Abstract

Optical coherence tomography (OCT) is a recently emerging non-invasive diagnostic tool useful in several medical applications such as ophthalmology, cardiology, gastroenterology and dermatology. One of the major problems with OCT pertains to its low contrast due to the presence of multiplicative speckle noise, which limits the signal-to-noise ratio (SNR) and obscures low-intensity and small features. In this paper, we recommend a new method using the 3D curvelet based K-times singular value decomposition (K-SVD) algorithm for speckle noise reduction and contrast enhancement of the intra-retinal layers of 3D Spectral-Domain OCT (3D-SDOCT) images. In order to benefit from the near-optimum properties of curvelet transform (such as good directional selectivity) on top of dictionary learning, we propose a new plan in dictionary learning by using the curvelet atoms as the initial dictionary. For this reason, the curvelet transform of the noisy image is taken and then the noisy coefficients matrix in each scale, rotation and spatial coordinates is passed through the K-SVD denoising algorithm with predefined 3D initial dictionary that is adaptively selected from thresholded coefficients in the same subband of the image. During the denoising of curvelet coefficients, we can also modify them for the purpose of contrast enhancement of intra-retinal layers. We demonstrate the ability of our proposed algorithm in the speckle noise reduction of 17 publicly available 3D OCT data sets, each of which contains 100 B-scans of size 512×1000 with and without neovascular age-related macular degeneration (AMD) images acquired using SDOCT, Bioptigen imaging systems. Experimental results show that an improvement from 1.27 to 7.81 in contrast to noise ratio (CNR), and from 38.09 to 1983.07 in equivalent number of looks (ENL) is achieved, which would outperform existing state-of-the-art OCT despeckling methods.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

A. Abbasi, A. Monadjemi, L. Fang, H. Rabbani, and Y. Yang, “Three-dimensional optical coherence tomography image denoising through multi-input fully-convolutional networks,” Comput. Biol. Med. 108, 1–8 (2019).
[Crossref]

F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
[Crossref]

2018 (1)

A. Abbasi, A. Monadjemi, L. Fang, and H. Rabbani, “Optical coherence tomography retinal image reconstruction via nonlocal weighted sparse representation,” J. Biomed. Opt. 23(03), 1–11 (2018).
[Crossref]

2017 (2)

M. Esmaeili, A. M. Dehnavi, H. Rabbani, and F. Hajizadeh, “Speckle noise reduction in optical coherence tomography using two-dimensional curvelet-based dictionary learning,” J Med Signals Sens 7(2), 86 (2017).
[Crossref]

F. Zaki, Y. Wang, and H. Su, “Noise adaptive wavelet thresholding for speckle noise removal in optical coherence tomography,” Biomed. Opt. Express 8(5), 2720–2731 (2017).
[Crossref]

2016 (1)

A. Baghaie, R. M. D’Souza, and Z. Yu, “Application of Independent Component Analysis Techniques in Speckle Noise Reduction of Retinal OCT Images,” Optik 127(15), 5783–5791 (2016).
[Crossref]

2015 (1)

R. Kafieh, H. Rabbani, and I. Selesnick, “Three dimensional data-driven multi scale atomic representation of optical coherence tomography,” IEEE Trans. Med. Imaging 34(5), 1042–1062 (2015).
[Crossref]

2014 (1)

S. Farsiu, S. J. Chiu, R. V. O’Connell, F. A. Folgar, E. Yuan, J. A. Izatt, and C. A. TothAge-Related Eye Disease Study 2 Ancillary Spectral Domain Optical Coherence Tomography Study Group, “Quantitative Classification of Eyes with and without Intermediate Age-related Macular Degeneration Using Optical Coherence Tomography,” Ophthalmology 121(1), 162–172 (2014).
[Crossref]

2013 (4)

H. Rabbani, M. Sonka, and M. D. Abramoff, “Optical Coherence tomography noise reduction using anisotropic local bivariate Gaussian mixture prior in 3D complex wavelet domain,” Int. J. Biomed. Imaging 2013, 1–23 (2013).
[Crossref]

R. Kafieh, H. Rabbani, M. Abramoff, and M. Sonka, “Curvature correction of retinal OCTs using graph-based geometry detection,” Phys. Med. Biol. 58(9), 2925–2938 (2013).
[Crossref]

L. Fang, S. Li, R. P. McNabb, Q. Nie, A. N. Kuo, C. A. Toth, J. A. Izatt, and S. Farsiu, “Fast acquisition and reconstruction of optical coherence tomography images via sparse representation,” IEEE Trans. Med. Imaging 32(11), 2034–2049 (2013).
[Crossref]

F. Luan and Y. Wu, “Application of RPCA in optical coherence tomography for speckle noise reduction,” Laser Phys. Lett. 10(3), 035603 (2013).
[Crossref]

2012 (3)

L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express 3(5), 927–942 (2012).
[Crossref]

M. Esmaeili, H. Rabbani, and A. M. Dehnavi, “Automatic optic disk boundary extraction by the use of curvelet transform and deformable variational level set model,” Pattern Recognit. 45(7), 2832–2842 (2012).
[Crossref]

P. S. Negi and D. Labate, “3-D discrete shearlet transform and video processing,” IEEE Trans. on Image Process. 21(6), 2944–2954 (2012).
[Crossref]

2011 (1)

A. Woiselle, J. L. Starck, and J. Fadili, “3-D Data Denoising and Inpainting with the Low-Redundancy Fast Curvelet Transform,” J Math Imaging Vis 39(2), 121–139 (2011).
[Crossref]

2010 (7)

2009 (5)

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]

S. Chitchian, M. A. Fiddy, and N. M. Fried, “Denoising during optical coherence tomography of the prostate nerves via wavelet shrinkage using dual-tree complex wavelet transform,” J. Biomed. Opt. 14(1), 014031 (2009).
[Crossref]

Z. Jian, Z. Yu, and L. Yu, “Speckle attenuation in optical coherence tomography by curvelet shrinkage,” Opt. Lett. 34(10), 1516–1518 (2009).
[Crossref]

P. Puvanathasan and K. Bizheva, “Interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in optical coherence tomography images,” Opt. Express 17(2), 733–746 (2009).
[Crossref]

A. Mishra, A. Wong, K. Bizheva, and D. A. Clausi, “Intra-retinal layer segmentation in optical coherence tomography images,” Opt. Express 17(26), 23719–23728 (2009).
[Crossref]

2008 (4)

A. M. Bagci, M. Shahidi, R. Ansari, M. Blair, N. P. Blair, and R. Zelkha, “Thickness Profiles of Retinal Layers by Optical Coherence Tomography Image Segmentation,” Am. J. Ophthalmol. 146(5), 679–687.e1 (2008).
[Crossref]

M. K. Garvin, M. D. Abràmoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka,, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging 27(10), 1495–1505 (2008).
[Crossref]

A. Pizurica, L. Jovanov, B. Huysmans, V. Zlokolica, P. De Keyser, F. Dhaenens, and W. Philips, “Multiresolution Denoising for Optical Coherence Tomography: A Review and Evaluation,” Curr. Med. Imaging Rev. 4(4), 270–284 (2008).
[Crossref]

M. Mayer, R. Tornow, R. Bock, and F. Kruse, “Automatic nerve fiber layer segmentation and geometry correction on spectral domain OCT images using fuzzy C-means clustering,” Invest. Ophthalmol. Visual Sci. 49(13), 1880 (2008).

