## Energy-guided learning approach to compressive FD-OCT |

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

http://dx.doi.org/10.1364/OE.21.000329

Acrobat PDF (12319 KB)

### Abstract

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

## 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]

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 Sci **52**, 2425–2436 (2011). [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 Imaging **42**(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. Neurosci **5**(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. Express **2**(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. Express **19**(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. Express **12**, 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. Express **11**(18), 2183 (2003). [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. Express **12**, 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. Express **11**(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. Theory **52**, 489–509 (2006). [CrossRef]

12. D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory **52**, 1289–1306 (2006). [CrossRef]

12. D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory **52**, 1289–1306 (2006). [CrossRef]

11. E. Candës, 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]

14. E.J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory **52**, 5406–5425 (2004). [CrossRef]

*L*

_{0}minimization. This concept has been widely used in clinical image reconstruction,and specifically in magnetic resonance imaging (MRI) [15

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]

*L*

_{1}minimization [11

11. E. Candës, 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]

*L*

_{0}minimization [16

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

19. N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE **7570**, 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. Express **18**, 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. Express **2**, 2690–2697 (2011) [CrossRef]

*k*-space data, which has strong implications for data acquisition. However, those studies utilized either simulated OCT signals or actual images of onions, which have very different and much less complex morphology as compared to living biological tissues such as the human retina, cornea, skin, etc. In our previous work [22

22. C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, “Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express **20**, 10200–10211 (2012). [CrossRef] [PubMed]

*L*

_{1}minimization approach. However, the experimental results showed that for tissues with complex morphology, such as human retina, cornea and skin, at least 40%–50% of the originally sampled data is required to generate a reconstructed image of sufficiently good quality.

**Sparse representation basis**: Sufficiently sparse representation of images provides an unique solution for the reconstruction problem. Sparse representation basis and its implications in CS are well researched [23–2723. 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]

]27. E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,”Communications on Pure and Applied Mathematics

**59**, 1207–1221 (2006). [CrossRef]**Image reconstruction**: Efficient reconstruction methods have been used to reconstruct the original image. Common reconstruction methods, such as: greedy methods [28, 2928. J. A. Tropp, “Greed is good: algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory

**50**, 2231–2242 (2004). [CrossRef]],29. J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory

**51**, 1030–1051 (2006). [CrossRef]*L*_{1}minimization [11**52**, 489–509 (2006). [CrossRef]] and other have been proven efficient in finding the sparsest solution for CS [3222. C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, “Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express

**20**, 10200–10211 (2012). [CrossRef] [PubMed]]. Image reconstruction methods have been well studied.32. E. J. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl

**23**, 969–985 (2007). [CrossRef]**Generalization of the sampling procedure:**Common sampling procedure in the CS research community is sampling the entire image randomly and uniformly based on Gaussian distributions and discrete Bernoulli distributions [33]. Those sensing distributions satisfy the restricted isometry property (RIP) with a controlled probability [13,1433. S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation

**28**, 277–289 (2008). [CrossRef],3414. E.J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies,” IEEE Trans. Inf. Theory

**52**, 5406–5425 (2004). [CrossRef]–36]. Improvements in this area have been minimal when compared to the other two areas. In recent years there has been interest in optimizing the sampling probability density. Representations of MRI images have nonrandom structures since most of the image energy is concentrated close to the representation domain origin [1534. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation

**28**, 253–263 (2008). [CrossRef]]. Therefore, it was proposed [1515. 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]**58**, 1182–1195 (2007). [CrossRef] [PubMed],3837. Z. Wang and G. Arce, “Variable density compressed image sampling,”IEEE Tran. on Image Proc.

**19**, 264–270 (2010). [CrossRef]] to consider a variable density random under-sampling which would sample closer to the origin and farther in the periphery of the representation domain. The proposed sampling function is expected to adjust the probability density according to the power of distance from the origin [1538. G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett

**18**, 595–598 (2011). [CrossRef]**58**, 1182–1195 (2007). [CrossRef] [PubMed]] to use a similar method of variable density random under-sampling for the images domain. Based on the same concept, it was proposed to apply this variable density random under-sampling approach to OCT [39**19**, 264–270 (2010). [CrossRef]] though a static sampling pattern. Those non-uniform sensing approaches are static, considering general representation domains properties and hardware constraints [4039. X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE

**7904**, 79041C (2011). [CrossRef], 4140. M.F. Duarte and Y.C. Elda, “Structured compressed sensing from theory to applications,” IEEE Tran. Sig. Proc. Lett

**59**, 4053–4085 (2011). [CrossRef]] in order to improve reconstruction performance.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. Express **20**, 17281–17296 (2012). [CrossRef] [PubMed]

20. X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express **18**, 22010–22019 (2010). [CrossRef] [PubMed]

46. B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE **2950**, 2–7 (1996). [CrossRef]

## 2. Methodology

### 2.1. FD-OCT

20. X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express **18**, 22010–22019 (2010). [CrossRef] [PubMed]

*K*in the

*k*-space domain should obey where

*x*is the maximum scanning range, and Δ

_{max}*k*is the spectral bandwidth, which is inversely proportional to the OCT axial resolution. A large value for

*K*is necessary to achieve a long scanning range in OCT, which means that CCD or CMOS linear array cameras with large number of pixels, or digitizers with high sampling rates are required for developing long scanning range FD-OCT and SS-OCT systems respectively.

