Abstract

Optical coherence tomography (OCT) is a non-invasive technique with a large array of applications in clinical imaging and biological tissue visualization. However, the presence of speckle noise affects the analysis of OCT images and their diagnostic utility. In this article, we introduce a new OCT denoising algorithm. The proposed method is founded on a numerical optimization framework based on maximum-a-posteriori estimate of the noise-free OCT image. It combines a novel speckle noise model, derived from local statistics of empirical spectral domain OCT (SD-OCT) data, with a Huber variant of total variation regularization for edge preservation. The proposed approach exhibits satisfying results in terms of speckle noise reduction as well as edge preservation, at reduced computational cost.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]

2017 (2)

D. Jesus and D. Iskander, “Assessment of corneal properties based on statistical modeling of OCT speckle,” Biomed. Opt. Express 8(1), 162–176 (2017).
[Crossref] [PubMed]

L. Fang, S. Li, D. Cunefare, and S. Farsiu, “Segmentation Based Sparse Reconstruction of Optical Coherence Tomography Images,” IEEE Trans. Med. Imag. 36(2), 407–421 (2017).
[Crossref]

2016 (1)

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

2015 (5)

G. Gong, H. Zhang, and M. Yao, “Speckle noise reduction algorithm with total variation regularization in optical coherence tomography,” Opt. Express 23(19), 24699–24712 (2015).
[Crossref] [PubMed]

J. Duan, C. Tench, I. Gottlob, F. Proudlock, and L. Bai, “New variational image decomposition model for simultaneously denoising and segmenting optical coherence tomography images, “ Phys. Med. Biol. 60(22), 8901–8922 (2015).
[Crossref] [PubMed]

L. Bian, J. Suo, F. Chen, and Q. Dai, “Multiframe denoising of high-speed optical coherence tomography data using interframe and intraframe priors,” J. Biomed. Opt. 20(3), 036006 (2015).
[Crossref] [PubMed]

J. Aum, J. Kim, and J. Jeong, “Effective speckle noise suppression in optical coherence tomography images using nonlocal means denoising filter with double Gaussian anisotropic kernels,” Appl. Opt. 54(13), D43–D50 (2015).
[Crossref]

R. Kafieh, H. Rabbani, and I. Selesnick, “Three Dimensional Data-Driven Multi Scale Atomic Representation of Optical Coherence Tomography,” IEEE Trans. Med. Imag. 34(5), 1042–1062 (2015).
[Crossref]

2014 (2)

2013 (4)

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. Imag. 32(11), 2034–2049 (2013).
[Crossref]

H. Woo and S. Yun, “Proximal linearized alternating direction method for multiplicative denoising,” SIAM J. Sci. Comput. 35(2), B336–B358 (2013).
[Crossref]

A. Cameron, D. Lui, A. Boroomand, J. Glaister, A. Wong, and K. Bizheva, “Stochastic speckle noise compensation in optical coherence tomography using non-stationary spline-based speckle noise modelling,” Biomed. Opt. Express 4(9), 1769–1785 (2013).
[Crossref] [PubMed]

B. Chong and Y. Zhu, “Speckle reduction in optical coherence tomography images of human finger skin by wavelet modified {BM3D} filter,” Opt. Commun. 291, 461–469 (2013).
[Crossref]

2012 (2)

2011 (2)

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends. Mach. Learn. 3(1), 1–122 (2011).
[Crossref]

A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging,” J. Math. Imaging Vis. 40(1), 120–145 (2011).
[Crossref]

2010 (3)

2007 (6)

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. Imag. 26(6), 761–771 (2007).
[Crossref]

A. Desjardins, B. Vakoc, W. Oh, S. Motaghiannezam, G. Tearney, and B. Bouma, “Angle-resolved Optical Coherence Tomography with sequential angular selectivity for speckle reduction,” Opt. Express 15(10), 6200–6209 (2007).
[Crossref] [PubMed]

D. Popescu, M. Hewko, and M. Sowa, “Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample,” Opt. Commun. 269(1), 247–251 (2007).
[Crossref]

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography images using digital filtering,” J. Opt. Soc. Am. A 24(7), 1901–1910 (2007).
[Crossref]

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]

P. Puvanathasan and K. Bizheva, “Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set,” Opt. Express 15(24), 15747–15758 (2007).
[Crossref] [PubMed]

2005 (1)

Ali, M.