2007 (5)

M. Baroni, P. Fortunato, and A. La Torre, “Towards quantitative analysis of retinal features in optical coherence tomography,” J. Biomed. Eng. 29(4), 432–441 (2007).
[Crossref]

A. Ozcan, A. Bilenca, and A. E. Desjardins, “Speckle reduction in optical coherence tomography images using digital filtering,” J. Opt. Soc. Am. A 24, 1901–1910 (2007).
[Crossref]

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

H. M. Salinas and D. C. Fernandez, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging 26(6), 761–771 (2007).
[Crossref]

A. Fuller, R. Zawadzki, S. Choi, D. Wiley, J. Werner, and B. Hamann, “Segmentation of three-dimensional retinal image data,” IEEE Trans. Visual. Comput. Graphics 13(6), 1719–1726 (2007).
[Crossref]

2006 (3)

E. Candès, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5(3), 861–899 (2006).
[Crossref]

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

A. E. Desjardins, B. J. Vakoc, G. J. Tearney, and B. E. Bouma, , “Speckle reduction in OCT using massively-parallel detection and frequency-domain ranging,” Opt. Express 14(11), 4736–4745 (2006).
[Crossref]

2005 (5)

D. L. Marks, T. S. Ralston, and S. A. Boppart, “Speckle reduction by I-divergence regularization in optical coherence tomography,” J. Opt. Soc. Am. A 22(11), 2366–2371 (2005).
[Crossref]

B. Sander, M. Larsen, L. Thrane, J. Hougaard, and T. Jørgensen, “Enhanced optical coherence tomography imaging by multiple scan averaging,” Br. J. Ophthalmol. 89(2), 207–212 (2005).
[Crossref]

E. Gotzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005).
[Crossref]

A. G. Podoleanu, “Optical coherence tomography,” Br. J. Radiol. 78(935), 976–988 (2005).
[Crossref]

H. Ishikawa, D. M. Stein, G. Wollstein, S. Beaton, J. G. Fujimoto, and J. S. Schuman,, “Macular segmentation with optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 46(6), 2012–2017 (2005).
[Crossref]

2004 (4)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. on Image Process. 13(4), 600–612 (2004).
[Crossref]

A. Herzog, K. L. Boyer, and C. Roberts, “Robust extraction of the optic nerve head in optical coherence tomography,” Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis 3117, 395–407 (2004).
[Crossref]

R. D. Ferguson, D. X. Hammer, L. A. Paunescu, S. Beaton, and J. S. Schuman, “Tracking optical coherence tomography,” Opt. Lett. 29(18), 2139–2141 (2004).
[Crossref]

D. C. Fernandez et al., “Comparing total macular volume changes measured by optical coherence tomography with retinal lesion volume estimated by active contours,” Invest. Ophthalmol. Visual Sci. 45(13), U61 (2004).

2003 (3)

M. Pircher, E. Götzinger, R. Leitgel, A. F. Fercher, and C. K. Hitzenberger,, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
[Crossref]

N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by “path length encoded” angular compounding,” J. Biomed. Opt. 8(2), 260–263 (2003).
[Crossref]

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]

2002 (2)

J. L. Starck, E. J. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. on Image Process. 11(6), 670–684 (2002).
[Crossref]

Y. Yu and S. T. Acton, “Speckle reducing anisotropic diffusion,” IEEE Trans. on Image Process. 11(11), 1260–1270 (2002).
[Crossref]

2001 (2)

D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomography using a Markov boundary model,” IEEE Trans. Med. Imaging 20(9), 900–916 (2001).
[Crossref]

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]

2000 (3)

J. Rogowska and M. E. Brezinski, “Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 19(12), 1261–1266 (2000).
[Crossref]

A. George, J. L. Dillensinger, M. Weber, and A. Pechereau, “Optical coherence tomography image processing,” Invest. Ophthalmol. Visual Sci. 41(4), S173 (2000).

M. Bashkansky and J. Reintjes, , “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett. 25(8), 545–547 (2000).
[Crossref]

1999 (1)

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

1995 (2)

M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
[Crossref] [PubMed]

M. R. Hee, J. A. Izatt, E. A. Swanson, D. Huang, J. S. Schuman, C. P. Lin, C. A. Puliafito, and J. G. Fujimoto, , “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113(3), 325–332 (1995).
[Crossref]

1991 (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 (1991).
[Crossref]

1989 (1)

T. Loupas, W. N. Mcdicken, and P. L. Allan, “An Adaptive Weighted Median Filter for Speckle Suppression in Medical Ultrasonic Images,” IEEE Trans. Circuits Syst. 36(1), 129–135 (1989).
[Crossref]

Abbasi, A.

A. Abbasi, A. Monadjemi, L. Fang, H. Rabbani, and Y. Yang, “Three-dimensional optical coherence tomography image denoising through multi-input fully-convolutional networks,” Comput. Biol. Med. 108, 1–8 (2019).
[Crossref]

A. Abbasi, A. Monadjemi, L. Fang, and H. Rabbani, “Optical coherence tomography retinal image reconstruction via nonlocal weighted sparse representation,” J. Biomed. Opt. 23(03), 1–11 (2018).
[Crossref]

Abramoff, M.

R. Kafieh, H. Rabbani, M. Abramoff, and M. Sonka, “Curvature correction of retinal OCTs using graph-based geometry detection,” Phys. Med. Biol. 58(9), 2925–2938 (2013).
[Crossref]

Abramoff, M. D.

H. Rabbani, M. Sonka, and M. D. Abramoff, “Optical Coherence tomography noise reduction using anisotropic local bivariate Gaussian mixture prior in 3D complex wavelet domain,” Int. J. Biomed. Imaging 2013, 1–23 (2013).
[Crossref]

Abràmoff, M. D.

M. K. Garvin, M. D. Abràmoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka,, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging 27(10), 1495–1505 (2008).
[Crossref]

Acton, S. T.

