Abstract

Laser Doppler holography (LDH) is a full-field interferometric imaging technique recently applied in ophthalmology to measure blood flow, a parameter of high clinical interest. From the temporal fluctuations of digital holograms acquired at ultrafast frame rates, LDH reveals retinal and choroidal blood flow with a few milliseconds of temporal resolution. However, LDH experiences difficulties to detect slower blood flow as it requires to work with low Doppler frequency shifts which are corrupted by eye motion. We here demonstrate the use of a spatio-temporal decomposition adapted from Doppler ultrasound that provides a basis appropriate to the discrimination of blood flow from eye motion. A singular value decomposition (SVD) can be used as a simple, robust, and efficient way to separate the Doppler fluctuations of blood flow from those of strong spatial coherence such as eye motion. We show that the SVD outperforms the conventional Fourier based filter to reveal slower blood flow, and dramatically improves the ability of LDH to reveal vessels of smaller size or with a pathologically reduced blood flow.

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

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    [Crossref]
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    [Crossref]

2019 (3)

2018 (3)

2017 (3)

G. S. Alberti, H. Ammari, F. Romero, and T. Wintz, “Mathematical analysis of ultrafast ultrasound imaging,” SIAM J. Appl. Math. 77(1), 1–25 (2017).
[Crossref]

A. Baghaie, Z. Yu, and R. M. D Souza, “Involuntary eye motion correction in retinal optical coherence tomography: Hardware or software solution?” Med. Image Anal. 37, 129–145 (2017).
[Crossref]

C. Pfäffle, H. Spahr, D. Hillmann, H. Sudkamp, G. Franke, P. Koch, and G. Hüttmann, “Reduction of frame rate in full-field swept-source optical coherence tomography by numerical motion correction,” Biomed. Opt. Express 8(3), 1499–1511 (2017).
[Crossref]

2016 (2)

2015 (2)

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

R. Otazo, E. Candes, and D. K. Sodickson, “Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components,” Magn. Reson. Med. 73(3), 1125–1136 (2015).
[Crossref]

2014 (6)

M. Tanter and M. Fink, “Ultrafast imaging in biomedical ultrasound,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 61(1), 102–119 (2014).
[Crossref]

R. A. Leitgeb, R. M. Werkmeister, C. Blatter, and L. Schmetterer, “Doppler optical coherence tomography,” Prog. Retinal Eye Res. 41, 26–43 (2014).
[Crossref]

C. Magnain, A. Castel, T. Boucneau, M. Simonutti, I. Ferezou, A. Rancillac, T. Vitalis, J.-A. Sahel, M. Paques, and M. Atlan, “Holographic laser Doppler imaging of microvascular blood flow,” J. Opt. Soc. Am. A 31(12), 2723–2735 (2014).
[Crossref]

R. J. Zawadzki, A. G. Capps, D. Y. Kim, A. Panorgias, S. B. Stevenson, B. Hamann, and J. S. Werner, “Progress on developing adaptive optics–optical coherence tomography for in vivo retinal imaging: monitoring and correction of eye motion artifacts,” IEEE J. Sel. Top. Quantum Electron. 20(2), 322–333 (2014).
[Crossref]

M. F. Kraus, J. J. Liu, J. Schottenhamml, C.-L. Chen, A. Budai, L. Branchini, T. Ko, H. Ishikawa, G. Wollstein, J. Schuman, J. S. Duker, J. G. Fujimoto, and J. Hornegger, “Quantitative 3D-OCT motion correction with tilt and illumination correction, robust similarity measure and regularization,” Biomed. Opt. Express 5(8), 2591–2613 (2014).
[Crossref]

X. Liu, M. Kirby, and F. Zhao, “Motion analysis and removal in intensity variation based OCT angiography,” Biomed. Opt. Express 5(11), 3833–3847 (2014).
[Crossref]

2011 (1)

H. Gao, H. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (prism),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

2010 (2)

M. Simonutti, M. Paques, J. A. Sahel, M. Gross, B. Samson, C. Magnain, and M. Atlan, “Holographic laser doppler ophthalmoscopy,” Opt. Lett. 35(12), 1941–1943 (2010).
[Crossref]

K. Singh, C. Dion, S. Costantino, M. Wajszilber, M. Lesk, and T. Ozaki, “Development of a novel instrument to measure the pulsatile movement of ocular tissues,” Exp. Eye Res. 91(1), 63–68 (2010).
[Crossref]

2006 (2)

S. Martinez-Conde, “Fixational eye movements in normal and pathological vision,” Prog. Brain Res. 154, 151–176 (2006).
[Crossref]

S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14(17), 7821–7840 (2006).
[Crossref]

2005 (1)

M. Paques, O. Baillart, O. Genevois, A. Gaudric, B. Lévy, and J. Sahel, “Systolodiastolic variations of blood flow during central retinal vein occlusion: exploration by dynamic angiography,” Br. J. Ophthalmol. 89(8), 1036–1040 (2005).
[Crossref]

Alberti, G. S.

