## Sparsity based denoising of spectral domain optical coherence tomography images |

Biomedical Optics Express, Vol. 3, Issue 5, pp. 927-942 (2012)

http://dx.doi.org/10.1364/BOE.3.000927

Acrobat PDF (2648 KB)

### Abstract

In this paper, we make contact with the field of compressive sensing and present a development and generalization of tools and results for reconstructing irregularly sampled tomographic data. In particular, we focus on denoising Spectral-Domain Optical Coherence Tomography (SDOCT) volumetric data. We take advantage of customized scanning patterns, in which, a selected number of B-scans are imaged at higher signal-to-noise ratio (SNR). We learn a sparse representation dictionary for each of these high-SNR images, and utilize such dictionaries to denoise the low-SNR B-scans. We name this method multiscale sparsity based tomographic denoising (MSBTD). We show the qualitative and quantitative superiority of the MSBTD algorithm compared to popular denoising algorithms on images from normal and age-related macular degeneration eyes of a multi-center clinical trial. We have made the corresponding data set and software freely available online.

© 2012 OSA

## 1. Introduction

1. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express **11**(18), 2183–2189 (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,” Science **254**(5035), 1178–1181 (1991). [CrossRef] [PubMed]

3. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. **4**(1), 95–105 (1999). [CrossRef]

4. B. Karamata, K. Hassler, M. Laubscher, and T. Lasser, “Speckle statistics in optical coherence tomography,” J. Opt. Soc. Am. A **22**(4), 593–596 (2005). [CrossRef] [PubMed]

*a priori*parametric or non-parametric model for the signal and noise (e.g. Wiener filtering [5], kernel regression [6], or wavelets [7

7. S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. **9**(9), 1532–1546 (2000). [CrossRef] [PubMed]

8. P. Chatterjee and P. Milanfar, “Practical bounds on image denoising: from estimation to information,” IEEE Trans. Image Process. **20**(5), 1221–1233 (2011). [CrossRef] [PubMed]

9. A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express **18**(8), 8338–8352 (2010). [CrossRef] [PubMed]

12. Z. Jian, L. Yu, B. Rao, B. J. Tromberg, and Z. Chen, “Three-dimensional speckle suppression in Optical Coherence Tomography based on the curvelet transform,” Opt. Express **18**(2), 1024–1032 (2010). [CrossRef] [PubMed]

13. A. W. Scott, S. Farsiu, L. B. Enyedi, D. K. Wallace, and C. A. Toth, “Imaging the infant retina with a hand-held spectral-domain optical coherence tomography device,” Am. J. Ophthalmol. **147**(2), 364–373.e2 (2009). [CrossRef] [PubMed]

14. M. A. Mayer, A. Borsdorf, M. Wagner, J. Hornegger, C. Y. Mardin, and R. P. Tornow, “Wavelet denoising of multiframe optical coherence tomography data,” Biomed. Opt. Express **3**(3), 572–589 (2012). [CrossRef] [PubMed]

## 2. Methods

32. S. Farsiu, M. Elad, and P. Milanfar, “A practical approach to superresolution,” Proc. SPIE **6077**, 607703, 607703-15 (2006). [CrossRef]

33. R. Estrada, C. Tomasi, M. T. Cabrera, D. K. Wallace, S. F. Freedman, and S. Farsiu, “Enhanced video indirect ophthalmoscopy (VIO) via robust mosaicing,” Biomed. Opt. Express **2**(10), 2871–2887 (2011). [CrossRef] [PubMed]

### 2.1. Sparse representation of SDOCT images

*L*images (B-scans), each representing a 2D slice,

34. M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. **15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

37. J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simulation **7**(1), 214–241 (2008). [CrossRef]

38. A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. **51**(1), 34–81 (2009). [CrossRef]

**X**. A vector representation of this patch can be obtained by lexicographic ordering:

*P>Q*implies that the dictionary is redundant and

**α**corresponding to a particular dictionary are zeros or very small (sparsity), relatively few well-chosen measurements suffice to reconstruct the images in this class [21

21. R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. **50**(7), 072601–072613 (2011). [CrossRef]

**D**, the sparse solution of the denoising problem [34

34. M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. **15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

*ω*is the error tolerance.