Y. Yu and S. T. Acton, “Speckle reducing anisotropic diffusion,” IEEE Trans. on Image Process. 11(11), 1260–1270 (2002).
[Crossref]

Aharon, M.

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

Aja, S.

S. Aja, C. Alberola, and J. Ruiz, “Fuzzy anisotropic diffusion for speckle filtering,” 2001 Ieee International Conference on Acoustics, Speech, and Signal Processing, Vols I-Vi, Proceedings21261–1264 (2001).

Alberola, C.

S. Aja, C. Alberola, and J. Ruiz, “Fuzzy anisotropic diffusion for speckle filtering,” 2001 Ieee International Conference on Acoustics, Speech, and Signal Processing, Vols I-Vi, Proceedings21261–1264 (2001).

Allan, P. L.

T. Loupas, W. N. Mcdicken, and P. L. Allan, “An Adaptive Weighted Median Filter for Speckle Suppression in Medical Ultrasonic Images,” IEEE Trans. Circuits Syst. 36(1), 129–135 (1989).
[Crossref]

Anantrasirichai, N.

N. Anantrasirichai, L. Nicholson, J. Morgan, and I. Erchova, “Adaptive-weighted bilateral filtering for optical coherence tomography,” Image Processing (ICIP), 2013 20th IEEE International Conference on 1110-1114 (2013).

Ansari, R.

A. M. Bagci, M. Shahidi, R. Ansari, M. Blair, N. P. Blair, and R. Zelkha, “Thickness Profiles of Retinal Layers by Optical Coherence Tomography Image Segmentation,” Am. J. Ophthalmol. 146(5), 679–687.e1 (2008).
[Crossref]

Bagci, A. M.

A. M. Bagci, M. Shahidi, R. Ansari, M. Blair, N. P. Blair, and R. Zelkha, “Thickness Profiles of Retinal Layers by Optical Coherence Tomography Image Segmentation,” Am. J. Ophthalmol. 146(5), 679–687.e1 (2008).
[Crossref]

Baghaie, A.

A. Baghaie, R. M. D’Souza, and Z. Yu, “Application of Independent Component Analysis Techniques in Speckle Noise Reduction of Retinal OCT Images,” Optik 127(15), 5783–5791 (2016).
[Crossref]

Bao, P.

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]

Baroni, M.

M. Baroni, P. Fortunato, and A. La Torre, “Towards quantitative analysis of retinal features in optical coherence tomography,” J. Biomed. Eng. 29(4), 432–441 (2007).
[Crossref]

Bashkansky, M.

Beaton, S.

H. Ishikawa, D. M. Stein, G. Wollstein, S. Beaton, J. G. Fujimoto, and J. S. Schuman,, “Macular segmentation with optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 46(6), 2012–2017 (2005).
[Crossref]

R. D. Ferguson, D. X. Hammer, L. A. Paunescu, S. Beaton, and J. S. Schuman, “Tracking optical coherence tomography,” Opt. Lett. 29(18), 2139–2141 (2004).
[Crossref]

Bernardes, R.

Bilenca, A.

Bizheva, K.

Blair, M.

A. M. Bagci, M. Shahidi, R. Ansari, M. Blair, N. P. Blair, and R. Zelkha, “Thickness Profiles of Retinal Layers by Optical Coherence Tomography Image Segmentation,” Am. J. Ophthalmol. 146(5), 679–687.e1 (2008).
[Crossref]

Blair, N. P.

A. M. Bagci, M. Shahidi, R. Ansari, M. Blair, N. P. Blair, and R. Zelkha, “Thickness Profiles of Retinal Layers by Optical Coherence Tomography Image Segmentation,” Am. J. Ophthalmol. 146(5), 679–687.e1 (2008).
[Crossref]

Blu, T.

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

Bock, R.

M. Mayer, R. Tornow, R. Bock, and F. Kruse, “Automatic nerve fiber layer segmentation and geometry correction on spectral domain OCT images using fuzzy C-means clustering,” Invest. Ophthalmol. Visual Sci. 49(13), 1880 (2008).

Bonesi, M.

M. Bonesi, S. G. Proskurin, and I. V. Meglinski, “Imaging of subcutaneous blood vessels and flow velocity profiles by optical coherence tomography,” Laser Phys. 20(4), 891–899 (2010).
[Crossref]

Bonin, T.

L. Ramrath, G. Moreno, H. Mueller, T. Bonin, G. Huettmann, and A. Schweikard, “Towards multi-directional OCT for speckle noise reduction,” Med Image Comput Comput Assist Interv11(Pt 1), 815–823 (2008).

Boppart, S. A.

Bouma, B. E.

A. E. Desjardins, B. J. Vakoc, G. J. Tearney, and B. E. Bouma, , “Speckle reduction in OCT using massively-parallel detection and frequency-domain ranging,” Opt. Express 14(11), 4736–4745 (2006).
[Crossref]

N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by “path length encoded” angular compounding,” J. Biomed. Opt. 8(2), 260–263 (2003).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. on Image Process. 13(4), 600–612 (2004).
[Crossref]

Boyer, K.

D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomography using a Markov boundary model,” IEEE Trans. Med. Imaging 20(9), 900–916 (2001).
[Crossref]

Boyer, K. L.

A. Herzog, K. L. Boyer, and C. Roberts, “Robust extraction of the optic nerve head in optical coherence tomography,” Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis 3117, 395–407 (2004).
[Crossref]

Brezinski, M. E.

J. Rogowska and M. E. Brezinski, “Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 19(12), 1261–1266 (2000).
[Crossref]

Cai, N.

F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
[Crossref]

Candes, E.

L. Ying, L. Demanet, and E. Candes, “3D discrete curvelet transform,” Applied and Computational Mathematics50 (2005).

Candes, E. J.

J. L. Starck, E. J. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. on Image Process. 11(6), 670–684 (2002).
[Crossref]

Candès, E.

E. Candès, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5(3), 861–899 (2006).
[Crossref]

Chang, W.

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 (1991).
[Crossref]

Chen, X.

F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
[Crossref]

Chen, Y.

F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
[Crossref]

Chitchian, S.

S. Chitchian, M. A. Fiddy, and N. M. Fried, “Denoising during optical coherence tomography of the prostate nerves via wavelet shrinkage using dual-tree complex wavelet transform,” J. Biomed. Opt. 14(1), 014031 (2009).
[Crossref]

Chiu, S. J.

S. Farsiu, S. J. Chiu, R. V. O’Connell, F. A. Folgar, E. Yuan, J. A. Izatt, and C. A. TothAge-Related Eye Disease Study 2 Ancillary Spectral Domain Optical Coherence Tomography Study Group, “Quantitative Classification of Eyes with and without Intermediate Age-related Macular Degeneration Using Optical Coherence Tomography,” Ophthalmology 121(1), 162–172 (2014).
[Crossref]

Choi, S.