M. Ali and B. Hadj, “Segmentation of OCT skin images by classification of speckle statistical parameters,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2010), pp. 613–616.

Aum, J.

Bai, L.

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

J. Duan, C. Tench, I. Gottlob, F. Proudlock, and L. Bai, “New variational image decomposition model for simultaneously denoising and segmenting optical coherence tomography images, “ Phys. Med. Biol. 60(22), 8901–8922 (2015).
[Crossref] [PubMed]

Bian, L.

L. Bian, J. Suo, F. Chen, and Q. Dai, “Multiframe denoising of high-speed optical coherence tomography data using interframe and intraframe priors,” J. Biomed. Opt. 20(3), 036006 (2015).
[Crossref] [PubMed]

Bilenca, A.

Bizheva, K.

Boroomand, A.

Borsdorf, A.

Bouma, B.

Bouma, B. E.

Boyd, S.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends. Mach. Learn. 3(1), 1–122 (2011).
[Crossref]

Cameron, A.

Chambolle, A.

A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging,” J. Math. Imaging Vis. 40(1), 120–145 (2011).
[Crossref]

Chen, F.

L. Bian, J. Suo, F. Chen, and Q. Dai, “Multiframe denoising of high-speed optical coherence tomography data using interframe and intraframe priors,” J. Biomed. Opt. 20(3), 036006 (2015).
[Crossref] [PubMed]

Chen, Z.

Chiu, S. J.

Chong, B.

B. Chong and Y. Zhu, “Speckle reduction in optical coherence tomography images of human finger skin by wavelet modified {BM3D} filter,” Opt. Commun. 291, 461–469 (2013).
[Crossref]

Chu, E.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends. Mach. Learn. 3(1), 1–122 (2011).
[Crossref]

Clausi, D.A.

Cunefare, D.

L. Fang, S. Li, D. Cunefare, and S. Farsiu, “Segmentation Based Sparse Reconstruction of Optical Coherence Tomography Images,” IEEE Trans. Med. Imag. 36(2), 407–421 (2017).
[Crossref]

Dabov, K.

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]

Dai, Q.

L. Bian, J. Suo, F. Chen, and Q. Dai, “Multiframe denoising of high-speed optical coherence tomography data using interframe and intraframe priors,” J. Biomed. Opt. 20(3), 036006 (2015).
[Crossref] [PubMed]

Desjardins, A.

Desjardins, A. E.

Duan, J.

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

J. Duan, C. Tench, I. Gottlob, F. Proudlock, and L. Bai, “New variational image decomposition model for simultaneously denoising and segmenting optical coherence tomography images, “ Phys. Med. Biol. 60(22), 8901–8922 (2015).
[Crossref] [PubMed]

Eckstein, J.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends. Mach. Learn. 3(1), 1–122 (2011).
[Crossref]

Egiazarian, K.

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]

Fang, L.

L. Fang, S. Li, D. Cunefare, and S. Farsiu, “Segmentation Based Sparse Reconstruction of Optical Coherence Tomography Images,” IEEE Trans. Med. Imag. 36(2), 407–421 (2017).
[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. Imag. 32(11), 2034–2049 (2013).
[Crossref]

L. Fang, S. Li, Q. Nie, J. 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] [PubMed]

Farhat, G.

Farsiu, S.

