Abstract

Light field microscopy, featuring with snapshot large-scale three-dimensional (3D) fluorescence imaging, has aroused great interests in various biological applications, especially for high-speed 3D calcium imaging. Traditional 3D deconvolution algorithms based on the beam propagation model facilitate high-resolution 3D reconstructions. However, such a high-precision model is not robust enough for the experimental data with different system errors such as optical aberrations and background fluorescence, which bring great periodic artifacts and reduce the image contrast. In order to solve this problem, here we propose a phase-space deconvolution method for light field microscopy, which fully exploits the smoothness prior in the phase-space domain. By modeling the imaging process in the phase-space domain, we convert the spatially-nonuniform point spread function (PSF) into a spatially-uniform one with a much smaller size. Experiments on various biological samples and resolution charts are demonstrated to verify the contrast enhancement with much fewer artifacts and 10-times less computational cost by our method without any hardware modifications required.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2018 (6)

M. Shaw, H. Zhan, M. Elmi, V. Pawar, C. Essmann, and M. A. Srinivasan, “Three-dimensional behavioural phenotyping of freely moving C. elegans using quantitative light field microscopy,” PLoS One 13(7), e0200108 (2018).
[Crossref] [PubMed]

M. Martínez-Corral and B. Javidi, “Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems,” Adv. Opt. Photonics 10(3), 512 (2018).
[Crossref]

H. Li, C. Guo, D. Kim-Holzapfel, W. Li, Y. Altshuller, B. Schroeder, W. Liu, Y. Meng, J. B. French, K.-I. Takamaru, M. A. Frohman, and S. Jia, “Fast, volumetric live-cell imaging using high-resolution light-field microscopy,” Biomed. Opt. Express 10(1), 29–49 (2018).
[Crossref] [PubMed]

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
[PubMed]

M. A. Taylor, T. Nöbauer, A. Pernia-Andrade, F. Schlumm, and A. Vaziri, “Brain-wide 3D light-field imaging of neuronal activity with speckle-enhanced resolution,” Optica 5(4), 345 (2018).
[Crossref]

2017 (6)

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

J. Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “TrackMate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref] [PubMed]

H.-Y. Liu, J. Zhong, and L. Waller, “Multiplexed phase-space imaging for 3D fluorescence microscopy,” Opt. Express 25(13), 14986–14995 (2017).
[Crossref] [PubMed]

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref] [PubMed]

Z. Xiao, Q. Wang, G. Zhou, and J. Yu, “Aliasing Detection and Reduction Scheme on Angularly Undersampled Light Fields,” IEEE Trans. Image Process. 26(5), 2103–2115 (2017).
[Crossref] [PubMed]

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
[Crossref] [PubMed]

2016 (4)

J. Wu, B. Xiong, X. Lin, J. He, J. Suo, and Q. Dai, “Snapshot hyperspectral volumetric microscopy,” Sci. Rep. 6(1), 24624 (2016).
[Crossref] [PubMed]

E. Lee, S. Yang, M. Han, and J. Kim, “Depth-based refocusing for reducing directional aliasing artifacts,” Opt. Express 24(24), 28065–28079 (2016).
[Crossref] [PubMed]

X. Ou, J. Chung, R. Horstmeyer, and C. Yang, “Aperture scanning Fourier ptychographic microscopy,” Biomed. Opt. Express 7(8), 3140–3150 (2016).
[Crossref] [PubMed]

C. J. Niedworok, A. P. Y. Brown, M. Jorge Cardoso, P. Osten, S. Ourselin, M. Modat, and T. W. Margrie, “aMAP is a validated pipeline for registration and segmentation of high-resolution mouse brain data,” Nat. Commun. 7(1), 11879 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (2)

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

N. Cohen, S. Yang, A. Andalman, M. Broxton, L. Grosenick, K. Deisseroth, M. Horowitz, and M. Levoy, “Enhancing the performance of the light field microscope using wavefront coding,” Opt. Express 22(20), 24817–24839 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[Crossref]

T. T. Do, L. Gan, N. H. Nguyen, and T. D. Tran, “Fast and efficient compressive sensing using structurally random matrices,” IEEE Trans. Signal Process. 60(1), 139–154 (2012).
[Crossref]