A. Fuller, R. Zawadzki, S. Choi, D. Wiley, J. Werner, and B. Hamann, “Segmentation of three-dimensional retinal image data,” IEEE Trans. Visual. Comput. Graphics 13(6), 1719–1726 (2007).
[Crossref]

Chong, G. T.

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]

Cincotti, G.

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]

Clausi, D. A.

D’Souza, R. M.

A. Baghaie, R. M. D’Souza, and Z. Yu, “Application of Independent Component Analysis Techniques in Speckle Noise Reduction of Retinal OCT Images,” Optik 127(15), 5783–5791 (2016).
[Crossref]

De Keyser, P.

A. Pizurica, L. Jovanov, B. Huysmans, V. Zlokolica, P. De Keyser, F. Dhaenens, and W. Philips, “Multiresolution Denoising for Optical Coherence Tomography: A Review and Evaluation,” Curr. Med. Imaging Rev. 4(4), 270–284 (2008).
[Crossref]

Deghani, A.

M. Esmaeili, H. Rabbani, A. Mehri, and A. Deghani, “Extraction of Retinal Blood Vessels by Curvelet Transform,” 2009 16th IEEE International Conference on Image Processing, Vols 1-6, pp. 3353-+ (2009).

Dehnavi, A. M.

M. Esmaeili, A. M. Dehnavi, H. Rabbani, and F. Hajizadeh, “Speckle noise reduction in optical coherence tomography using two-dimensional curvelet-based dictionary learning,” J Med Signals Sens 7(2), 86 (2017).
[Crossref]

M. Esmaeili, H. Rabbani, and A. M. Dehnavi, “Automatic optic disk boundary extraction by the use of curvelet transform and deformable variational level set model,” Pattern Recognit. 45(7), 2832–2842 (2012).
[Crossref]

Demanet, L.

E. Candès, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5(3), 861–899 (2006).
[Crossref]

L. Ying, L. Demanet, and E. Candes, “3D discrete curvelet transform,” Applied and Computational Mathematics50 (2005).

Desjardins, A. E.

Dhaenens, F.

A. Pizurica, L. Jovanov, B. Huysmans, V. Zlokolica, P. De Keyser, F. Dhaenens, and W. Philips, “Multiresolution Denoising for Optical Coherence Tomography: A Review and Evaluation,” Curr. Med. Imaging Rev. 4(4), 270–284 (2008).
[Crossref]

Dillensinger, J. L.

A. George, J. L. Dillensinger, M. Weber, and A. Pechereau, “Optical coherence tomography image processing,” Invest. Ophthalmol. Visual Sci. 41(4), S173 (2000).

Donoho, D.

E. Candès, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5(3), 861–899 (2006).
[Crossref]

Donoho, D. L.

J. L. Starck, E. J. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. on Image Process. 11(6), 670–684 (2002).
[Crossref]

Drexler, W.

Duker, J. S.

M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
[Crossref] [PubMed]

Elad, M.

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

Erchova, I.

N. Anantrasirichai, L. Nicholson, J. Morgan, and I. Erchova, “Adaptive-weighted bilateral filtering for optical coherence tomography,” Image Processing (ICIP), 2013 20th IEEE International Conference on 1110-1114 (2013).

Esmaeili, M.

M. Esmaeili, A. M. Dehnavi, H. Rabbani, and F. Hajizadeh, “Speckle noise reduction in optical coherence tomography using two-dimensional curvelet-based dictionary learning,” J Med Signals Sens 7(2), 86 (2017).
[Crossref]

M. Esmaeili, H. Rabbani, and A. M. Dehnavi, “Automatic optic disk boundary extraction by the use of curvelet transform and deformable variational level set model,” Pattern Recognit. 45(7), 2832–2842 (2012).
[Crossref]

M. Esmaeili, H. Rabbani, A. Mehri, and A. Deghani, “Extraction of Retinal Blood Vessels by Curvelet Transform,” 2009 16th IEEE International Conference on Image Processing, Vols 1-6, pp. 3353-+ (2009).

Fadili, J.

A. Woiselle, J. L. Starck, and J. Fadili, “3-D Data Denoising and Inpainting with the Low-Redundancy Fast Curvelet Transform,” J Math Imaging Vis 39(2), 121–139 (2011).
[Crossref]

A. Woiselle, J. L. Starck, and J. Fadili, “3D curvelet transforms and astronomical data restoration,” Appl Comput Harmon A. 28(2), 171–188 (2010).
[Crossref]

Fang, L.

A. Abbasi, A. Monadjemi, L. Fang, H. Rabbani, and Y. Yang, “Three-dimensional optical coherence tomography image denoising through multi-input fully-convolutional networks,” Comput. Biol. Med. 108, 1–8 (2019).
[Crossref]

A. Abbasi, A. Monadjemi, L. Fang, and H. Rabbani, “Optical coherence tomography retinal image reconstruction via nonlocal weighted sparse representation,” J. Biomed. Opt. 23(03), 1–11 (2018).
[Crossref]

L. Fang, S. Li, R. P. McNabb, Q. Nie, A. N. Kuo, C. A. Toth, J. A. Izatt, and S. Farsiu, “Fast acquisition and reconstruction of optical coherence tomography images via sparse representation,” IEEE Trans. Med. Imaging 32(11), 2034–2049 (2013).
[Crossref]

L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express 3(5), 927–942 (2012).
[Crossref]

Farsiu, S.

S. Farsiu, S. J. Chiu, R. V. O’Connell, F. A. Folgar, E. Yuan, J. A. Izatt, and C. A. TothAge-Related Eye Disease Study 2 Ancillary Spectral Domain Optical Coherence Tomography Study Group, “Quantitative Classification of Eyes with and without Intermediate Age-related Macular Degeneration Using Optical Coherence Tomography,” Ophthalmology 121(1), 162–172 (2014).
[Crossref]

L. Fang, S. Li, R. P. McNabb, Q. Nie, A. N. Kuo, C. A. Toth, J. A. Izatt, and S. Farsiu, “Fast acquisition and reconstruction of optical coherence tomography images via sparse representation,” IEEE Trans. Med. Imaging 32(11), 2034–2049 (2013).
[Crossref]

L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express 3(5), 927–942 (2012).
[Crossref]

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]

Fercher, A. F.

M. Pircher, E. Götzinger, R. Leitgel, A. F. Fercher, and C. K. Hitzenberger,, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
[Crossref]

Ferguson, R. D.

Fernandez, D. C.