G. S. Alberti, H. Ammari, F. Romero, and T. Wintz, “Mathematical analysis of ultrafast ultrasound imaging,” SIAM J. Appl. Math. 77(1), 1–25 (2017).
[Crossref]

Ammari, H.

G. S. Alberti, H. Ammari, F. Romero, and T. Wintz, “Mathematical analysis of ultrafast ultrasound imaging,” SIAM J. Appl. Math. 77(1), 1–25 (2017).
[Crossref]

Arnal, B.

J. Baranger, B. Arnal, F. Perren, O. Baud, M. Tanter, and C. Demené, “Adaptive spatiotemporal svd clutter filtering for ultrafast Doppler imaging using similarity of spatial singular vectors,” IEEE Trans. Med. Imaging 37(7), 1574–1586 (2018).
[Crossref]

Atlan, M.

Baghaie, A.

A. Baghaie, Z. Yu, and R. M. D Souza, “Involuntary eye motion correction in retinal optical coherence tomography: Hardware or software solution?” Med. Image Anal. 37, 129–145 (2017).
[Crossref]

Baillart, O.

M. Paques, O. Baillart, O. Genevois, A. Gaudric, B. Lévy, and J. Sahel, “Systolodiastolic variations of blood flow during central retinal vein occlusion: exploration by dynamic angiography,” Br. J. Ophthalmol. 89(8), 1036–1040 (2005).
[Crossref]

Baranger, J.

J. Baranger, B. Arnal, F. Perren, O. Baud, M. Tanter, and C. Demené, “Adaptive spatiotemporal svd clutter filtering for ultrafast Doppler imaging using similarity of spatial singular vectors,” IEEE Trans. Med. Imaging 37(7), 1574–1586 (2018).
[Crossref]

Baud, O.

J. Baranger, B. Arnal, F. Perren, O. Baud, M. Tanter, and C. Demené, “Adaptive spatiotemporal svd clutter filtering for ultrafast Doppler imaging using similarity of spatial singular vectors,” IEEE Trans. Med. Imaging 37(7), 1574–1586 (2018).
[Crossref]

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Bergel, A.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Biran, V.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Blatter, C.

R. A. Leitgeb, R. M. Werkmeister, C. Blatter, and L. Schmetterer, “Doppler optical coherence tomography,” Prog. Retinal Eye Res. 41, 26–43 (2014).
[Crossref]

Boucneau, T.

Branchini, L.

Budai, A.

Camino, A.

Candes, E.

R. Otazo, E. Candes, and D. K. Sodickson, “Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components,” Magn. Reson. Med. 73(3), 1125–1136 (2015).
[Crossref]

Capps, A. G.

R. J. Zawadzki, A. G. Capps, D. Y. Kim, A. Panorgias, S. B. Stevenson, B. Hamann, and J. S. Werner, “Progress on developing adaptive optics–optical coherence tomography for in vivo retinal imaging: monitoring and correction of eye motion artifacts,” IEEE J. Sel. Top. Quantum Electron. 20(2), 322–333 (2014).
[Crossref]

Castel, A.

Chen, C.-L.

Chen, Y.

Cohen, I.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Correas, J.-M.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Costantino, S.

K. Singh, C. Dion, S. Costantino, M. Wajszilber, M. Lesk, and T. Ozaki, “Development of a novel instrument to measure the pulsatile movement of ocular tissues,” Exp. Eye Res. 91(1), 63–68 (2010).
[Crossref]

D Souza, R. M.

A. Baghaie, Z. Yu, and R. M. D Souza, “Involuntary eye motion correction in retinal optical coherence tomography: Hardware or software solution?” Med. Image Anal. 37, 129–145 (2017).
[Crossref]

Deffieux, T.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Degardin, J.

Demené, C.

