Abstract

Optical coherence tomography (OCT) is an important interferometric diagnostic technique extensively applied in medical sciences. However, OCT images inevitably suffer from speckle noise, which reduces the accuracy of the diagnosis of ocular diseases. To deal with this problem, a speckle noise reduction method based on multi-linear principal component analysis (MPCA) is presented to denoise multi-frame OCT data. To well preserve local image features, nonlocal similar 3D blocks extracted from the data are first grouped using k-means++ clustering method. MPCA transform is then performed on each group and the transform coefficients are shrunk to remove speckle noise. Finally, the filtered OCT volume is obtained by inverse MPCA transform and aggregation. Experimental results show that the proposed method outperforms other compared approaches in terms of both speckle noise reduction and fine detail preservation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

H. Chen, S. Fu, H. Wang, H. Lv, and C. Zhang, “Speckle attenuation by adaptive singular value shrinking with generalized likelihood matching in optical coherence tomography,” J. Biomed. Opt. 23(3), 036014 (2018).
[Crossref]

H. Lv, S. Fu, C. Zhang, and L. Zhai, “Speckle noise reduction for optical coherence tomography based on adaptive 2D dictionary,” Laser Phys. Lett. 15(5), 055401 (2018).
[Crossref]

2017 (1)

C. Tang, L. Cao, J. Chen, and X. Zheng, “Speckle noise reduction for optical coherence tomography images via non-local weighted group low-rank representation,” Laser Phys. Lett. 14(5), 056002 (2017).
[Crossref]

2016 (1)

2015 (5)

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

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Reduction of speckle noise from optical coherence tomography images using multi-frame weighted nuclear norm minimization method,” J. Mod. Opt. 62(21), 1856–1864 (2015).
[Crossref]

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] [PubMed]

J. Aum, J. H. 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]

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]

2014 (1)

Y. Du, G. Liu, G. Feng, and Z. Chen, “Speckle reduction in optical coherence tomography images based on wave atoms,” J. Biomed. Opt. 19(5), 056009 (2014).
[Crossref] [PubMed]

2013 (4)

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
[Crossref] [PubMed]

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] [PubMed]

T. Klein, R. André, W. Wieser, T. Pfeiffer, and R. Huber, “Joint aperture detection for speckle reduction and increased collection efficiency in ophthalmic MHz OCT,” Biomed. Opt. Express 4(4), 619–634 (2013).
[Crossref] [PubMed]

J. Xu, H. Ou, E. Y. Lam, P. C. Chui, and K. K. Wong, “Speckle reduction of retinal optical coherence tomography based on contourlet shrinkage,” Opt. Lett. 38(15), 2900–2903 (2013).
[Crossref] [PubMed]

2012 (2)

2010 (5)

2009 (4)

P. Coupé, P. Hellier, C. Kervrann, and C. Barillot, “Nonlocal means-based speckle filtering for ultrasound images,” IEEE Trans. Image Process. 18(10), 2221–2229 (2009).
[Crossref] [PubMed]

R. Xu and Y. W. Chen, “Generalized N-dimensional principal component analysis (GND-PCA) and its application on construction of statistical appearance models for medical volumes with fewer samples,” Neurocomputing 72(10–12), 2276–2287 (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] [PubMed]

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

2008 (2)

H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, “MPCA: Multilinear principal component analysis of tensor objects,” IEEE Trans. Neural Networks. 19(1), 18–39 (2008).
[Crossref] [PubMed]

T. Bajraszewski, M. Wojtkowski, M. Szkulmowski, A. Szkulmowska, R. Huber, and A. Kowalczyk, “Improved spectral optical coherence tomography using optical frequency comb,” Opt. Express 16(6), 4163–4176 (2008).
[Crossref] [PubMed]

2007 (3)

2006 (1)

S. Aja-Fernández and C. Alberola-López, “On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering,” IEEE Trans. Image Process. 15(9), 2694–2701 (2006).
[Crossref] [PubMed]

2005 (1)