H. M. Salinas and D. C. Fernandez, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging 26(6), 761–771 (2007).
[Crossref]

D. C. Fernandez et al., “Comparing total macular volume changes measured by optical coherence tomography with retinal lesion volume estimated by active contours,” Invest. Ophthalmol. Visual Sci. 45(13), U61 (2004).

Fiddy, M. A.

S. Chitchian, M. A. Fiddy, and N. M. Fried, “Denoising during optical coherence tomography of the prostate nerves via wavelet shrinkage using dual-tree complex wavelet transform,” J. Biomed. Opt. 14(1), 014031 (2009).
[Crossref]

Flotte, T.

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 (1991).
[Crossref]

Folgar, F. A.

S. Farsiu, S. J. Chiu, R. V. O’Connell, F. A. Folgar, E. Yuan, J. A. Izatt, and C. A. TothAge-Related Eye Disease Study 2 Ancillary Spectral Domain Optical Coherence Tomography Study Group, “Quantitative Classification of Eyes with and without Intermediate Age-related Macular Degeneration Using Optical Coherence Tomography,” Ophthalmology 121(1), 162–172 (2014).
[Crossref]

Fortunato, P.

M. Baroni, P. Fortunato, and A. La Torre, “Towards quantitative analysis of retinal features in optical coherence tomography,” J. Biomed. Eng. 29(4), 432–441 (2007).
[Crossref]

Freedman, S. F.

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]

Fried, N. M.

S. Chitchian, M. A. Fiddy, and N. M. Fried, “Denoising during optical coherence tomography of the prostate nerves via wavelet shrinkage using dual-tree complex wavelet transform,” J. Biomed. Opt. 14(1), 014031 (2009).
[Crossref]

Fujimoto, J. G.

H. Ishikawa, D. M. Stein, G. Wollstein, S. Beaton, J. G. Fujimoto, and J. S. Schuman,, “Macular segmentation with optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 46(6), 2012–2017 (2005).
[Crossref]

M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
[Crossref] [PubMed]

M. R. Hee, J. A. Izatt, E. A. Swanson, D. Huang, J. S. Schuman, C. P. Lin, C. A. Puliafito, and J. G. Fujimoto, , “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113(3), 325–332 (1995).
[Crossref]

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 (1991).
[Crossref]

Fuller, A.

A. Fuller, R. Zawadzki, S. Choi, D. Wiley, J. Werner, and B. Hamann, “Segmentation of three-dimensional retinal image data,” IEEE Trans. Visual. Comput. Graphics 13(6), 1719–1726 (2007).
[Crossref]

Garvin, M. K.

M. K. Garvin, M. D. Abràmoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka,, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging 27(10), 1495–1505 (2008).
[Crossref]

George, A.

A. George, J. L. Dillensinger, M. Weber, and A. Pechereau, “Optical coherence tomography image processing,” Invest. Ophthalmol. Visual Sci. 41(4), S173 (2000).

Gotzinger, E.

Götzinger, E.

M. Pircher, E. Götzinger, R. Leitgel, A. F. Fercher, and C. K. Hitzenberger,, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
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N. Gour and P. Khanna, “Speckle denoising in optical coherence tomography images using residual deep convolutional neural network,” Multimedia Tools and Applications, 1–17 (2019).

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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 (1991).
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F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
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Hajizadeh, F.

M. Esmaeili, A. M. Dehnavi, H. Rabbani, and F. Hajizadeh, “Speckle noise reduction in optical coherence tomography using two-dimensional curvelet-based dictionary learning,” J Med Signals Sens 7(2), 86 (2017).
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Hee, M. R.

M. R. Hee, J. A. Izatt, E. A. Swanson, D. Huang, J. S. Schuman, C. P. Lin, C. A. Puliafito, and J. G. Fujimoto, , “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113(3), 325–332 (1995).
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M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
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Hermann, B.

Herzog, A.

A. Herzog, K. L. Boyer, and C. Roberts, “Robust extraction of the optic nerve head in optical coherence tomography,” Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis 3117, 395–407 (2004).
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E. Gotzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005).
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M. Pircher, E. Götzinger, R. Leitgel, A. F. Fercher, and C. K. Hitzenberger,, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
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Hougaard, J.

B. Sander, M. Larsen, L. Thrane, J. Hougaard, and T. Jørgensen, “Enhanced optical coherence tomography imaging by multiple scan averaging,” Br. J. Ophthalmol. 89(2), 207–212 (2005).
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F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
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M. R. Hee, J. A. Izatt, E. A. Swanson, D. Huang, J. S. Schuman, C. P. Lin, C. A. Puliafito, and J. G. Fujimoto, , “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113(3), 325–332 (1995).
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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 (1991).
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L. Ramrath, G. Moreno, H. Mueller, T. Bonin, G. Huettmann, and A. Schweikard, “Towards multi-directional OCT for speckle noise reduction,” Med Image Comput Comput Assist Interv11(Pt 1), 815–823 (2008).

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Huysmans, B.

A. Pizurica, L. Jovanov, B. Huysmans, V. Zlokolica, P. De Keyser, F. Dhaenens, and W. Philips, “Multiresolution Denoising for Optical Coherence Tomography: A Review and Evaluation,” Curr. Med. Imaging Rev. 4(4), 270–284 (2008).
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L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express 3(5), 927–942 (2012).
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M. R. Hee, J. A. Izatt, E. A. Swanson, D. Huang, J. S. Schuman, C. P. Lin, C. A. Puliafito, and J. G. Fujimoto, , “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113(3), 325–332 (1995).
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Jørgensen, T.

B. Sander, M. Larsen, L. Thrane, J. Hougaard, and T. Jørgensen, “Enhanced optical coherence tomography imaging by multiple scan averaging,” Br. J. Ophthalmol. 89(2), 207–212 (2005).
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A. Pizurica, L. Jovanov, B. Huysmans, V. Zlokolica, P. De Keyser, F. Dhaenens, and W. Philips, “Multiresolution Denoising for Optical Coherence Tomography: A Review and Evaluation,” Curr. Med. Imaging Rev. 4(4), 270–284 (2008).
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R. Kafieh, H. Rabbani, and I. Selesnick, “Three dimensional data-driven multi scale atomic representation of optical coherence tomography,” IEEE Trans. Med. Imaging 34(5), 1042–1062 (2015).
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R. Kafieh, H. Rabbani, M. Abramoff, and M. Sonka, “Curvature correction of retinal OCTs using graph-based geometry detection,” Phys. Med. Biol. 58(9), 2925–2938 (2013).
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Kardon, R.

M. K. Garvin, M. D. Abràmoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka,, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging 27(10), 1495–1505 (2008).
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N. Gour and P. Khanna, “Speckle denoising in optical coherence tomography images using residual deep convolutional neural network,” Multimedia Tools and Applications, 1–17 (2019).