**D**. One popular class of sparsity based denoising algorithms exploits the information of the noisy image itself to define the dictionary (which we denote as

34. M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. **15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

39. M. Aharon, M. Elad, and A. M. Bruckstein, “The K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. **54**(11), 4311–4322 (2006). [CrossRef]

**15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

### 2.2. Multiscale structural dictionary

**D**on these patches by the K-SVD algorithm [34

**15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

35. S. Li, L. Fang, and H. Yin, “An efficient dictionary learning algorithm and its application to 3-D medical image denoising,” IEEE Trans. Biomed. Eng. **59**(2), 417–427 (2012). [CrossRef] [PubMed]

40. R. Rubinstein, M. Zibulevsky, and M. Elad, “Double sparsity: learning sparse dictionaries for sparse signal approximation,” IEEE Trans. Signal Process. **58**(3), 1553–1564 (2010). [CrossRef]

41. P. Chatterjee and P. Milanfar, “Clustering-based denoising with locally learned dictionaries,” IEEE Trans. Image Process. **18**(7), 1438–1451 (2009). [CrossRef] [PubMed]

42. W. Dong, L. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. **20**(7), 1838–1857 (2011). [CrossRef] [PubMed]

43. H. Takeda, S. Farsiu, and P. Milanfar, “Kernel regression for image processing and reconstruction,” IEEE Trans. Image Process. **16**(2), 349–366 (2007). [CrossRef] [PubMed]

41. P. Chatterjee and P. Milanfar, “Clustering-based denoising with locally learned dictionaries,” IEEE Trans. Image Process. **18**(7), 1438–1451 (2009). [CrossRef] [PubMed]

42. W. Dong, L. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. **20**(7), 1838–1857 (2011). [CrossRef] [PubMed]

37. J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simulation **7**(1), 214–241 (2008). [CrossRef]

44. B. Ophir, M. Lustig, and M. Elad, “Multi-scale dictionary learning using wavelets,” IEEE J. Sel. Top. Signal Process. **5**(5), 1014–1024 (2011). [CrossRef]

*s*) to create the multiscale structural dictionary, which is the concatenation of the subdictionaries

### 2.3. Nonlocal denoising process

*V*pixels in each direction (i.e. for an image of size

*N*×

*M*, the number of the extracted patches (

*I*) is

#### 2.3.1. Subdictionary selection

42. W. Dong, L. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. **20**(7), 1838–1857 (2011). [CrossRef] [PubMed]

**20**(7), 1838–1857 (2011). [CrossRef] [PubMed]

35. S. Li, L. Fang, and H. Yin, “An efficient dictionary learning algorithm and its application to 3-D medical image denoising,” IEEE Trans. Biomed. Eng. **59**(2), 417–427 (2012). [CrossRef] [PubMed]

#### 2.3.2. Sparse representation of patches

*i*

^{th}denoised patch. The sparse vector

35. S. Li, L. Fang, and H. Yin, “An efficient dictionary learning algorithm and its application to 3-D medical image denoising,” IEEE Trans. Biomed. Eng. **59**(2), 417–427 (2012). [CrossRef] [PubMed]

46. A. Buades, B. Coll, and J.-M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. **4**(2), 490–530 (2005). [CrossRef]

47. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. **16**(8), 2080–2095 (2007). [CrossRef] [PubMed]

*J*patches with the highest similarity to the processed patch

48. S. Li and L. Fang, “Signal denoising with random refined orthogonal matching pursuit,” IEEE Trans. Instrum. Meas. **61**(1), 26–34 (2012). [CrossRef]

49. I. Daubechies, R. DeVore, M. Fornasier, and C. S. Gunturk, “Iteratively reweighted least squares minimization for sparse recovery,” Commun. Pure Appl. Math. **63**(1), 1–38 (2010). [CrossRef]

50. I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. **57**(11), 1413–1457 (2004). [CrossRef]

*I*) patches (

**15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

### 2.4. Algorithmic parameters

*V*between each processed patch is 1 and the number

*J*of similar patches in each searching window is 20. In the k-means clustering stage, the cluster number K is set to 70. Prior to the multiscale learning process, the original image is upsampled two times, each by a factor 1.25 and downsampled three times, each by a factor of 1.5625 to create the training images of six scales. The parameters of the iterative reweighted algorithm for solving the problem (4) are set to the default values in [31].