H. Kong, L. Wang, E. K. Teoh, X. Li, J. G. Wang, and R. Venkateswarlu, “Generalized 2D principal component analysis for face image representation and recognition,” Neural Networks 18(5–6), 585–594 (2005).
[Crossref] [PubMed]

2004 (2)

D. C. Adler, T. H. Ko, and J. G. Fujimoto, “Speckle reduction in optical coherence tomography images by use of a spatially adaptive wavelet filter,” Opt. Lett. 29(24), 2878–2880 (2004).
[Crossref]

J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, “Two-dimensional PCA: a new approach to appearance-based face representation and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 131–137 (2004).
[Crossref] [PubMed]

2003 (1)

M. Pircher, E. Götzinger, R. A. Leitgeb, 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] [PubMed]

2002 (2)

J. Rogowska and M. E. Brezinski, “Image processing techniques for noise removal, enhancement and segmentation of cartilage OCT images,” Phys. Med. Biol. 47(4), 641–655 (2002).
[Crossref] [PubMed]

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

Acton, S. T.

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

Adler, D. C.

Aja-Fernández, S.

S. Aja-Fernández and C. Alberola-López, “On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering,” IEEE Trans. Image Process. 15(9), 2694–2701 (2006).
[Crossref] [PubMed]

Alberola-López, C.

S. Aja-Fernández and C. Alberola-López, “On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering,” IEEE Trans. Image Process. 15(9), 2694–2701 (2006).
[Crossref] [PubMed]

André, R.

Araújo, A.

R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro, and J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter,” Opt. Express 18(23), 24084–24059 (2010).
[Crossref]

Arthur, D.

D. Arthur and S. Vassilvitskii, “k-means++: The advantages of careful seeding,” in Proceedings of ACM-SIAM symposium on Discrete algorithms (SIAM, 2007), pp. 1027–1035.

Aum, J.

Baghaie, A.

A. Baghaie, R. M. D’souza, and Z. Yu, “Sparse and low rank decomposition based batch image alignment for speckle reduction of retinal OCT images,” in Proceedings of IEEE International Symposimum on Biomedical Imaging (IEEE, 2015), pp. 226–230.

Bajraszewski, T.

Barbeiro, S.

R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro, and J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter,” Opt. Express 18(23), 24084–24059 (2010).
[Crossref]

Barillot, C.

P. Coupé, P. Hellier, C. Kervrann, and C. Barillot, “Nonlocal means-based speckle filtering for ultrasound images,” IEEE Trans. Image Process. 18(10), 2221–2229 (2009).
[Crossref] [PubMed]

Bernardes, R.

R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro, and J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter,” Opt. Express 18(23), 24084–24059 (2010).
[Crossref]

Bian, L.

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

Bilenca, A.

Bizheva, K.

Borsdorf, A.

Bouma, B. E.

Brezinski, M. E.

J. Rogowska and M. E. Brezinski, “Image processing techniques for noise removal, enhancement and segmentation of cartilage OCT images,” Phys. Med. Biol. 47(4), 641–655 (2002).
[Crossref] [PubMed]

Cao, L.

C. Tang, L. Cao, J. Chen, and X. Zheng, “Speckle noise reduction for optical coherence tomography images via non-local weighted group low-rank representation,” Laser Phys. Lett. 14(5), 056002 (2017).
[Crossref]

Chen, F.

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

Chen, H.

H. Chen, S. Fu, H. Wang, H. Lv, and C. Zhang, “Speckle attenuation by adaptive singular value shrinking with generalized likelihood matching in optical coherence tomography,” J. Biomed. Opt. 23(3), 036014 (2018).
[Crossref]

Chen, J.

C. Tang, L. Cao, J. Chen, and X. Zheng, “Speckle noise reduction for optical coherence tomography images via non-local weighted group low-rank representation,” Laser Phys. Lett. 14(5), 056002 (2017).
[Crossref]

Chen, Y. W.

R. Xu and Y. W. Chen, “Generalized N-dimensional principal component analysis (GND-PCA) and its application on construction of statistical appearance models for medical volumes with fewer samples,” Neurocomputing 72(10–12), 2276–2287 (2009).
[Crossref]

Chen, Z.

Chui, P. C.