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D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomography using a Markov boundary model,” IEEE Trans. Med. Imaging 20(9), 900–916 (2001).
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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).
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L. Fang, S. Li, R. P. McNabb, Q. Nie, A. N. Kuo, C. A. Toth, J. A. Izatt, and S. Farsiu, “Fast acquisition and reconstruction of optical coherence tomography images via sparse representation,” IEEE Trans. Med. Imaging 32(11), 2034–2049 (2013).
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B. Sander, M. Larsen, L. Thrane, J. Hougaard, and T. Jørgensen, “Enhanced optical coherence tomography imaging by multiple scan averaging,” Br. J. Ophthalmol. 89(2), 207–212 (2005).
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M. Pircher, E. Götzinger, R. Leitgel, A. F. Fercher, and C. K. Hitzenberger,, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
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L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express 3(5), 927–942 (2012).
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G. Kutyniok, W.-Q. Lim, and R. Reisenhofer, “Shearlab 3D: Faithful digital shearlet transforms based on compactly supported shearlets,” arXiv preprint arXiv:1402.5670 (2014).

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M. R. Hee, J. A. Izatt, E. A. Swanson, D. Huang, J. S. Schuman, C. P. Lin, C. A. Puliafito, and J. G. Fujimoto, , “Optical coherence tomography of the human retina,” Arch. Ophthalmol. 113(3), 325–332 (1995).
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F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
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Marshall, D.

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M. Mayer, R. Tornow, R. Bock, and F. Kruse, “Automatic nerve fiber layer segmentation and geometry correction on spectral domain OCT images using fuzzy C-means clustering,” Invest. Ophthalmol. Visual Sci. 49(13), 1880 (2008).

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T. Loupas, W. N. Mcdicken, and P. L. Allan, “An Adaptive Weighted Median Filter for Speckle Suppression in Medical Ultrasonic Images,” IEEE Trans. Circuits Syst. 36(1), 129–135 (1989).
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L. Fang, S. Li, R. P. McNabb, Q. Nie, A. N. Kuo, C. A. Toth, J. A. Izatt, and S. Farsiu, “Fast acquisition and reconstruction of optical coherence tomography images via sparse representation,” IEEE Trans. Med. Imaging 32(11), 2034–2049 (2013).
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M. Bonesi, S. G. Proskurin, and I. V. Meglinski, “Imaging of subcutaneous blood vessels and flow velocity profiles by optical coherence tomography,” Laser Phys. 20(4), 891–899 (2010).
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M. Esmaeili, H. Rabbani, A. Mehri, and A. Deghani, “Extraction of Retinal Blood Vessels by Curvelet Transform,” 2009 16th IEEE International Conference on Image Processing, Vols 1-6, pp. 3353-+ (2009).

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Monadjemi, A.

A. Abbasi, A. Monadjemi, L. Fang, H. Rabbani, and Y. Yang, “Three-dimensional optical coherence tomography image denoising through multi-input fully-convolutional networks,” Comput. Biol. Med. 108, 1–8 (2019).
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A. Abbasi, A. Monadjemi, L. Fang, and H. Rabbani, “Optical coherence tomography retinal image reconstruction via nonlocal weighted sparse representation,” J. Biomed. Opt. 23(03), 1–11 (2018).
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L. Ramrath, G. Moreno, H. Mueller, T. Bonin, G. Huettmann, and A. Schweikard, “Towards multi-directional OCT for speckle noise reduction,” Med Image Comput Comput Assist Interv11(Pt 1), 815–823 (2008).

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L. Fang, S. Li, R. P. McNabb, Q. Nie, A. N. Kuo, C. A. Toth, J. A. Izatt, and S. Farsiu, “Fast acquisition and reconstruction of optical coherence tomography images via sparse representation,” IEEE Trans. Med. Imaging 32(11), 2034–2049 (2013).
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S. Farsiu, S. J. Chiu, R. V. O’Connell, F. A. Folgar, E. Yuan, J. A. Izatt, and C. A. TothAge-Related Eye Disease Study 2 Ancillary Spectral Domain Optical Coherence Tomography Study Group, “Quantitative Classification of Eyes with and without Intermediate Age-related Macular Degeneration Using Optical Coherence Tomography,” Ophthalmology 121(1), 162–172 (2014).
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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).
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A. Pizurica, L. Jovanov, B. Huysmans, V. Zlokolica, P. De Keyser, F. Dhaenens, and W. Philips, “Multiresolution Denoising for Optical Coherence Tomography: A Review and Evaluation,” Curr. Med. Imaging Rev. 4(4), 270–284 (2008).
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E. Gotzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005).
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M. Pircher, E. Götzinger, R. Leitgel, A. F. Fercher, and C. K. Hitzenberger,, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
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A. Pizurica, L. Jovanov, B. Huysmans, V. Zlokolica, P. De Keyser, F. Dhaenens, and W. Philips, “Multiresolution Denoising for Optical Coherence Tomography: A Review and Evaluation,” Curr. Med. Imaging Rev. 4(4), 270–284 (2008).
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J. Ma and G. Plonka, “A review of curvelets and recent applications,” IEEE Signal Process. Mag. 27(2), 118–133 (2010).
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M. Bonesi, S. G. Proskurin, and I. V. Meglinski, “Imaging of subcutaneous blood vessels and flow velocity profiles by optical coherence tomography,” Laser Phys. 20(4), 891–899 (2010).
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M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
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Rabbani, H.

A. Abbasi, A. Monadjemi, L. Fang, H. Rabbani, and Y. Yang, “Three-dimensional optical coherence tomography image denoising through multi-input fully-convolutional networks,” Comput. Biol. Med. 108, 1–8 (2019).
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H. Rabbani, M. Sonka, and M. D. Abramoff, “Optical Coherence tomography noise reduction using anisotropic local bivariate Gaussian mixture prior in 3D complex wavelet domain,” Int. J. Biomed. Imaging 2013, 1–23 (2013).
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Ralston, T. S.

Ramrath, L.

L. Ramrath, G. Moreno, H. Mueller, T. Bonin, G. Huettmann, and A. Schweikard, “Towards multi-directional OCT for speckle noise reduction,” Med Image Comput Comput Assist Interv11(Pt 1), 815–823 (2008).

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M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
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Reisenhofer, R.

G. Kutyniok, W.-Q. Lim, and R. Reisenhofer, “Shearlab 3D: Faithful digital shearlet transforms based on compactly supported shearlets,” arXiv preprint arXiv:1402.5670 (2014).