J. Baranger, B. Arnal, F. Perren, O. Baud, M. Tanter, and C. Demené, “Adaptive spatiotemporal svd clutter filtering for ultrafast Doppler imaging using similarity of spatial singular vectors,” IEEE Trans. Med. Imaging 37(7), 1574–1586 (2018).
[Crossref]

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Dion, C.

K. Singh, C. Dion, S. Costantino, M. Wajszilber, M. Lesk, and T. Ozaki, “Development of a novel instrument to measure the pulsatile movement of ocular tissues,” Exp. Eye Res. 91(1), 63–68 (2010).
[Crossref]

Duker, J. S.

Ferezou, I.

Fink, M.

Franke, G.

Franqui, S.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Fujimoto, J. G.

Gao, H.

H. Gao, H. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (prism),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

Gao, S. S.

Gaudric, A.

M. Paques, O. Baillart, O. Genevois, A. Gaudric, B. Lévy, and J. Sahel, “Systolodiastolic variations of blood flow during central retinal vein occlusion: exploration by dynamic angiography,” Br. J. Ophthalmol. 89(8), 1036–1040 (2005).
[Crossref]

Genevois, O.

M. Paques, O. Baillart, O. Genevois, A. Gaudric, B. Lévy, and J. Sahel, “Systolodiastolic variations of blood flow during central retinal vein occlusion: exploration by dynamic angiography,” Br. J. Ophthalmol. 89(8), 1036–1040 (2005).
[Crossref]

Gennisson, J.-L.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Gross, M.

Hamann, B.

R. J. Zawadzki, A. G. Capps, D. Y. Kim, A. Panorgias, S. B. Stevenson, B. Hamann, and J. S. Werner, “Progress on developing adaptive optics–optical coherence tomography for in vivo retinal imaging: monitoring and correction of eye motion artifacts,” IEEE J. Sel. Top. Quantum Electron. 20(2), 322–333 (2014).
[Crossref]

Hillmann, D.

Hong, Y.

Hong, Y.-J.

Hornegger, J.

Huang, D.

Hüttmann, G.

Hwang, T. S.

Ishikawa, H.

Jia, Y.

Kim, D. Y.

R. J. Zawadzki, A. G. Capps, D. Y. Kim, A. Panorgias, S. B. Stevenson, B. Hamann, and J. S. Werner, “Progress on developing adaptive optics–optical coherence tomography for in vivo retinal imaging: monitoring and correction of eye motion artifacts,” IEEE J. Sel. Top. Quantum Electron. 20(2), 322–333 (2014).
[Crossref]

Kirby, M.

Ko, T.

Koch, P.

Kraus, M. F.

Leitgeb, R. A.

R. A. Leitgeb, R. M. Werkmeister, C. Blatter, and L. Schmetterer, “Doppler optical coherence tomography,” Prog. Retinal Eye Res. 41, 26–43 (2014).
[Crossref]

Lesk, M.

K. Singh, C. Dion, S. Costantino, M. Wajszilber, M. Lesk, and T. Ozaki, “Development of a novel instrument to measure the pulsatile movement of ocular tissues,” Exp. Eye Res. 91(1), 63–68 (2010).
[Crossref]

Lévy, B.

M. Paques, O. Baillart, O. Genevois, A. Gaudric, B. Lévy, and J. Sahel, “Systolodiastolic variations of blood flow during central retinal vein occlusion: exploration by dynamic angiography,” Br. J. Ophthalmol. 89(8), 1036–1040 (2005).
[Crossref]

Liu, J. J.

Liu, X.

Magnain, C.

Makita, S.

Martinez-Conde, S.

S. Martinez-Conde, “Fixational eye movements in normal and pathological vision,” Prog. Brain Res. 154, 151–176 (2006).
[Crossref]

Osher, S.

H. Gao, H. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (prism),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

Osmanski, B.-F.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Otazo, R.

R. Otazo, E. Candes, and D. K. Sodickson, “Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components,” Magn. Reson. Med. 73(3), 1125–1136 (2015).
[Crossref]

Ozaki, T.

K. Singh, C. Dion, S. Costantino, M. Wajszilber, M. Lesk, and T. Ozaki, “Development of a novel instrument to measure the pulsatile movement of ocular tissues,” Exp. Eye Res. 91(1), 63–68 (2010).
[Crossref]

Panorgias, A.