L. Fang, S. Li, D. Cunefare, and S. Farsiu, “Segmentation Based Sparse Reconstruction of Optical Coherence Tomography Images,” IEEE Trans. Med. Imag. 36(2), 407–421 (2017).
[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. Imag. 32(11), 2034–2049 (2013).
[Crossref]

L. Fang, S. Li, Q. Nie, J. 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] [PubMed]

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]

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. Imag. 26(6), 761–771 (2007).
[Crossref]

Foi, A.

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]

Glaister, J.

Gong, G.

Gottlob, I.

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

J. Duan, C. Tench, I. Gottlob, F. Proudlock, and L. Bai, “New variational image decomposition model for simultaneously denoising and segmenting optical coherence tomography images, “ Phys. Med. Biol. 60(22), 8901–8922 (2015).
[Crossref] [PubMed]

Hadj, B.

M. Ali and B. Hadj, “Segmentation of OCT skin images by classification of speckle statistical parameters,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2010), pp. 613–616.

Hassler, K.

Hewko, M.

D. Popescu, M. Hewko, and M. Sowa, “Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample,” Opt. Commun. 269(1), 247–251 (2007).
[Crossref]

Hornegger, J.

Iskander, D.

Izatt, J.

Izatt, J. A.

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. Imag. 32(11), 2034–2049 (2013).
[Crossref]

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]

Jeong, J.

Jesus, D.

Jian, Z.

Kafieh, R.

R. Kafieh, H. Rabbani, and I. Selesnick, “Three Dimensional Data-Driven Multi Scale Atomic Representation of Optical Coherence Tomography,” IEEE Trans. Med. Imag. 34(5), 1042–1062 (2015).
[Crossref]

T. Mahmudi, R. Kafieh, and H. Rabbani, “Comparison of macular OCTs in right and left eyes of normal people,” Proc. SPIE 9038, 90381W (2014).
[Crossref]

Karamata, B.

Katkovnik, V.

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]

Kim, J.

Kirillin, M.

Kolios, M.

Kuo, A. N.

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. Imag. 32(11), 2034–2049 (2013).
[Crossref]

Lasser, T.

Laubscher, M.

Li, S.

L. Fang, S. Li, D. Cunefare, and S. Farsiu, “Segmentation Based Sparse Reconstruction of Optical Coherence Tomography Images,” IEEE Trans. Med. Imag. 36(2), 407–421 (2017).
[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. Imag. 32(11), 2034–2049 (2013).
[Crossref]

L. Fang, S. Li, Q. Nie, J. 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] [PubMed]

Li, X. T.

Lu, W.

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

Lui, D.

Mahmudi, T.

T. Mahmudi, R. Kafieh, and H. Rabbani, “Comparison of macular OCTs in right and left eyes of normal people,” Proc. SPIE 9038, 90381W (2014).
[Crossref]

Mardin, C.Y.

Mayer, M.A.

McNabb, R. P.

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. Imag. 32(11), 2034–2049 (2013).
[Crossref]

Mishra, A.

Motaghiannezam, S.

Nicholas, P.

Nie, Q.

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. Imag. 32(11), 2034–2049 (2013).
[Crossref]

L. Fang, S. Li, Q. Nie, J. 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] [PubMed]

Oh, W.

Ozcan, A.

Parikh, N.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends. Mach. Learn. 3(1), 1–122 (2011).
[Crossref]

Peleato, B.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends. Mach. Learn. 3(1), 1–122 (2011).
[Crossref]

Pock, T.

A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging,” J. Math. Imaging Vis. 40(1), 120–145 (2011).
[Crossref]

Popescu, D.

D. Popescu, M. Hewko, and M. Sowa, “Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample,” Opt. Commun. 269(1), 247–251 (2007).
[Crossref]

Portilla, J.

J. Portilla, “Blind non-white noise removal in images using gaussian scale mixtures in the wavelet domain,” in Proceedings of IEEE Benelux Signal Processing Symposium (IEEE, 2004), pp. 17–20.