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
[Crossref] [PubMed]

J. Xu, H. Ou, E. Y. Lam, P. C. Chui, and K. K. Wong, “Speckle reduction of retinal optical coherence tomography based on contourlet shrinkage,” Opt. Lett. 38(15), 2900–2903 (2013).
[Crossref] [PubMed]

Clausi, D. A.

Coupé, P.

P. Coupé, P. Hellier, C. Kervrann, and C. Barillot, “Nonlocal means-based speckle filtering for ultrasound images,” IEEE Trans. Image Process. 18(10), 2221–2229 (2009).
[Crossref] [PubMed]

Cunha-Vaz, J.

R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro, and J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter,” Opt. Express 18(23), 24084–24059 (2010).
[Crossref]

Curatolo, A.

D’souza, R. M.

A. Baghaie, R. M. D’souza, and Z. Yu, “Sparse and low rank decomposition based batch image alignment for speckle reduction of retinal OCT images,” in Proceedings of IEEE International Symposimum on Biomedical Imaging (IEEE, 2015), pp. 226–230.

Dai, Q.

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

Dalalyan, A. S.

C. A. Deledalle, J. Salmon, and A. S. Dalalyan, “Image denoising with patch-based PCA: local versus global,” in Proceedings of British Machine Vision Conference (BMVA Press, 2011), pp. 25.1–25.10.

Deledalle, C. A.

C. A. Deledalle, J. Salmon, and A. S. Dalalyan, “Image denoising with patch-based PCA: local versus global,” in Proceedings of British Machine Vision Conference (BMVA Press, 2011), pp. 25.1–25.10.

Desjardins, A. E.

Dong, W.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recognit. 43(4), 1531–1549 (2010).
[Crossref]

Du, Y.

Y. Du, G. Liu, G. Feng, and Z. Chen, “Speckle reduction in optical coherence tomography images based on wave atoms,” J. Biomed. Opt. 19(5), 056009 (2014).
[Crossref] [PubMed]

Fang, L.

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] [PubMed]

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] [PubMed]

Farsiu, S.

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] [PubMed]

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] [PubMed]

Feng, G.

Y. Du, G. Liu, G. Feng, and Z. Chen, “Speckle reduction in optical coherence tomography images based on wave atoms,” J. Biomed. Opt. 19(5), 056009 (2014).
[Crossref] [PubMed]

Fercher, A. F.

M. Pircher, E. Götzinger, R. A. Leitgeb, 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] [PubMed]

Fernández, D. C.

H. M. Salinas and D. C. Fernández, “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] [PubMed]

Frangi, A. F.

J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, “Two-dimensional PCA: a new approach to appearance-based face representation and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 131–137 (2004).
[Crossref] [PubMed]

Fu, S.

H. Chen, S. Fu, H. Wang, H. Lv, and C. Zhang, “Speckle attenuation by adaptive singular value shrinking with generalized likelihood matching in optical coherence tomography,” J. Biomed. Opt. 23(3), 036014 (2018).
[Crossref]

H. Lv, S. Fu, C. Zhang, and L. Zhai, “Speckle noise reduction for optical coherence tomography based on adaptive 2D dictionary,” Laser Phys. Lett. 15(5), 055401 (2018).
[Crossref]

Fujimoto, J. G.

Gao, J.

Gong, G.

Götzinger, E.

M. Pircher, E. Götzinger, R. A. Leitgeb, 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] [PubMed]

Hellier, P.

P. Coupé, P. Hellier, C. Kervrann, and C. Barillot, “Nonlocal means-based speckle filtering for ultrasound images,” IEEE Trans. Image Process. 18(10), 2221–2229 (2009).
[Crossref] [PubMed]

Hillman, T. R.

Hitzenberger, C. K.

M. Pircher, E. Götzinger, R. A. Leitgeb, 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] [PubMed]

Hornegger, J.

Huber, R.

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

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] [PubMed]

Jeong, J.

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

Kennedy, B. F.

Kervrann, C.