R. J. Zawadzki, A. G. Capps, D. Y. Kim, A. Panorgias, S. B. Stevenson, B. Hamann, and J. S. Werner, “Progress on developing adaptive optics–optical coherence tomography for in vivo retinal imaging: monitoring and correction of eye motion artifacts,” IEEE J. Sel. Top. Quantum Electron. 20(2), 322–333 (2014).
[Crossref]

Paques, M.

Pellizzari, M.

Pernot, M.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Perren, F.

J. Baranger, B. Arnal, F. Perren, O. Baud, M. Tanter, and C. Demené, “Adaptive spatiotemporal svd clutter filtering for ultrafast Doppler imaging using similarity of spatial singular vectors,” IEEE Trans. Med. Imaging 37(7), 1574–1586 (2018).
[Crossref]

Pfäffle, C.

Puyo, L.

Rancillac, A.

Romero, F.

G. S. Alberti, H. Ammari, F. Romero, and T. Wintz, “Mathematical analysis of ultrafast ultrasound imaging,” SIAM J. Appl. Math. 77(1), 1–25 (2017).
[Crossref]

Sahel, J.

M. Paques, O. Baillart, O. Genevois, A. Gaudric, B. Lévy, and J. Sahel, “Systolodiastolic variations of blood flow during central retinal vein occlusion: exploration by dynamic angiography,” Br. J. Ophthalmol. 89(8), 1036–1040 (2005).
[Crossref]

Sahel, J. A.

Sahel, J.-A.

Samson, B.

Schmetterer, L.

R. A. Leitgeb, R. M. Werkmeister, C. Blatter, and L. Schmetterer, “Doppler optical coherence tomography,” Prog. Retinal Eye Res. 41, 26–43 (2014).
[Crossref]

Scholler, J.

Schottenhamml, J.

Schuman, J.

Sharma, U.

Sieu, L.-A.

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

Simonutti, M.

Singh, K.

K. Singh, C. Dion, S. Costantino, M. Wajszilber, M. Lesk, and T. Ozaki, “Development of a novel instrument to measure the pulsatile movement of ocular tissues,” Exp. Eye Res. 91(1), 63–68 (2010).
[Crossref]

Sodickson, D. K.

R. Otazo, E. Candes, and D. K. Sodickson, “Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components,” Magn. Reson. Med. 73(3), 1125–1136 (2015).
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Y. Chen, Y.-J. Hong, S. Makita, and Y. Yasuno, “Eye-motion-corrected optical coherence tomography angiography using lissajous scanning,” Biomed. Opt. Express 9(3), 1111–1129 (2018).
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L. Puyo, M. Paques, M. Fink, J.-A. Sahel, and M. Atlan, “Choroidal vasculature imaging with laser Doppler holography,” Biomed. Opt. Express 10(2), 995–1012 (2019).
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K. Singh, C. Dion, S. Costantino, M. Wajszilber, M. Lesk, and T. Ozaki, “Development of a novel instrument to measure the pulsatile movement of ocular tissues,” Exp. Eye Res. 91(1), 63–68 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. J. Zawadzki, A. G. Capps, D. Y. Kim, A. Panorgias, S. B. Stevenson, B. Hamann, and J. S. Werner, “Progress on developing adaptive optics–optical coherence tomography for in vivo retinal imaging: monitoring and correction of eye motion artifacts,” IEEE J. Sel. Top. Quantum Electron. 20(2), 322–333 (2014).
[Crossref]

IEEE Trans. Med. Imaging (2)

C. Demené, T. Deffieux, M. Pernot, B.-F. Osmanski, V. Biran, J.-L. Gennisson, L.-A. Sieu, A. Bergel, S. Franqui, J.-M. Correas, I. Cohen, O. Baud, and M. Tanter, “Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fultrasound sensitivity,” IEEE Trans. Med. Imaging 34(11), 2271–2285 (2015).
[Crossref]

J. Baranger, B. Arnal, F. Perren, O. Baud, M. Tanter, and C. Demené, “Adaptive spatiotemporal svd clutter filtering for ultrafast Doppler imaging using similarity of spatial singular vectors,” IEEE Trans. Med. Imaging 37(7), 1574–1586 (2018).
[Crossref]

IEEE Trans. Ultrason., Ferroelect., Freq. Contr. (1)

M. Tanter and M. Fink, “Ultrafast imaging in biomedical ultrasound,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 61(1), 102–119 (2014).
[Crossref]

Inverse Probl. (1)

H. Gao, H. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (prism),” Inverse Probl. 27(11), 115012 (2011).
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J. Opt. Soc. Am. A (1)