Proudlock, F.

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

J. Duan, C. Tench, I. Gottlob, F. Proudlock, and L. Bai, “New variational image decomposition model for simultaneously denoising and segmenting optical coherence tomography images, “ Phys. Med. Biol. 60(22), 8901–8922 (2015).
[Crossref] [PubMed]

Puvanathasan, P.

Rabbani, H.

R. Kafieh, H. Rabbani, and I. Selesnick, “Three Dimensional Data-Driven Multi Scale Atomic Representation of Optical Coherence Tomography,” IEEE Trans. Med. Imag. 34(5), 1042–1062 (2015).
[Crossref]

T. Mahmudi, R. Kafieh, and H. Rabbani, “Comparison of macular OCTs in right and left eyes of normal people,” Proc. SPIE 9038, 90381W (2014).
[Crossref]

Rao, B.

Salinas, H. M.

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. Imag. 26(6), 761–771 (2007).
[Crossref]

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J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

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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. Imag. 34(5), 1042–1062 (2015).
[Crossref]

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D. Popescu, M. Hewko, and M. Sowa, “Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample,” Opt. Commun. 269(1), 247–251 (2007).
[Crossref]

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L. Bian, J. Suo, F. Chen, and Q. Dai, “Multiframe denoising of high-speed optical coherence tomography data using interframe and intraframe priors,” J. Biomed. Opt. 20(3), 036006 (2015).
[Crossref] [PubMed]

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J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

J. Duan, C. Tench, I. Gottlob, F. Proudlock, and L. Bai, “New variational image decomposition model for simultaneously denoising and segmenting optical coherence tomography images, “ Phys. Med. Biol. 60(22), 8901–8922 (2015).
[Crossref] [PubMed]

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Toth, C. A.

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Vakoc, B.

Vitkin, A.

Wagner, M.

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Woo, H.

H. Woo and S. Yun, “Proximal linearized alternating direction method for multiplicative denoising,” SIAM J. Sci. Comput. 35(2), B336–B358 (2013).
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Yao, M.

Yu, L.

Yun, S.

H. Woo and S. Yun, “Proximal linearized alternating direction method for multiplicative denoising,” SIAM J. Sci. Comput. 35(2), B336–B358 (2013).
[Crossref]

Zhang, H.

Zhu, Y.

B. Chong and Y. Zhu, “Speckle reduction in optical coherence tomography images of human finger skin by wavelet modified {BM3D} filter,” Opt. Commun. 291, 461–469 (2013).
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Appl. Opt. (1)

Biomed. Opt. Express (4)

Biomed. Signal Process. Control (1)

J. Duan, W. Lu, C. Tench, I. Gottlob, F. Proudlock, N. Samani, and L. Bai, “Denoising optical coherence tomography using second order total generalized variation decomposition,” Biomed. Signal Process. Control 24, 120–127 (2016).
[Crossref]

Found. Trends. Mach. Learn. (1)

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IEEE Trans. image process. (1)

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).
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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. Imag. 34(5), 1042–1062 (2015).
[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. Imag. 26(6), 761–771 (2007).
[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. Imag. 32(11), 2034–2049 (2013).
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L. Fang, S. Li, D. Cunefare, and S. Farsiu, “Segmentation Based Sparse Reconstruction of Optical Coherence Tomography Images,” IEEE Trans. Med. Imag. 36(2), 407–421 (2017).
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J. Biomed. Opt. (1)

L. Bian, J. Suo, F. Chen, and Q. Dai, “Multiframe denoising of high-speed optical coherence tomography data using interframe and intraframe priors,” J. Biomed. Opt. 20(3), 036006 (2015).
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J. Opt. Soc. Am. A (2)

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D. Popescu, M. Hewko, and M. Sowa, “Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample,” Opt. Commun. 269(1), 247–251 (2007).
[Crossref]