P. Coupé, P. Hellier, C. Kervrann, and C. Barillot, “Nonlocal means-based speckle filtering for ultrasound images,” IEEE Trans. Image Process. 18(10), 2221–2229 (2009).
[Crossref] [PubMed]

Kim, J. H.

Klein, T.

Ko, T. H.

Kong, H.

H. Kong, L. Wang, E. K. Teoh, X. Li, J. G. Wang, and R. Venkateswarlu, “Generalized 2D principal component analysis for face image representation and recognition,” Neural Networks 18(5–6), 585–594 (2005).
[Crossref] [PubMed]

Kowalczyk, A.

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

Lakshminarayanan, V.

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Reduction of speckle noise from optical coherence tomography images using multi-frame weighted nuclear norm minimization method,” J. Mod. Opt. 62(21), 1856–1864 (2015).
[Crossref]

Lam, E. Y.

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
[Crossref] [PubMed]

J. Xu, H. Ou, E. Y. Lam, P. C. Chui, and K. K. Wong, “Speckle reduction of retinal optical coherence tomography based on contourlet shrinkage,” Opt. Lett. 38(15), 2900–2903 (2013).
[Crossref] [PubMed]

Leitgeb, R. A.

M. Pircher, E. Götzinger, R. A. Leitgeb, 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] [PubMed]

Li, A.

Li, S.

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] [PubMed]

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] [PubMed]

Li, X.

H. Kong, L. Wang, E. K. Teoh, X. Li, J. G. Wang, and R. Venkateswarlu, “Generalized 2D principal component analysis for face image representation and recognition,” Neural Networks 18(5–6), 585–594 (2005).
[Crossref] [PubMed]

Liu, G.

Y. Du, G. Liu, G. Feng, and Z. Chen, “Speckle reduction in optical coherence tomography images based on wave atoms,” J. Biomed. Opt. 19(5), 056009 (2014).
[Crossref] [PubMed]

Lu, H.

H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, “MPCA: Multilinear principal component analysis of tensor objects,” IEEE Trans. Neural Networks. 19(1), 18–39 (2008).
[Crossref] [PubMed]

Lv, H.

H. Lv, S. Fu, C. Zhang, and L. Zhai, “Speckle noise reduction for optical coherence tomography based on adaptive 2D dictionary,” Laser Phys. Lett. 15(5), 055401 (2018).
[Crossref]

H. Chen, S. Fu, H. Wang, H. Lv, and C. Zhang, “Speckle attenuation by adaptive singular value shrinking with generalized likelihood matching in optical coherence tomography,” J. Biomed. Opt. 23(3), 036014 (2018).
[Crossref]

Maduro, C.

R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro, and J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter,” Opt. Express 18(23), 24084–24059 (2010).
[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. Imaging 32(11), 2034–2049 (2013).
[Crossref] [PubMed]

Mishra, A.

Motaghiannezam, S. M. R.

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

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] [PubMed]

Oh, W. Y.

Ou, H.

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
[Crossref] [PubMed]

J. Xu, H. Ou, E. Y. Lam, P. C. Chui, and K. K. Wong, “Speckle reduction of retinal optical coherence tomography based on contourlet shrinkage,” Opt. Lett. 38(15), 2900–2903 (2013).
[Crossref] [PubMed]

Ozcan, A.

Pfeiffer, T.

Pircher, M.

M. Pircher, E. Götzinger, R. A. Leitgeb, 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] [PubMed]

Plataniotis, K. N.

H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, “MPCA: Multilinear principal component analysis of tensor objects,” IEEE Trans. Neural Networks. 19(1), 18–39 (2008).
[Crossref] [PubMed]

Puvanathasan, P.

Raahemifar, K.

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Reduction of speckle noise from optical coherence tomography images using multi-frame weighted nuclear norm minimization method,” J. Mod. Opt. 62(21), 1856–1864 (2015).
[Crossref]

Rabbani, H.

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] [PubMed]

Rao, B.

Rogowska, J.

J. Rogowska and M. E. Brezinski, “Image processing techniques for noise removal, enhancement and segmentation of cartilage OCT images,” Phys. Med. Biol. 47(4), 641–655 (2002).
[Crossref] [PubMed]

Salinas, H. M.