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R. Otazo, E. Candes, and D. K. Sodickson, “Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components,” Magn. Reson. Med. 73(3), 1125–1136 (2015).
[Crossref]

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A. Baghaie, Z. Yu, and R. M. D Souza, “Involuntary eye motion correction in retinal optical coherence tomography: Hardware or software solution?” Med. Image Anal. 37, 129–145 (2017).
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Opt. Express (2)

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S. Martinez-Conde, “Fixational eye movements in normal and pathological vision,” Prog. Brain Res. 154, 151–176 (2006).
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Prog. Retinal Eye Res. (1)

R. A. Leitgeb, R. M. Werkmeister, C. Blatter, and L. Schmetterer, “Doppler optical coherence tomography,” Prog. Retinal Eye Res. 41, 26–43 (2014).
[Crossref]

SIAM J. Appl. Math. (1)

G. S. Alberti, H. Ammari, F. Romero, and T. Wintz, “Mathematical analysis of ultrafast ultrasound imaging,” SIAM J. Appl. Math. 77(1), 1–25 (2017).
[Crossref]

Supplementary Material (2)

NameDescription
» Visualization 1       Power Doppler blood flow movie without/with SVD correction (2-33 kHz)
» Visualization 2       Power Doppler blood flow movie: low (2-6 kHz) and high (6-33 kHz) flow are encoded in red and cyan

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Figures (5)

Fig. 1.
Fig. 1. Singular value decomposition (SVD). (a) The 3D matrix of complex-valued holograms $H(x,y,t)$ is reshaped into a 2D space-time matrix, and decomposed in a product of 3 matrices following Eq. (1). $U$ and $V$ are the spatial and temporal eigenvectors, and $\Delta$ is the diagonal matrix of singular values $\lambda _i$. (b) Ordered singular values in dB. (c) Fourier transform magnitude of the temporal eigenvectors weighted by singular values, the arrow indicates high frequency clutter. (d) Individual or averaged spatial eigenvectors: the first vectors show clutter whereas vectors associated to singular values of lower energy reveal blood flow.
Fig. 2.
Fig. 2. Blood flow images improvement thanks to the SVD filtering. The left and right column show the standard power Doppler images and their SVD filtered version in the presence of: (a) retinal motion, (b) corneal reflections, and (c) camera jitter.
Fig. 3.
Fig. 3. Filtering the eye movements with SVD. (a) DPSD in the presence of mild and strong motion, the vertical dashed line indicates the 2 kHz threshold used to calculate the power Doppler. The SVD filtering removes contribution of higher frequencies than the 2 kHz cutoff. (b) Corresponding power Doppler images: in the presence of strong motion the SVD allows to preserve the blood flow signal.(c) Spectrograms ($t_\textrm {win} = 15.3 \; {\rm ms}$): the SVD filter rejects the pulsatile eye motion thus allowing to lower the frequency cutoff. (d) Power Doppler variations in the artery ($t_\textrm {win} = 15.3 \; {\rm ms}$).
Fig. 4.
Fig. 4. Imaging blood flow in a case of retinal vein occlusion. (a) The 10-30 kHz power Doppler image does not show blood flow in the occluded vein. (b) the 1-6 kHz range fails to reveal it because of eye motion. (c) With a SVD filtering the blood flow at low frequency can be revealed. (d) Composite image of the low/high flow in cyan/red; the occluded vessel (arrow) can be easily identified. (e) Composite image of the systole/diastole in orange/blue. (f) Fluorescein angiography in the same region cannot image through the preretinal hemorrhage.
Fig. 5.
Fig. 5. Imaging the choroid with LDH, OCT (Plex Elite 9000, Zeiss), and ICG-angiography (Spectralis, Heidelberg). The LDH montages have been stitched from 5x5 images obtained by fusing the 2-6 and 10-30 kHz frequency ranges in cyan and red. The access to the low frequency range made routinely possible by SVD is critical to reveal choroidal veins.

Equations (5)

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H = U Δ V
H ( x , y , t ) = i = 1 n t λ i U i ( x , y ) V i ( t )
H f ( x , y , t ) = i = n c + 1 n t λ i U i ( x , y ) V i ( t )
S ( x , y , t n , f ) = | t n t n + t win H f ( x , y , τ ) exp ( 2 i π f τ ) d τ | 2
M 0 ( x , y , t n ) = f 1 f 2 S ( x , y , t n , f ) d f

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