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A. Herzog, K. L. Boyer, and C. Roberts, “Robust extraction of the optic nerve head in optical coherence tomography,” Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis 3117, 395–407 (2004).
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D. Koozekanani, K. Boyer, and C. Roberts, “Retinal thickness measurements from optical coherence tomography using a Markov boundary model,” IEEE Trans. Med. Imaging 20(9), 900–916 (2001).
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M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
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B. Sander, M. Larsen, L. Thrane, J. Hougaard, and T. Jørgensen, “Enhanced optical coherence tomography imaging by multiple scan averaging,” Br. J. Ophthalmol. 89(2), 207–212 (2005).
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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).
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J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4(1), 95–105 (1999).
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H. Ishikawa, D. M. Stein, G. Wollstein, S. Beaton, J. G. Fujimoto, and J. S. Schuman,, “Macular segmentation with optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 46(6), 2012–2017 (2005).
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L. Ramrath, G. Moreno, H. Mueller, T. Bonin, G. Huettmann, and A. Schweikard, “Towards multi-directional OCT for speckle noise reduction,” Med Image Comput Comput Assist Interv11(Pt 1), 815–823 (2008).

Selesnick, I.

R. Kafieh, H. Rabbani, and I. Selesnick, “Three dimensional data-driven multi scale atomic representation of optical coherence tomography,” IEEE Trans. Med. Imaging 34(5), 1042–1062 (2015).
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Serranho, P.

Shahidi, M.

A. M. Bagci, M. Shahidi, R. Ansari, M. Blair, N. P. Blair, and R. Zelkha, “Thickness Profiles of Retinal Layers by Optical Coherence Tomography Image Segmentation,” Am. J. Ophthalmol. 146(5), 679–687.e1 (2008).
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Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. on Image Process. 13(4), 600–612 (2004).
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Shi, F.

F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
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Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. on Image Process. 13(4), 600–612 (2004).
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Sonka, M.

H. Rabbani, M. Sonka, and M. D. Abramoff, “Optical Coherence tomography noise reduction using anisotropic local bivariate Gaussian mixture prior in 3D complex wavelet domain,” Int. J. Biomed. Imaging 2013, 1–23 (2013).
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Starck, J. L.

A. Woiselle, J. L. Starck, and J. Fadili, “3-D Data Denoising and Inpainting with the Low-Redundancy Fast Curvelet Transform,” J Math Imaging Vis 39(2), 121–139 (2011).
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A. Woiselle, J. L. Starck, and J. Fadili, “3D curvelet transforms and astronomical data restoration,” Appl Comput Harmon A. 28(2), 171–188 (2010).
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J. L. Starck, E. J. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. on Image Process. 11(6), 670–684 (2002).
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H. Ishikawa, D. M. Stein, G. Wollstein, S. Beaton, J. G. Fujimoto, and J. S. Schuman,, “Macular segmentation with optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 46(6), 2012–2017 (2005).
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J. Portilla, V. Strella, M. J. Wainwright, and E. P. Simoncelli, “Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain,” 2001 International Conference on Image Processing, Vol II, Proceedings2, 37–40 (2001).

Su, H.

Swanson, E. A.

M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
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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 (1991).
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N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by “path length encoded” angular compounding,” J. Biomed. Opt. 8(2), 260–263 (2003).
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B. Sander, M. Larsen, L. Thrane, J. Hougaard, and T. Jørgensen, “Enhanced optical coherence tomography imaging by multiple scan averaging,” Br. J. Ophthalmol. 89(2), 207–212 (2005).
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Wainwright, M. J.

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Wang, Y.

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. on Image Process. 13(4), 600–612 (2004).
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A. Woiselle, J. L. Starck, and J. Fadili, “3-D Data Denoising and Inpainting with the Low-Redundancy Fast Curvelet Transform,” J Math Imaging Vis 39(2), 121–139 (2011).
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H. Ishikawa, D. M. Stein, G. Wollstein, S. Beaton, J. G. Fujimoto, and J. S. Schuman,, “Macular segmentation with optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 46(6), 2012–2017 (2005).
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Wong, C.

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M. K. Garvin, M. D. Abràmoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka,, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging 27(10), 1495–1505 (2008).
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F. Luan and Y. Wu, “Application of RPCA in optical coherence tomography for speckle noise reduction,” Laser Phys. Lett. 10(3), 035603 (2013).
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A. Abbasi, A. Monadjemi, L. Fang, H. Rabbani, and Y. Yang, “Three-dimensional optical coherence tomography image denoising through multi-input fully-convolutional networks,” Comput. Biol. Med. 108, 1–8 (2019).
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Yu, Z.

A. Baghaie, R. M. D’Souza, and Z. Yu, “Application of Independent Component Analysis Techniques in Speckle Noise Reduction of Retinal OCT Images,” Optik 127(15), 5783–5791 (2016).
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J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4(1), 95–105 (1999).
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M. R. Hee, C. A. Puliafito, C. Wong, J. S. Duker, E. Reichel, B. Rutledge, J. S. Schuman, E. A. Swanson, and J. G. Fujimoto, “Quantitative assessment of macular edema with optical coherence tomography,” Arch. Ophthalmol. 113(8), 1019–1029 (1995).
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M. K. Garvin, M. D. Abràmoff, R. Kardon, S. R. Russell, X. Wu, and M. Sonka,, “Intraretinal layer segmentation of macular optical coherence tomography images using optimal 3-D graph search,” IEEE Trans. Med. Imaging 27(10), 1495–1505 (2008).
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IEEE Trans. Visual. Comput. Graphics (1)

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Int. J. Biomed. Imaging (1)

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F. Luan and Y. Wu, “Application of RPCA in optical coherence tomography for speckle noise reduction,” Laser Phys. Lett. 10(3), 035603 (2013).
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E. Candès, L. Demanet, D. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5(3), 861–899 (2006).
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Ophthalmology (1)

S. Farsiu, S. J. Chiu, R. V. O’Connell, F. A. Folgar, E. Yuan, J. A. Izatt, and C. A. TothAge-Related Eye Disease Study 2 Ancillary Spectral Domain Optical Coherence Tomography Study Group, “Quantitative Classification of Eyes with and without Intermediate Age-related Macular Degeneration Using Optical Coherence Tomography,” Ophthalmology 121(1), 162–172 (2014).
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Opt. Express (7)

Opt. Lett. (3)

Optik (1)

A. Baghaie, R. M. D’Souza, and Z. Yu, “Application of Independent Component Analysis Techniques in Speckle Noise Reduction of Retinal OCT Images,” Optik 127(15), 5783–5791 (2016).
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R. Kafieh, H. Rabbani, M. Abramoff, and M. Sonka, “Curvature correction of retinal OCTs using graph-based geometry detection,” Phys. Med. Biol. 58(9), 2925–2938 (2013).
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F. Shi, N. Cai, Y. Gu, D. Hu, Y. Ma, Y. Chen, and X. Chen, “DeSpecNet: a CNN-based method for speckle reduction in retinal optical coherence tomography images,” Phys. Med. Biol. 64(17), 175010 (2019).
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Science (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 (1991).
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Figures (15)