### 2.2. Compressive FD-OCT

*f*, from only a small subset of sampled signal in

*k*-space domain. Let an undersampled reconstruction

*f*be expressed as where Φ is a measurement operator defining which of the spectral sites are measured (non-measured

_{u}*k*-space indices will be assigned to 0 by Φ). Our goal is to reconstruct

*f*(

*x*) from a sparse sampling of

*F*(

*k*). With only few measurements made, which is essentially an ill-posed inverse problem [47], and multi solutions exist if there is no regularization.

**52**, 489–509 (2006). [CrossRef]

12. D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory **52**, 1289–1306 (2006). [CrossRef]

*f*(

*x*) can be obtained by maximizing the sparsity of the signal in the transformed domain and enforcing data fidelity in the

*k*-space domain. This can be formulated as a constrained

*L*

_{0}minimization problem. Unfortunately, solving the

*L*

_{0}problem is essentially NP hard, intractable in practice [48

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

**52**, 489–509 (2006). [CrossRef]

12. D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory **52**, 1289–1306 (2006). [CrossRef]

*L*

_{0}and

*L*

_{1}minimization lead to the same solutions. Theoretically, solving the

*L*

_{1}problem can get exactly the same solution as solving the

*L*

_{0}problem, at the cost of a substantial increase in the number of measurements required [16

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

*L*

_{1}minimization framework, which is known to have an edge-preservation effect [50]. Both Mohan et al. [19

19. N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE **7570**, 75700L–75700L-5 (2010). [CrossRef]

**18**, 22010–22019 (2010). [CrossRef] [PubMed]

*L*

_{1}minimization framework, which represents the state-of-the-art in sparse OCT reconstruction, and their results show that OCT imagery can be reconstructed in a meaningful manner using sparsely sampled measurements in

*k*-space. Our previous work used a homotopic non-local regularization reconstruction approach [22

**20**, 10200–10211 (2012). [CrossRef] [PubMed]

### 2.3. Energy guided CS model

34. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation **28**, 253–263 (2008). [CrossRef]

35. E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique **386**, 589–592 (2008). [CrossRef]

**58**, 1182–1195 (2007). [CrossRef] [PubMed]

*K*sampling frequency locations denoted by Ω

*, with the measured value at each sampling location: Subsequently, Ω*

_{K}*is partitioned into two complementary sets Ω*

_{K}*and*

_{T}*is*

_{T}*T*and the cardinality of

*K*−

*T*). The subset Ω

*denotes sampled frequency locations and*

_{T}*is generated based on a probability function*

_{T}*p*(

_{S}*k*) that provides a quantitative measure of ESD at frequency sampling location

*k*

*M*≤

*K*discrete sampling functions. The linear measurements of

*F*(Eq. (1)) can be generally written as: where

*m*= 1, 2,...,

*M*and

*ε*denotes measurement noise.

_{m}*ȳ*and

*ε̄*is

*M*× 1 vector and Φ

*is*

_{T}*M*×

*K*sampling matrix.

*M*<

*K*in the energy-guided learning model, the sampling basis is modified to account for the lack of observations at frequency locations in

*φ*values at location

_{T,m}*k*are realizations of a random variable

*k*whose probability is defined in Eq. (11): The probability of random variable

*k*is defined with weight

*π*∈ [0, 1] which sets the under sampling level (for example, if 50% compression rate is required,

*π*is set to 0.5). Here the probability density function (PDF) of

*δ*(

*k*) has zero mean with zero variance, while

*p*is based on learned spectral measured coefficients PDF. Thus,

_{S}*p*(

_{T}*k*) = 0 with probability (1 −

*πp*(

_{S}*k*)).

### 2.4. Implementation

*p*to be the measured coefficients PDF (Eq. (12)) that will be used to implement the sparse sampling probability density

_{S}*p*(Eq. (11)): where

_{T}*F*represents the

_{i}*i*reflectivity profile (A-scan), contains spatial information at the

_{th}*i*location. The absolute operator |

_{th}*F*(

_{i}*k*)| is selected based on experiments. In the energy-guided learning approach, the measurement sparsity is guided by the measurements PDF model. Therefore a sampling method, such as been used in Monte Carlo approximation [51], can be used for sampling from the learned PDF. Since

*p*is an univariant distribution, Inverse Transform Sampling method can be used [51] which is define [52]: Let