### 2.5. Data sets

51. S. J. Chiu, J. A. Izatt, R. V. O’Connell, K. P. Winter, C. A. Toth, and S. Farsiu, “Validated automatic segmentation of AMD pathology including drusen and geographic atrophy in SD-OCT images,” Invest. Ophthalmol. Vis. Sci. **53**(1), 53–61 (2012). [CrossRef] [PubMed]

### 2.6. Data processing

52. P. Thévenaz, U. E. Ruttimann, and M. Unser, “A pyramid approach to subpixel registration based on intensity,” IEEE Trans. Image Process. **7**(1), 27–41 (1998). [CrossRef] [PubMed]

53. W. Dong, “Sparsity-based Image Denoising via Dictionary Learning and Structural Clustering,” http://www4.comp.polyu.edu.hk/~cslzhang/code.htm.

### 2.7. Quantitative measures of performance

55. G. Cincotti, G. Loi, and M. Pappalardo, “Frequency decomposition and compounding of ultrasound medical images with wavelet packets,” IEEE Trans. Med. Imaging **20**(8), 764–771 (2001). [CrossRef] [PubMed]

56. P. Bao and L. Zhang, “Noise reduction for magnetic resonance images via adaptive multiscale products thresholding,” IEEE Trans. Med. Imaging **22**(9), 1089–1099 (2003). [CrossRef] [PubMed]

57. M. D. Robinson, C. A. Toth, J. Y. Lo, and S. Farsiu, “Efﬁcient fourier-wavelet super-resolution,” IEEE Trans. Image Process. **19**(10), 2669–2681 (2010). [CrossRef] [PubMed]

*h*pixel in the reference noiseless image

^{th}**R**,

*h*pixel of the denoised image

^{th}*H*is the total number of pixels, and

**R**.

52. P. Thévenaz, U. E. Ruttimann, and M. Unser, “A pyramid approach to subpixel registration based on intensity,” IEEE Trans. Image Process. **7**(1), 27–41 (1998). [CrossRef] [PubMed]

## 3. Experimental results

58. G. T. Chong, S. Farsiu, S. F. Freedman, N. Sarin, A. F. Koreishi, J. A. Izatt, and C. A. Toth, “Abnormal foveal morphology in ocular albinism imaged with spectral-domain optical coherence tomography,” Arch. Ophthalmol. **127**(1), 37–44 (2009). [CrossRef] [PubMed]

59. F. Luisier, T. Blu, and M. Unser, “A new SURE approach to image denoising: interscale orthonormal wavelet thresholding,” IEEE Trans. Image Process. **16**(3), 593–606 (2007). [CrossRef] [PubMed]

**15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

47. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. **16**(8), 2080–2095 (2007). [CrossRef] [PubMed]

58. G. T. Chong, S. Farsiu, S. F. Freedman, N. Sarin, A. F. Koreishi, J. A. Izatt, and C. A. Toth, “Abnormal foveal morphology in ocular albinism imaged with spectral-domain optical coherence tomography,” Arch. Ophthalmol. **127**(1), 37–44 (2009). [CrossRef] [PubMed]

**15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

47. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. **16**(8), 2080–2095 (2007). [CrossRef] [PubMed]

59. F. Luisier, T. Blu, and M. Unser, “A new SURE approach to image denoising: interscale orthonormal wavelet thresholding,” IEEE Trans. Image Process. **16**(3), 593–606 (2007). [CrossRef] [PubMed]

### 3.1. Experiment 1: denoising based on learned dictionary from a nearby high-SNR Scan

60. S. J. Chiu, X. T. Li, P. Nicholas, C. A. Toth, J. A. Izatt, and S. Farsiu, “Automatic segmentation of seven retinal layers in SDOCT images congruent with expert manual segmentation,” Opt. Express **18**(18), 19413–19428 (2010). [CrossRef] [PubMed]

58. G. T. Chong, S. Farsiu, S. F. Freedman, N. Sarin, A. F. Koreishi, J. A. Izatt, and C. A. Toth, “Abnormal foveal morphology in ocular albinism imaged with spectral-domain optical coherence tomography,” Arch. Ophthalmol. **127**(1), 37–44 (2009). [CrossRef] [PubMed]

59. F. Luisier, T. Blu, and M. Unser, “A new SURE approach to image denoising: interscale orthonormal wavelet thresholding,” IEEE Trans. Image Process. **16**(3), 593–606 (2007). [CrossRef] [PubMed]