H. M. Salinas and D. C. Fernández, “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).
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C. A. Deledalle, J. Salmon, and A. S. Dalalyan, “Image denoising with patch-based PCA: local versus global,” in Proceedings of British Machine Vision Conference (BMVA Press, 2011), pp. 25.1–25.10.

Sampson, D. D.

Schmitt, J. M.

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

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).
[Crossref] [PubMed]

Serranho, P.

R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro, and J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter,” Opt. Express 18(23), 24084–24059 (2010).
[Crossref]

Shi, G.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recognit. 43(4), 1531–1549 (2010).
[Crossref]

Sun, C.

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
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Suo, J.

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

Szkulmowska, A.

Szkulmowski, M.

Tang, C.

C. Tang, L. Cao, J. Chen, and X. Zheng, “Speckle noise reduction for optical coherence tomography images via non-local weighted group low-rank representation,” Laser Phys. Lett. 14(5), 056002 (2017).
[Crossref]

Tearney, G. J.

Teoh, E. K.

H. Kong, L. Wang, E. K. Teoh, X. Li, J. G. Wang, and R. Venkateswarlu, “Generalized 2D principal component analysis for face image representation and recognition,” Neural Networks 18(5–6), 585–594 (2005).
[Crossref] [PubMed]

Thapa, D.

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Reduction of speckle noise from optical coherence tomography images using multi-frame weighted nuclear norm minimization method,” J. Mod. Opt. 62(21), 1856–1864 (2015).
[Crossref]

Tornow, P. R.

Toth, C. 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. Imaging 32(11), 2034–2049 (2013).
[Crossref] [PubMed]

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] [PubMed]

Troberg, B. J.

Tromberg, B. J.

Vakoc, B. J.

Vassilvitskii, S.

D. Arthur and S. Vassilvitskii, “k-means++: The advantages of careful seeding,” in Proceedings of ACM-SIAM symposium on Discrete algorithms (SIAM, 2007), pp. 1027–1035.

Venetsanopoulos, A. N.

H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, “MPCA: Multilinear principal component analysis of tensor objects,” IEEE Trans. Neural Networks. 19(1), 18–39 (2008).
[Crossref] [PubMed]

Venkateswarlu, R.

H. Kong, L. Wang, E. K. Teoh, X. Li, J. G. Wang, and R. Venkateswarlu, “Generalized 2D principal component analysis for face image representation and recognition,” Neural Networks 18(5–6), 585–594 (2005).
[Crossref] [PubMed]

Wagner, M.

Wang, H.

H. Chen, S. Fu, H. Wang, H. Lv, and C. Zhang, “Speckle attenuation by adaptive singular value shrinking with generalized likelihood matching in optical coherence tomography,” J. Biomed. Opt. 23(3), 036014 (2018).
[Crossref]

Wang, J. G.

H. Kong, L. Wang, E. K. Teoh, X. Li, J. G. Wang, and R. Venkateswarlu, “Generalized 2D principal component analysis for face image representation and recognition,” Neural Networks 18(5–6), 585–594 (2005).
[Crossref] [PubMed]

Wang, L.

H. Kong, L. Wang, E. K. Teoh, X. Li, J. G. Wang, and R. Venkateswarlu, “Generalized 2D principal component analysis for face image representation and recognition,” Neural Networks 18(5–6), 585–594 (2005).
[Crossref] [PubMed]

Wieser, W.

Wojtkowski, M.

Wong, A.

Wong, K. K.

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
[Crossref] [PubMed]

J. Xu, H. Ou, E. Y. Lam, P. C. Chui, and K. K. Wong, “Speckle reduction of retinal optical coherence tomography based on contourlet shrinkage,” Opt. Lett. 38(15), 2900–2903 (2013).
[Crossref] [PubMed]

Xiang, S. H.

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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Xu, J.

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
[Crossref] [PubMed]

J. Xu, H. Ou, E. Y. Lam, P. C. Chui, and K. K. Wong, “Speckle reduction of retinal optical coherence tomography based on contourlet shrinkage,” Opt. Lett. 38(15), 2900–2903 (2013).
[Crossref] [PubMed]

Xu, R.