B. Chong and Y. Zhu, “Speckle reduction in optical coherence tomography images of human finger skin by wavelet modified {BM3D} filter,” Opt. Commun. 291, 461–469 (2013).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Phys. Med. Biol. (1)

J. Duan, C. Tench, I. Gottlob, F. Proudlock, and L. Bai, “New variational image decomposition model for simultaneously denoising and segmenting optical coherence tomography images, “ Phys. Med. Biol. 60(22), 8901–8922 (2015).
[Crossref] [PubMed]

Proc. SPIE (1)

T. Mahmudi, R. Kafieh, and H. Rabbani, “Comparison of macular OCTs in right and left eyes of normal people,” Proc. SPIE 9038, 90381W (2014).
[Crossref]

SIAM J. Sci. Comput. (1)

H. Woo and S. Yun, “Proximal linearized alternating direction method for multiplicative denoising,” SIAM J. Sci. Comput. 35(2), B336–B358 (2013).
[Crossref]

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J. Portilla, “Blind non-white noise removal in images using gaussian scale mixtures in the wavelet domain,” in Proceedings of IEEE Benelux Signal Processing Symposium (IEEE, 2004), pp. 17–20.

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Supplementary Material (1)

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» Code 1       Source Code and Data

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Figures (6)

Fig. 1
Fig. 1

Segmentation obtained for OCT images. (a) Original OCT image of phantom structure. (b) Segmented image of phantom structure, with 2 regions. (c) Original OCT image of a biofilm sample. (d) Segmented image of biofilm sample, with 3 regions.

Fig. 2
Fig. 2

Illustration of the relationship between the local standard deviation and the local mean in OCT images. (a,b) Masks used for this computation for the images of phantom structure and biofilm sample respectively. For each pixel, the mean and standard deviation are computed over a local 9-by-9 window. Pixels lying between 2 different clusters (represented in red) are not considered in this computation. (c,d) Graphics showing the local standard deviation against the local mean, respectively for the phantom image and biofilm image.

Fig. 3
Fig. 3

(a) A selected homogeneous region of a 3D-printed phantom sample with layered structure. (b) Empirical probability distribution functions of intensity values in the selected region before (blue) and after (red) a square-root transformation, and the fitted Gaussian distribution (black) to the transformed distribution. (c) The Q-Q plot of the transformed distribution and the fitted Gaussian distribution. The dashed red line corresponds to quantiles of the fitted Gaussian distribution.

Fig. 4
Fig. 4

Denoising results of 4 sample images. Odd rows: whole images. Even rows: zoomedin images of the selected region.

Fig. 5
Fig. 5

Original noisy images with selected regions of interest (ROIs) marked in boxes for calculation of: CNR (red), ENL (cyan), EP (green). (a) 3D-printed phantom with layered structure. (b) Biofilm on a membrane. (c) Orange pulp. (d) Chicken skin.

Fig. 6
Fig. 6

Comparison of segmentation results on denoised retinal images using: (a) Gaussian filter. (b) Log-space BM3D. (c) K-SVD. (d) General Bayesian. (e) TGV decomposition. (f) Proposed.

Tables (2)

Tables Icon

Algorithm 1 Our denoising algorithm

Tables Icon

Table 1 Performance metrics computed for different methods. The Average is taken over corresponding ROIs and over all samples. The standard deviation of each metric is also included. * EP is calculated only on the 3D-printed phantom sample.