### 3.2. Experiment 2: denoising based on learned dictionary from a distant high-SNR scan

**127**(1), 37–44 (2009). [CrossRef] [PubMed]

**16**(3), 593–606 (2007). [CrossRef] [PubMed]

**15**(12), 3736–3745 (2006). [CrossRef] [PubMed]

**16**(8), 2080–2095 (2007). [CrossRef] [PubMed]

**127**(1), 37–44 (2009). [CrossRef] [PubMed]

**16**(3), 593–606 (2007). [CrossRef] [PubMed]

26. 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,” Biomed. Opt. Express **2**(9), 2690–2697 (2011). [CrossRef] [PubMed]

## 4. Discussion and Conclusions

57. M. D. Robinson, C. A. Toth, J. Y. Lo, and S. Farsiu, “Efﬁcient fourier-wavelet super-resolution,” IEEE Trans. Image Process. **19**(10), 2669–2681 (2010). [CrossRef] [PubMed]

## Acknowledgments

## References and links

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5. | J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain,” in |

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7. | S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. |

8. | P. Chatterjee and P. Milanfar, “Practical bounds on image denoising: from estimation to information,” IEEE Trans. Image Process. |

9. | A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express |

10. | M. Gargesha, M. W. Jenkins, A. M. Rollins, and D. L. Wilson, “Denoising and 4D visualization of OCT images,” Opt. Express |

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12. | Z. Jian, L. Yu, B. Rao, B. J. Tromberg, and Z. Chen, “Three-dimensional speckle suppression in Optical Coherence Tomography based on the curvelet transform,” Opt. Express |

13. | A. W. Scott, S. Farsiu, L. B. Enyedi, D. K. Wallace, and C. A. Toth, “Imaging the infant retina with a hand-held spectral-domain optical coherence tomography device,” Am. J. Ophthalmol. |

14. | M. A. Mayer, A. Borsdorf, M. Wagner, J. Hornegger, C. Y. Mardin, and R. P. Tornow, “Wavelet denoising of multiframe optical coherence tomography data,” Biomed. Opt. Express |

15. | E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory |

16. | D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory |

17. | D. Healy and D. J. Brady, “Compression at the physical interface,” IEEE Signal Process. Mag. |

18. | S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. |

19. | S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE J. Sel. Top. Signal Process. |

20. | M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. |

21. | R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. |

22. | “Age-Related Eye Disease Study 2 Ancillary Spectral Domain Optical Coherence Tomography Study (A2ASDOCT)” (2008–2013), http://clinicaltrials.gov/ct2/show/NCT00734487 |

23. | S. Farsiu, J. Christofferson, B. Eriksson, P. Milanfar, B. Friedlander, A. Shakouri, and R. Nowak, “Statistical detection and imaging of objects hidden in turbid media using ballistic photons,” Appl. Opt. |

24. | X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express |

25. | E. Lebed, P. J. Mackenzie, M. V. Sarunic, and M. F. Beg, “Rapid volumetric OCT image acquisition using compressive sampling,” Opt. Express |

26. | 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,” Biomed. Opt. Express |

27. | N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE |

28. | S. Jiao, R. Knighton, X. Huang, G. Gregori, and C. Puliafito, “Simultaneous acquisition of sectional and fundus ophthalmic images with spectral-domain optical coherence tomography,” Opt. Express |

29. | M. D. Robinson, S. J. Chiu, C. A. Toth, J. Izatt, J. Y. Lo, and S. Farsiu, “Novel applications of super-resolution in medical imaging,” in |

30. | W. Dong, X. Li, L. Zhang, and G. Shi, “Sparsity-based image denoising via dictionary learning and structural clustering,” in |

31. | W. Dong, L. Zhang, and G. Shi, “Centralized sparse representation for image restoration,” Proc. IEEE |

32. | S. Farsiu, M. Elad, and P. Milanfar, “A practical approach to superresolution,” Proc. SPIE |

33. | R. Estrada, C. Tomasi, M. T. Cabrera, D. K. Wallace, S. F. Freedman, and S. Farsiu, “Enhanced video indirect ophthalmoscopy (VIO) via robust mosaicing,” Biomed. Opt. Express |

34. | M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. |

35. | S. Li, L. Fang, and H. Yin, “An efficient dictionary learning algorithm and its application to 3-D medical image denoising,” IEEE Trans. Biomed. Eng. |