R. Xu and Y. W. Chen, “Generalized N-dimensional principal component analysis (GND-PCA) and its application on construction of statistical appearance models for medical volumes with fewer samples,” Neurocomputing 72(10–12), 2276–2287 (2009).
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Yang, J.

J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, “Two-dimensional PCA: a new approach to appearance-based face representation and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 131–137 (2004).
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Yang, J. Y.

J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, “Two-dimensional PCA: a new approach to appearance-based face representation and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 131–137 (2004).
[Crossref] [PubMed]

Yang, V. X.

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
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Yao, M.

Yu, H.

Yu, L.

Yu, Y.

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

Yu, Z.

Z. Jian, Z. Yu, L. Yu, B. Rao, Z. Chen, and B. J. Tromberg, “Speckle attenuation in optical coherence tomography by curvelet shrinkage,” Opt. Lett. 34(10), 1516–1518 (2009).
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A. Baghaie, R. M. D’souza, and Z. Yu, “Sparse and low rank decomposition based batch image alignment for speckle reduction of retinal OCT images,” in Proceedings of IEEE International Symposimum on Biomedical Imaging (IEEE, 2015), pp. 226–230.

Yung, K. M.

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

Zhai, L.

H. Lv, S. Fu, C. Zhang, and L. Zhai, “Speckle noise reduction for optical coherence tomography based on adaptive 2D dictionary,” Laser Phys. Lett. 15(5), 055401 (2018).
[Crossref]

Zhang, C.

H. Lv, S. Fu, C. Zhang, and L. Zhai, “Speckle noise reduction for optical coherence tomography based on adaptive 2D dictionary,” Laser Phys. Lett. 15(5), 055401 (2018).
[Crossref]

H. Chen, S. Fu, H. Wang, H. Lv, and C. Zhang, “Speckle attenuation by adaptive singular value shrinking with generalized likelihood matching in optical coherence tomography,” J. Biomed. Opt. 23(3), 036014 (2018).
[Crossref]

Zhang, D.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recognit. 43(4), 1531–1549 (2010).
[Crossref]

J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, “Two-dimensional PCA: a new approach to appearance-based face representation and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 131–137 (2004).
[Crossref] [PubMed]

Zhang, H.

Zhang, L.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recognit. 43(4), 1531–1549 (2010).
[Crossref]

Zheng, X.

C. Tang, L. Cao, J. Chen, and X. Zheng, “Speckle noise reduction for optical coherence tomography images via non-local weighted group low-rank representation,” Laser Phys. Lett. 14(5), 056002 (2017).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (3)

IEEE Trans. Image Process. (3)

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

S. Aja-Fernández and C. Alberola-López, “On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering,” IEEE Trans. Image Process. 15(9), 2694–2701 (2006).
[Crossref] [PubMed]

P. Coupé, P. Hellier, C. Kervrann, and C. Barillot, “Nonlocal means-based speckle filtering for ultrasound images,” IEEE Trans. Image Process. 18(10), 2221–2229 (2009).
[Crossref] [PubMed]

IEEE Trans. Med. Imaging (3)

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] [PubMed]

H. M. Salinas and D. C. Fernández, “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] [PubMed]

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] [PubMed]

IEEE Trans. Neural Networks. (1)

H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, “MPCA: Multilinear principal component analysis of tensor objects,” IEEE Trans. Neural Networks. 19(1), 18–39 (2008).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, “Two-dimensional PCA: a new approach to appearance-based face representation and recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 131–137 (2004).
[Crossref] [PubMed]

J. Biomed. Opt. (6)

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

H. Chen, S. Fu, H. Wang, H. Lv, and C. Zhang, “Speckle attenuation by adaptive singular value shrinking with generalized likelihood matching in optical coherence tomography,” J. Biomed. Opt. 23(3), 036014 (2018).
[Crossref]

Y. Du, G. Liu, G. Feng, and Z. Chen, “Speckle reduction in optical coherence tomography images based on wave atoms,” J. Biomed. Opt. 19(5), 056009 (2014).
[Crossref] [PubMed]