Equations (27)

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z ( x ) = u ( x ) s ( x ) ,
𝔼 ( z ( x ) ) = u ( x ) .
σ ( z ( x ) ) = α u ( x ) = α 𝔼 ( z ( x ) ) , and
z ( x ) ~ 𝒩 ( μ ( x ) , v ( x ) ) ,
σ ( s ) = α .
s ( x ) ~ 𝒩 ( μ ( x ) u ( x ) , v ( x ) u ( x ) ) ,
s ( x ) ~ X 2 with X ~ 𝒩 ( μ ( x ) u ( x ) , v ( x ) u ( x ) ) ,
μ ( x ) u ( x ) = c 1 , v ( x ) u ( x ) = c 2 x Ω ,
𝔼 ( X 2 ) [ μ ( x ) u ( x ) ] 2 + v ( x ) u ( x ) = μ ( x ) 2 + v ( x ) u ( x ) , 𝔼 ( X 4 ) [ μ ( x ) u ( x ) ] 4 + 6 [ μ ( x ) u ( x ) ] 2 v ( x ) u ( x ) + 3 [ v ( x ) u ( x ) ] 2 = μ ( x ) 4 + 6 μ ( x ) 2 v ( x ) + 3 v ( x ) 2 u ( x ) 2 .
1 = 𝔼 ( s ) = 𝔼 ( X 2 ) = μ ( x 2 ) + v ( x ) u ( x ) ,
μ ( x ) 2 + v ( x ) = u ( x ) .
α 2 = σ ( s ) 2 = σ ( X 2 ) 2 = 𝔼 ( X 4 ) 𝔼 ( X 2 ) 2 ,
α 2 = 4 μ ( x ) 2 v ( x ) + 2 v ( x ) 2 u ( x ) 2 .
c 1 = μ ( x ) μ ( x ) = ( 1 α 2 2 ) 1 4 and c 2 = v ( x ) u ( x ) = 1 ( 1 α 2 2 ) 1 2 .
f ( z | u ) = i , j 1 2 c 2 π exp ( ( z i , j u i , j c 1 ) 2 2 c 2 ) 1 2 z i , j u i , j .
u MAP = argmax u U g ( u ) f ( z | u ) = argmax u U log ( g ( u ) ) log ( f ( z | u ) ) = argmin u U log ( g ( u ) ) + 1 2 c 2 z u c 1 2 2 + 1 2 i , j log ( u i , j ) .
min u U ^ log ( g ( u ) ) + 1 2 c 2 z e 1 2 u c 1 2 2 + 1 2 i , j u i , j .
u H = i , j | ( u ) i , j | β ,
| ( u ) i , j | β = { | ( u ) i , j | 2 β if | ( u ) i , j | β | ( u ) i , j | β 2 if | ( u ) i , j | > β
L γ ( u , w , p ) : = f ( u ) + λ w H + p , w u + γ 2 w u 2 2 .
f ( u ) + γ 2 w u 2 2 f ( u 0 ) + γ 2 w u 0 2 2 + u f ( u 0 ) + γ div ( w u 0 ) , u u 0 + 1 2 δ u u 0 2 2 .
L γ ( u , w , p ) : = f ( u k ) + γ 2 w u k 2 2 + u f ( u k ) + γ div ( w u k ) , u u k + 1 2 δ u u k 2 2 + λ w H + p , w u ,
1 : u k + 1 = u k δ ( 1 2 z 2 c 2 e 1 2 u ( z e 1 2 u c 1 ) + γ div ( w k u k ) + div ( p k ) ) , 2 : w i , j k + 1 = max ( ( u k + 1 ) i , j p i , j k γ 2 λ γ , ( u k + 1 ) i , j p i , j k γ 2 1 + λ γ β ) ( u k + 1 ) i , j p i , j k γ ( u k + 1 ) i , j p i , j k γ 2 ,
CNR r = | μ r μ b | 0.5 ( σ r 2 + σ b 2 ) ,
CNR = 1 N r = 1 N CNR r .
ENL = 1 N r = 1 N μ r 2 σ r 2 ,
EP = 1 N r = 1 N i , j ROI r ( Δ i r Δ i r ¯ ) ( Δ u r Δ u r ¯ ) i , j ROI r ( Δ i r Δ i r ¯ ) 2 i , j ROI r ( Δ u r Δ u r ¯ ) 2 ,