for

*l*= 9, we only selected

*n*from about 660 to 760; for

*l*= 601, roughly for 460 <

*n*< 560; and for

*l*= 930, around 350 <

*n*< 450. The 3 A-lines for the different methods are presented in Fig. 6. As shown in (c) for the TV regularization, two peaks corresponding to the two layers in the sample can be observed clearly in the reconstruction, whether for deep, intermediate, or shallow regions. In contrast, for FFT and NUDFT, the two peaks corresponding to the intermediate and deep regions are difficult to be identified. We locate the value of

*n*for each peak in Fig. 6(c). Then

*p*(

_{s}*z*) at these locations using the three methods are summarized in Table 1. Note that,

_{n}*n*= 384, 497, and 704 are for the first sample layer, while the other three are for the second layer. As expected, generally

*p*(

_{s}*z*) becomes smaller as

_{n}*n*increases or the depth is enlarged. For example, for the first layer, as

*n*increases from 384 to 704, the normalized

*p*(

_{s}*z*) decreases from −5.60 dB to −21.68 dB in the FFT method, from 0 dB to −16.23 dB in the NUDFT method, and from −1.68 dB to −12.91 dB in the TV method. However, the difference between the minimum and maximum

_{n}*p*(

_{s}*z*) varies with the three schemes. The smallest is the 12.91 dB in the TV method, which is 3.32 dB smaller than that for NUDFT (16.23 dB) and 7.71 dB smaller than that for FFT (20.62 dB).

_{n}*α*

_{1}= 20 and

*α*

_{2}= 100. Comparing the three reconstructions for the orange flesh sample, the TV regularization shows the best reconstruction quality. In the reconstruction using the FFT method for the pearl sample, once again we observe the artifact at a large depth region, which does not exist in the other two reconstruction schemes. For the pearl sample we also observe speckle noise. This is suppressed with TV regularization, because TV acts as a prior to enhance the edges and reduce random noise.

## 5. Conclusions

## Acknowledgments

## References and links

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,” Science |

2. | W. Drexler and J. G. Fujimoto, |

3. | M. Wojtkowski, “High-speed optical coherence tomography: basics and applications,” Appl. Opt. |

4. | D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev. |

5. | R. Zhu, J. Xu, C. Zhang, A. C. Chan, Q. Li, P. Chui, E. Y. Lam, and K. K. Wong, “Dual-band time-multiplexing swept-source OCT based on optical parametric amplification,” to be published in IEEE J. Sel. Top. Quantum Electron. |

6. | T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express |

7. | K. H. Y. Cheng, B. A. Standish, V. X. D. Yang, K. K. Y. Cheung, X. Gu, E. Y. Lam, and K. K. Y. Wong, “Wavelength-swept spectral and pulse shaping utilizing hybrid Fourier domain modelocking by fiber optical parametric and erbium-doped fiber amplifiers,” Opt. Express |

8. | R. A. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express |

9. | S.-H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, “High-speed spectral-domain optical coherence tomography at 1.3 |

10. | M. Brezinski, |

11. | Y. Watanabe, S. Maeno, K. Aoshima, H. Hasegawa, and H. Koseki, “Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units,” Appl. Opt. |

12. | K. Zhang and J. U. Kang, “Graphic processing unit accelerated non-uniform fast Fourier transform for ultrahigh-speed, real-time Fourier-domain OCT,” Opt. Express |

13. | K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express |

14. | H. K. Chan and S. Tang, “High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform,” Biomed. Opt. Express |

15. | L. I. Rudin, S. Osher, and E. Fatemi, “An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs),” IEEE Microwave Guided Wave Lett . |

16. | L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. |

17. | M. Jeon, J. Kim, U. Jung, C. Lee, W. Jung, and S. A. Boppart, “Full-range k-domain linearization in spectral-domain optical coherence tomography,” Appl. Opt. |

18. | E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. |

19. | L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D: Nonlinear Phenomena |

20. | J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniform samples in spectral domain optical coherence tomography,” in |

21. | J. Ke, R. Zhu, and E. Y. Lam, “Image reconstruction from nonuniformly-spaced samples in Fourier domain optical coherence tomography,” Proc. SPIE |

22. | Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A |

23. | X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A |

24. | G. H. Golub and C. F. Van Loan, |

25. | S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learning |

26. | Y. Huang, M. K. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulat. |

27. | X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express |

28. | A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision |

29. | J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. |

**OCIS Codes**

(100.3020) Image processing : Image reconstruction-restoration

(100.3190) Image processing : Inverse problems

(110.4500) Imaging systems : Optical coherence tomography

(110.1758) Imaging systems : Computational imaging

**ToC Category:**

Image Reconstruction and Inverse Problems

**History**

Original Manuscript: February 1, 2012

Revised Manuscript: March 7, 2012

Manuscript Accepted: March 9, 2012

Published: March 21, 2012

**Citation**

Jun Ke and Edmund Y. Lam, "Image reconstruction from nonuniformly spaced samples in spectral-domain optical coherence tomography," Biomed. Opt. Express **3**, 741-752 (2012)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-4-741

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### References

- 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]
- W. Drexler and J. G. Fujimoto, Optical Coherence Tomography Technology and Applications (Springer-Verlag, Berlin, 2008). [CrossRef]
- M. Wojtkowski, “High-speed optical coherence tomography: basics and applications,” Appl. Opt.49, D3–D60 (2010). [CrossRef]
- D. P. Popescu, L.-P. Choo-Smith, C. Flueraru, Y. Mao, S. Chang, J. Disano, S. Sherif, and M. G. Sowa, “Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications,” Biophys. Rev.3, 155–169 (2011). [CrossRef]
- R. Zhu, J. Xu, C. Zhang, A. C. Chan, Q. Li, P. Chui, E. Y. Lam, and K. K. Wong, “Dual-band time-multiplexing swept-source OCT based on optical parametric amplification,” to be published in IEEE J. Sel. Top. Quantum Electron.
- T.-H. Tsai, B. Potsaid, M. F. Kraus, C. Zhou, Y. K. Tao, J. Hornegger, and J. G. Fujimoto, “Piezoelectric-transducer-based miniature catheter for ultrahigh-speed endoscopic optical coherence tomography,” Opt. Express2, 2438–2448 (2011). [CrossRef]
- K. H. Y. Cheng, B. A. Standish, V. X. D. Yang, K. K. Y. Cheung, X. Gu, E. Y. Lam, and K. K. Y. Wong, “Wavelength-swept spectral and pulse shaping utilizing hybrid Fourier domain modelocking by fiber optical parametric and erbium-doped fiber amplifiers,” Opt. Express18, 1909–1915 (2010). [CrossRef] [PubMed]
- R. A. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express11, 889–893 (2003). [CrossRef] [PubMed]
- S.-H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, “High-speed spectral-domain optical coherence tomography at 1.3μm wavelength,” Opt. Express11, 3598–3604 (2003). [CrossRef] [PubMed]
- M. Brezinski, Optical Coherence Tomography: Principles and Applications (Elsevier, 2006).
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