Fig. 1.
Fig. 1. 3D rendering of a curvelet atom in (a) space domain, (b) frequency domain, and (c) discrete frequency domain. The shaded area separates the proposed 3D wedge associated with curvelet atom.
Fig. 2.
Fig. 2. Results of reconstruction of 3D-OCT images from the thresholded curvelet coefficients.(a) initial image, (b) extracted image by taking inverse 3D curvelet transform of thresholded coefficients.
Fig. 3.
Fig. 3. The outline of the proposed method.
Fig. 4.
Fig. 4. Samples of the selected 2D-initial dictionaries used for denoising the curvelet coefficient matrix in each scale and rotation. The dictionary size in (a) and (b) is 16×128 in scale 6 with 2 different orientations (l = 5 and 7 respectively) and in (c),(d) is 16×256 for scale 7 with 2 different orientations (l = 5 and 7 respectively) of the coefficient matrix.
Fig. 5.
Fig. 5. Results of reconstruction of 3D-OCT images from the enhanced curvelet coefficients. (a,c) Initial images, and (b,d) Obtained images by proposed method.
Fig. 6.
Fig. 6. Selected background and foreground ROIs for evaluation. Image shows 11 selected regions, which bigger ellipse outside the retinal region is used as the background ROI and other circles represent the foreground ROIs.
Fig. 7.
Fig. 7. Local structure similarity map,(a) Original noisy image (b) Average image (c) Denoised image (d) SSIM map
Fig. 8.
Fig. 8. Reconstructed image by thresholded shearlet coefficients.
Fig. 9.
Fig. 9. The shearlet coefficients of first level in detailed subbands.
Fig. 10.
Fig. 10. The result of the shearlet based K-SVD denoising method (a) Initial image, (b) Reconstructed image by applying inverse shearlet transform to the K-SVD-based denoised coefficients
Fig. 11.
Fig. 11. Visual comparison of different SDOCT retinal image denoising methods. (a) The original noisy image (b) The denoising results using K-SVD method [41]. (c) The denoising results using the Tikhonov method [33]. (d) The denoising results using MSBTD method [19]. (e) The denoising results using AWBF method [47]. (f) The denoising results using NWSR algorithm [72]. (g) Results of the proposed method.
Fig. 12.
Fig. 12. Visual comparison of dictionary learning for image denoising in the image and transform domain. (a) Original noisy image. (b) The denoised image by our proposed method. (c), (d), (e) are the results of K-SVD-based denoising in the image domain with σ=5,15 and 25, respectively.
Fig. 13.
Fig. 13. Reconstructed image by thresholding curvelet coefficients at each subband by Tj,l,p=kσ1σ2 (a) Original noisy image,(b) Reconstructed image with k = 0.01 and (c) k = 2.
Fig. 14.
Fig. 14. The effect of decomposition level in the reconstructed despeckled image of our proposed method. (a) Initial noisy image, (b) Denoising results using 4 level decomposition and (c) 8 level decomposition of curvelet transform in our denoising method.
Fig. 15.
Fig. 15. Visual performance of the proposed method on images taken by various OCT imaging systems. (a),(c) and (e) show the initial noisy images taken by Topcon, Nidek and zeiss imaging system respectively and (b),(d) and (f) illustrates the results of our proposed method.

Tables (2)

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Table 1. Available denoising methods in OCT images [5, a]

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Table 2. Mean and std of the CNRs, MSRs, ENL, TP and EP for 17 SDOCT retinal images using Methods of Tikhonov (15), K-SVD [38], MSBTD (37), NWSR (68), 3D CWDL (5) and Proposed Method.

Equations (16)

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ϕ a , b , θ ( x ) = ϕ a , 0 , 0 ( R θ ( x b ) )
ϕ ^ a , b , θ ( ξ ) = e i b , ξ ϕ ^ a , 0 , 0 ( R θ ξ ) = e i b , ξ U a ( R θ ξ )
c j , k , l ( f ) = R 2 f ^ ( ξ ) U j ( R θ j , l ξ ) e i b k j , l , ξ d ξ
c ~ j , k , l ( f ) = R 2 f ^ ( ξ ) U ~ j ( S θ j , l 1 ξ ) e i b ~ k j , l , ξ d ξ
c ~ j , k , l ( f ) = R 2 f ^ ( ξ ) U ~ j ( S θ j , l 1 ξ ) e i k j , ξ d ξ
{ ( ξ 1 , ξ 2 , ξ 3 ) T : 2 j 1 ξ 1 2 j + 1 , 2 j / 2 3 ξ 2 2 ξ 1 2 j / 2 , 2 j / 2 3 ξ 3 2 ξ 1 2 j / 2 } .
tan θ j , l = l 2 j / 2 l = 2 j / 2 + 1 , , 2 j / 2 + 1 ,
tan υ j , m = m 2 j / 2 m = 2 j / 2 + 1 , , 2 j / 2 + 1 ,
φ ~ j , k , l , m = φ ~ j , 0 , 0 , 0 ( S T θ j , l , υ j , m ( x b ~ k j , l , m ) )
ϕ ~ ^ j , k , l , m = e i b ~ k j , l , m , ξ ϕ ~ ^ j , 0 , 0 , 0 ( S θ j , l υ j , m 1 ξ ) = e i b ~ k j , l , m , ξ U ~ j ( S θ j , l υ j , m 1 ξ )
C ~ j , k , l , m ( f ) = f , ϕ ~ j , k , l , m = R 3 f ^ ( ξ ) U ~ j ( S θ j , l , υ j , m 1 ξ ) e i b ~ k j , l , m , ξ d ξ = R 3 f ^ ( S θ j , l , υ j , m ξ ) U ~ j ( ξ ) e i k j , ξ d ξ
C ( j , l , p ) = { C ( j , l , p ) i f C ( j , l , p ) T j,l,p 0 e l s e
α ^ i , C ^ = argmin( α i , C | | C Y | | 2 2 + λ | | D α i  -  R i C | | F 2  +  i μ i | | α i | | 0 )
i min α i | | α i | | 0 s . t . | | R i C D α i | | 2 2 ( g σ ) 2
C ( j,l,p ) = ( λ I + i R i T R i ) 1 ( λ Y + i R i T D α i )
K c ( A ) = { 2 A if A < N | A N | 0.3 A if N A < 3 N | M A | 0.5 A if 3 N A

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