J. Xu, H. Ou, C. Sun, P. C. Chui, V. X. Yang, E. Y. Lam, and K. K. Wong, “Wavelet domain compounding for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 18(9), 096002 (2013).
[Crossref] [PubMed]

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

M. Pircher, E. Götzinger, R. A. Leitgeb, 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] [PubMed]

J. Mod. Opt. (1)

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Reduction of speckle noise from optical coherence tomography images using multi-frame weighted nuclear norm minimization method,” J. Mod. Opt. 62(21), 1856–1864 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

Laser Phys. Lett. (2)

C. Tang, L. Cao, J. Chen, and X. Zheng, “Speckle noise reduction for optical coherence tomography images via non-local weighted group low-rank representation,” Laser Phys. Lett. 14(5), 056002 (2017).
[Crossref]

H. Lv, S. Fu, C. Zhang, and L. Zhai, “Speckle noise reduction for optical coherence tomography based on adaptive 2D dictionary,” Laser Phys. Lett. 15(5), 055401 (2018).
[Crossref]

Neural Networks (1)

H. Kong, L. Wang, E. K. Teoh, X. Li, J. G. Wang, and R. Venkateswarlu, “Generalized 2D principal component analysis for face image representation and recognition,” Neural Networks 18(5–6), 585–594 (2005).
[Crossref] [PubMed]

Neurocomputing (1)

R. Xu and Y. W. Chen, “Generalized N-dimensional principal component analysis (GND-PCA) and its application on construction of statistical appearance models for medical volumes with fewer samples,” Neurocomputing 72(10–12), 2276–2287 (2009).
[Crossref]

Opt. Express (7)

Z. Jian, L. Yu, B. Rao, B. J. Troberg, 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]

A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. R. Motaghiannezam, G. J. Tearney, and B. E. Bouma, “Angle-resolved optical coherence tomography with sequential angular selectivity for speckle reduction,” Opt. Express 15(10), 6200–6209 (2007).
[Crossref] [PubMed]

T. Bajraszewski, M. Wojtkowski, M. Szkulmowski, A. Szkulmowska, R. Huber, and A. Kowalczyk, “Improved spectral optical coherence tomography using optical frequency comb,” Opt. Express 16(6), 4163–4176 (2008).
[Crossref] [PubMed]

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]

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]

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] [PubMed]

R. Bernardes, C. Maduro, P. Serranho, A. Araújo, S. Barbeiro, and J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter,” Opt. Express 18(23), 24084–24059 (2010).
[Crossref]

Opt. Lett. (5)

Pattern Recognit. (1)

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recognit. 43(4), 1531–1549 (2010).
[Crossref]

Phys. Med. Biol. (1)

J. Rogowska and M. E. Brezinski, “Image processing techniques for noise removal, enhancement and segmentation of cartilage OCT images,” Phys. Med. Biol. 47(4), 641–655 (2002).
[Crossref] [PubMed]

Other (3)

C. A. Deledalle, J. Salmon, and A. S. Dalalyan, “Image denoising with patch-based PCA: local versus global,” in Proceedings of British Machine Vision Conference (BMVA Press, 2011), pp. 25.1–25.10.

A. Baghaie, R. M. D’souza, and Z. Yu, “Sparse and low rank decomposition based batch image alignment for speckle reduction of retinal OCT images,” in Proceedings of IEEE International Symposimum on Biomedical Imaging (IEEE, 2015), pp. 226–230.

D. Arthur and S. Vassilvitskii, “k-means++: The advantages of careful seeding,” in Proceedings of ACM-SIAM symposium on Discrete algorithms (SIAM, 2007), pp. 1027–1035.