C. Brede, M. Friedrich, A. L. Jordán-Garrote, S. S. Riedel, C. A. Bäuerlein, K. G. Heinze, T. Bopp, S. Schulz, A. Mottok, C. Kiesel, K. Mattenheimer, M. Ritz, V. von Krosigk, A. Rosenwald, H. Einsele, R. S. Negrin, G. S. Harms, and A. Beilhack, “Mapping immune processes in intact tissues at cellular resolution,” J. Clin. Invest. 122(12), 4439–4446 (2012).
[Crossref] [PubMed]

2009 (1)

2006 (1)

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

1981 (1)

R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Signal Process. Speech, and Signal Processing 29(6), 1153–1160 (1981).
[Crossref]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

Altshuller, Y.

Andalman, A.

Bai, L.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref] [PubMed]

Ball, G.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

Bäuerlein, C. A.

C. Brede, M. Friedrich, A. L. Jordán-Garrote, S. S. Riedel, C. A. Bäuerlein, K. G. Heinze, T. Bopp, S. Schulz, A. Mottok, C. Kiesel, K. Mattenheimer, M. Ritz, V. von Krosigk, A. Rosenwald, H. Einsele, R. S. Negrin, G. S. Harms, and A. Beilhack, “Mapping immune processes in intact tissues at cellular resolution,” J. Clin. Invest. 122(12), 4439–4446 (2012).
[Crossref] [PubMed]

Bednarek, S. Y.

J. Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “TrackMate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref] [PubMed]

Beilhack, A.

C. Brede, M. Friedrich, A. L. Jordán-Garrote, S. S. Riedel, C. A. Bäuerlein, K. G. Heinze, T. Bopp, S. Schulz, A. Mottok, C. Kiesel, K. Mattenheimer, M. Ritz, V. von Krosigk, A. Rosenwald, H. Einsele, R. S. Negrin, G. S. Harms, and A. Beilhack, “Mapping immune processes in intact tissues at cellular resolution,” J. Clin. Invest. 122(12), 4439–4446 (2012).
[Crossref] [PubMed]

Betzig, E.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
[PubMed]

Bopp, T.

C. Brede, M. Friedrich, A. L. Jordán-Garrote, S. S. Riedel, C. A. Bäuerlein, K. G. Heinze, T. Bopp, S. Schulz, A. Mottok, C. Kiesel, K. Mattenheimer, M. Ritz, V. von Krosigk, A. Rosenwald, H. Einsele, R. S. Negrin, G. S. Harms, and A. Beilhack, “Mapping immune processes in intact tissues at cellular resolution,” J. Clin. Invest. 122(12), 4439–4446 (2012).
[Crossref] [PubMed]

Boyden, E. S.

R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

Brede, C.

C. Brede, M. Friedrich, A. L. Jordán-Garrote, S. S. Riedel, C. A. Bäuerlein, K. G. Heinze, T. Bopp, S. Schulz, A. Mottok, C. Kiesel, K. Mattenheimer, M. Ritz, V. von Krosigk, A. Rosenwald, H. Einsele, R. S. Negrin, G. S. Harms, and A. Beilhack, “Mapping immune processes in intact tissues at cellular resolution,” J. Clin. Invest. 122(12), 4439–4446 (2012).
[Crossref] [PubMed]

Brown, A. P. Y.

C. J. Niedworok, A. P. Y. Brown, M. Jorge Cardoso, P. Osten, S. Ourselin, M. Modat, and T. W. Margrie, “aMAP is a validated pipeline for registration and segmentation of high-resolution mouse brain data,” Nat. Commun. 7(1), 11879 (2016).
[Crossref] [PubMed]

Broxton, M.

Chai, Y.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref] [PubMed]

Chen, L.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Biotechnol. 36(5), 451–459 (2018).
[Crossref] [PubMed]

Chung, J.

Cohen, N.

Collins, Z. M.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
[PubMed]

Cong, L.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref] [PubMed]

Cunniff, B.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
[PubMed]

Dai, Q.

J. Wu, B. Xiong, X. Lin, J. He, J. Suo, and Q. Dai, “Snapshot hyperspectral volumetric microscopy,” Sci. Rep. 6(1), 24624 (2016).
[Crossref] [PubMed]

X. Lin, J. Wu, G. Zheng, and Q. Dai, “Camera array based light field microscopy,” Biomed. Opt. Express 6(9), 3179–3189 (2015).
[Crossref] [PubMed]

Dambournet, D.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
[PubMed]

Deisseroth, K.