36. | J. Mairal, M. Elad, and G. Sapiro, “Sparse representation for color image restoration,” IEEE Trans. Image Process. |

37. | J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simulation |

38. | A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. |

39. | M. Aharon, M. Elad, and A. M. Bruckstein, “The K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. |

40. | R. Rubinstein, M. Zibulevsky, and M. Elad, “Double sparsity: learning sparse dictionaries for sparse signal approximation,” IEEE Trans. Signal Process. |

41. | P. Chatterjee and P. Milanfar, “Clustering-based denoising with locally learned dictionaries,” IEEE Trans. Image Process. |

42. | W. Dong, L. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process. |

43. | H. Takeda, S. Farsiu, and P. Milanfar, “Kernel regression for image processing and reconstruction,” IEEE Trans. Image Process. |

44. | B. Ophir, M. Lustig, and M. Elad, “Multi-scale dictionary learning using wavelets,” IEEE J. Sel. Top. Signal Process. |

45. | Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition,” in |

46. | A. Buades, B. Coll, and J.-M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. |

47. | K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. |

48. | S. Li and L. Fang, “Signal denoising with random refined orthogonal matching pursuit,” IEEE Trans. Instrum. Meas. |

49. | I. Daubechies, R. DeVore, M. Fornasier, and C. S. Gunturk, “Iteratively reweighted least squares minimization for sparse recovery,” Commun. Pure Appl. Math. |

50. | I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. |

51. | S. J. Chiu, J. A. Izatt, R. V. O’Connell, K. P. Winter, C. A. Toth, and S. Farsiu, “Validated automatic segmentation of AMD pathology including drusen and geographic atrophy in SD-OCT images,” Invest. Ophthalmol. Vis. Sci. |

52. | P. Thévenaz, U. E. Ruttimann, and M. Unser, “A pyramid approach to subpixel registration based on intensity,” IEEE Trans. Image Process. |

53. | W. Dong, “Sparsity-based Image Denoising via Dictionary Learning and Structural Clustering,” http://www4.comp.polyu.edu.hk/~cslzhang/code.htm. |

54. | A. Foi, “Noise estimation and removal in MR imaging: The variance stabilization approach,” in 2011 |

55. | G. Cincotti, G. Loi, and M. Pappalardo, “Frequency decomposition and compounding of ultrasound medical images with wavelet packets,” IEEE Trans. Med. Imaging |

56. | P. Bao and L. Zhang, “Noise reduction for magnetic resonance images via adaptive multiscale products thresholding,” IEEE Trans. Med. Imaging |

57. | M. D. Robinson, C. A. Toth, J. Y. Lo, and S. Farsiu, “Efﬁcient fourier-wavelet super-resolution,” IEEE Trans. Image Process. |

58. | G. T. Chong, S. Farsiu, S. F. Freedman, N. Sarin, A. F. Koreishi, J. A. Izatt, and C. A. Toth, “Abnormal foveal morphology in ocular albinism imaged with spectral-domain optical coherence tomography,” Arch. Ophthalmol. |

59. | F. Luisier, T. Blu, and M. Unser, “A new SURE approach to image denoising: interscale orthonormal wavelet thresholding,” IEEE Trans. Image Process. |

60. | S. J. Chiu, X. T. Li, P. Nicholas, C. A. Toth, J. A. Izatt, and S. Farsiu, “Automatic segmentation of seven retinal layers in SDOCT images congruent with expert manual segmentation,” Opt. Express |

**OCIS Codes**

(030.4280) Coherence and statistical optics : Noise in imaging systems

(100.0100) Image processing : Image processing

(100.2980) Image processing : Image enhancement

(110.4500) Imaging systems : Optical coherence tomography

(170.4460) Medical optics and biotechnology : Ophthalmic optics and devices

(170.5755) Medical optics and biotechnology : Retina scanning

**ToC Category:**

Image Reconstruction and Inverse Problems

**History**

Original Manuscript: March 6, 2012

Revised Manuscript: April 6, 2012

Manuscript Accepted: April 10, 2012

Published: April 12, 2012

**Citation**

Leyuan Fang, Shutao Li, Qing Nie, Joseph A. Izatt, Cynthia A. Toth, and Sina Farsiu, "Sparsity based denoising of spectral domain optical coherence tomography images," Biomed. Opt. Express **3**, 927-942 (2012)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-5-927

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### References

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