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Figures (6)

Fig. 1
Fig. 1 The PSNR of the proposed method under different parameters. (a) influence of parameter η. (b) influence of parameter γ.
Fig. 2
Fig. 2 Reference images. (a) pig eye data. (b) human retinal data.
Fig. 3
Fig. 3 The despeckled results of deferent methods. (a) Noisy image. (b) Averaged image (three frames). (c)–(h) Results of MSBTD method, PNLM method, Baysian method, complex diffusion method, multi-frame wavelet method and the proposed method.
Fig. 4
Fig. 4 Closeups of the red rectangle region in Fig. 3(a). (a) Noisy image. (b) Averaged image (three frames). (c)–(h) Results of MSBTD method, PNLM method, Baysian method, complex diffusion method, multi-frame wavelet method and the proposed method.
Fig. 5
Fig. 5 The despeckled results of different methods. (a) Noisy image. (b) Averaged image (five frames). (c)–(h) Results of MSBTD method, PNLM method, Baysian method, complex diffusion method, multi-frame wavelet method and proposed method.
Fig. 6
Fig. 6 Closeups of the red rectangle region in Fig. 5(a). (a) Noisy image. (b) Averaged image (five frames). (c)–(h) Results of MSBTD method, PNLM method, Baysian method, complex diffusion method, multi-frame wavelet method and proposed method.

Tables (4)

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Algorithm 1 MPCA transform

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Algorithm 2 Proposed multi-frame OCT images denoising method

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Table 1 Performance metrics for different methods operating on the pig eye data.

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Table 2 Performance metrics for different methods operating on the human retinal data.

Equations (17)

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𝒜 = 𝒮 × 1 U ( 1 ) × 2 U ( 2 ) × × N U ( N )
A ( n ) = U ( n ) S ( n ) ( U ( n + 1 ) U ( n + 2 ) U ( N ) U ( 1 ) U ( 2 ) U ( n 1 ) ) T
Y = [ y 1 1 y 2 1 y n 1 y 1 2 y 2 2 y n 2 y 1 m y 2 m y n m ]
min U ( 1 ) , U ( 2 ) , U ( 3 ) , 𝒮 i k i = 1 n k 𝒴 i k 𝒮 i k × 1 U ( 1 ) × 2 U ( 2 ) × 3 U ( 3 ) F 2 s . t . U ( 1 ) T U ( 1 ) = I h , U ( 2 ) T U ( 2 ) = I w , U ( 3 ) T U ( 3 ) = I S
max U ( 1 ) , U ( 2 ) , U ( 3 ) i = 1 n k 𝒴 i k × 1 U ( 1 ) T × 2 U ( 2 ) T × 3 U ( 3 ) T F 2 s . t . U ( 1 ) T U ( 1 ) = I h , U ( 2 ) T U ( 2 ) = I w , U ( 3 ) T U ( 3 ) = I S
Φ ( n ) = i = 1 n k Y i ( n ) k U Φ ( n ) U Φ ( n ) T Y i ( n ) k T
U Φ ( n ) = ( U ( n + 1 ) U ( n + 2 ) U ( N ) U ( 1 ) U ( 2 ) U ( n 1 ) )
𝒴 i k = i 1 = 1 h i 2 = 1 w i 3 = 1 S 𝒮 i k ( i 1 , i 2 , i 3 ) u i 1 ( 1 ) u i 2 ( 2 ) u i 3 ( 3 )
𝒮 ^ i k = 𝒲 k 𝒮 i k
𝒲 k ( i 1 , i 2 , i 3 ) = max ( i = 1 n k ( 𝒮 i k ( i 1 , i 2 , i 3 ) ) 2 / n k σ 2 i = 1 n k ( 𝒮 i k ( i 1 , i 2 , i 3 ) ) 2 / n k , 0 )
𝒳 ^ i k = 𝒮 ^ i k × 1 U ( 1 ) × 2 U ( 2 ) × 3 U ( 3 ) , i = 1 , 2 , , n k
𝒴 t = 𝒳 ^ t 1 + η ( 𝒴 𝒳 ^ t 1 )
σ ^ t = γ σ 2 𝒴 𝒴 t 2 2
XCOR = j = 1 N I j I ^ j [ j = 1 N I j 2 ] [ j = 1 N I ^ j 2 ]
PSNR = 10 × log 10 ( MAX 2 1 N j = 1 N ( I j I ^ j ) 2 )
CNR = | μ f μ b | 0.5 ( σ f 2 + σ b 2 )
ENL = μ f 2 σ f 2

Metrics