_{S}*C*(

*x*) be the cumulative density function (CDF) of random variable

*x*, if random variable

*y*comes from uniform (0,1) distribution, then random variable

*z*=

*C*

^{−1}(

*y*) comes from the distribution of

*x. C*

^{−1}can be realized from the learned PDF (Eq. (12)). Let define random variable

*ω*with a given probability distribution function (Eq. (12)) and let define

*I*(

*k*) as the inverse

*CDF*of the learned PDF (Eq. (12)): where

*P*denotes probability that the random variable

*ω*value is less or equal to

*x*. For illustration purposes, learned distribution of different type of tissues are demonstrated in Fig. 2. Retinal and corneal PDF are presented at Fig. 2(b), Fig. 2(c). PDF of different type of tissue is examined as well - fingertip, Fig. 2(d). In addition an example of cornea background light is demonstrated in Fig. 2(a). In the case of sampling PDF learned from retina data acquisitions, it can be seen that the energy is concentrated at two ranges, highest energy range at samples 600–800 and secondary energy peak at samples 250–350. For sampling PDF learned from cornea data acquisitions, it can be seen that the energy is concentrated at two ranges, highest energy range at samples 550–650 and secondary energy peak at samples 250–300. The fingertip PDF is more uniformly distributed in comparison to retinal and corneal PDF. Sampling PDF learned from fingertip data acquisitions. It can be seen that the energy is concentrated at two ranges, highest energy range at samples 350–750 and secondary energy peak at samples 100–150

*k*frequency location of

*F*(

*k*). The first learning step is concluded once the sampling probability (Eq. (11)) as well as subset Ω

*are determined. Based on comprehensive testing using OCT datasets of different types of tissues, it was found that the energy-guided compressive FD-OCT without the DC term has no notable impact on performance.*

_{T}*F*is sampled by Φ

*(Eq. (8)) with probability*

^{T}*p*(Eq. (11)) in order to measure higher energy coefficients at higher accuracy. The samples from subset Ω

_{T}*are used for creating the sampling basis*

_{T}*φ*that create sampling matrix Φ

_{T,k}*(Eq. (8)). The acquired samples used to reconstruct the OCT images at a higher reconstruction quality.*

^{T}## 3. Results and discussions

**20**, 10200–10211 (2012). [CrossRef] [PubMed]

*p*(Eq. (11)) is adjusted

_{S}*φ*(Eq. (10)) values for the conventional CS approach at location

_{T,m}*k*are realizations of a random variable

*k*whose probability is adjusted as well and is defined in Eq. (15): Both the sampling matrices used in conventional CS reconstruction and the proposed energy-guided compressive sensing reconstruction are random matrices. The difference between the matrices is that the conventional CS sparse sampling matrix contains zeros at random locations which are distributed uniformly, representing non-sampled locations, while the proposed energy-guided compressive sensing matrix includes zeros at random locations which are distributed based on underlying data.

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

*λ*= 1020nm,

_{c}*δλ*= 110nm,

*P*= 10mW) and a 47kHz InGaAs linear array, 1024 pixel camera (SUI, Goodrich) interfaced with a high performance spectrometer (P&P Optica). The FD-OCT system provides 3

_{out}*μ*m axial and 15

*μ*m lateral resolution in the human corneal and fingertip tissue, and 6

*μ*m axial resolution in the human retina. The OCT images were acquired from healthy subjects using an imaging procedure carried out in accordance with the University of Waterloo research ethics regulations. To reconstruct OCT images from only a percentage of the camera pixels, the original data is sampled in the spectral domain using pseudo-random mask which its distribution is based on underlying data. The obtained spectral data is then used to populate the

*k*-space grid according to the known functional dependency of wavenumber on the pixel index [20

**18**, 22010–22019 (2010). [CrossRef] [PubMed]

**18**, 22010–22019 (2010). [CrossRef] [PubMed]

**18**, 22010–22019 (2010). [CrossRef] [PubMed]

46. B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE **2950**, 2–7 (1996). [CrossRef]

**20**, 10200–10211 (2012). [CrossRef] [PubMed]

*f*(

*x*) is original image,

*f*̂(

*x*) is reconstructed image, and

*N*is the number of pixels in each image.

39. X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE **7904**, 79041C (2011). [CrossRef]

## 4. Conclusions

## Acknowledgments

## References and links

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

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 Sci |

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33. | S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, “Uniform uncertainty principle for Bernoulli and subgaussian ensembles,” Constructive Approximation |

34. | R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation |

35. | E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique |

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. |

38. | G. Puy, P. Vandergheynst, and Y. Wiaux, “On variable density compressive sampling,” IEEE Sig. Proc. Lett |

39. | X. Liu and J.U. Kang, “sparse OCT: optimizing compressed sensing in spectral domain optical coherence tomography,” Proc. SPIE |

40. | M.F. Duarte and Y.C. Elda, “Structured compressed sensing from theory to applications,” IEEE Tran. Sig. Proc. Lett |

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. Express |

44. | S.M. Potter, A. Mart, and J. Pine, “High-speed CCD movie camera with random pixel selection for neurobiology research,” Proc. SPIE |

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. SPIE |

46. | B. Dierickx, D. Scheffer, G. Meynants, W. Ogiers, and J. Vlummens, “Random addressable active pixel image sensors,” Proc. SPIE |

47. | P. Fieguth, |

48. | B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. |

49. | G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” |

50. | 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). |

51. | C. P. Robert and G. Casella, “Stable signal recovery from incomplete and inaccurate measurements,” |

52. | H. Chen, |

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. Lett |

**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

**History**

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*

**Citation**

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)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-329

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