Demmerle, J.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

Do, T. T.

T. T. Do, L. Gan, N. H. Nguyen, and T. D. Tran, “Fast and efficient compressive sensing using structurally random matrices,” IEEE Trans. Signal Process. 60(1), 139–154 (2012).
[Crossref]

Dobbie, I. M.

J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
[Crossref] [PubMed]

Drubin, D. G.

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J. Demmerle, C. Innocent, A. J. North, G. Ball, M. Müller, E. Miron, A. Matsuda, I. M. Dobbie, Y. Markaki, and L. Schermelleh, “Strategic and practical guidelines for successful structured illumination microscopy,” Nat. Protoc. 12(5), 988–1010 (2017).
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Pernía-Andrade, A. J.

T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
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R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
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Scholpp, S.

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M. Shaw, H. Zhan, M. Elmi, V. Pawar, C. Essmann, and M. A. Srinivasan, “Three-dimensional behavioural phenotyping of freely moving C. elegans using quantitative light field microscopy,” PLoS One 13(7), e0200108 (2018).
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J. Wu, B. Xiong, X. Lin, J. He, J. Suo, and Q. Dai, “Snapshot hyperspectral volumetric microscopy,” Sci. Rep. 6(1), 24624 (2016).
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T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
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T. T. Do, L. Gan, N. H. Nguyen, and T. D. Tran, “Fast and efficient compressive sensing using structurally random matrices,” IEEE Trans. Signal Process. 60(1), 139–154 (2012).
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T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. M. Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14(8), 811–818 (2017).
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T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
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M. A. Taylor, T. Nöbauer, A. Pernia-Andrade, F. Schlumm, and A. Vaziri, “Brain-wide 3D light-field imaging of neuronal activity with speckle-enhanced resolution,” Optica 5(4), 345 (2018).
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Waller, L.

Wang, K.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
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Z. Xiao, Q. Wang, G. Zhou, and J. Yu, “Aliasing Detection and Reduction Scheme on Angularly Undersampled Light Fields,” IEEE Trans. Image Process. 26(5), 2103–2115 (2017).
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R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
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J. Wu, B. Xiong, X. Lin, J. He, J. Suo, and Q. Dai, “Snapshot hyperspectral volumetric microscopy,” Sci. Rep. 6(1), 24624 (2016).
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Z. Xiao, Q. Wang, G. Zhou, and J. Yu, “Aliasing Detection and Reduction Scheme on Angularly Undersampled Light Fields,” IEEE Trans. Image Process. 26(5), 2103–2115 (2017).
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J. Wu, B. Xiong, X. Lin, J. He, J. Suo, and Q. Dai, “Snapshot hyperspectral volumetric microscopy,” Sci. Rep. 6(1), 24624 (2016).
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Yang, W.

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Yashiro, H.

T. L. Liu, S. Upadhyayula, D. E. Milkie, V. Singh, K. Wang, I. A. Swinburne, K. R. Mosaliganti, Z. M. Collins, T. W. Hiscock, J. Shea, A. Q. Kohrman, T. N. Medwig, D. Dambournet, R. Forster, B. Cunniff, Y. Ruan, H. Yashiro, S. Scholpp, E. M. Meyerowitz, D. Hockemeyer, D. G. Drubin, B. L. Martin, D. Q. Matus, M. Koyama, S. G. Megason, T. Kirchhausen, and E. Betzig, “Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms,” Science 360(6386), 1392 (2018).
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R. Prevedel, Y.-G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
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Z. Xiao, Q. Wang, G. Zhou, and J. Yu, “Aliasing Detection and Reduction Scheme on Angularly Undersampled Light Fields,” IEEE Trans. Image Process. 26(5), 2103–2115 (2017).
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Supplementary Material (2)

NameDescription
» Code 1       Matlab code for "Phase-space deconvolution for light field microscopy"
» Visualization 1       The dynamics of a freely-moving histone-labeled C. elegans imaged at 50 volumes per second.

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Figures (7)

Fig. 1
Fig. 1 Schematic of the experimental setup and the principle of phase-space deconvolution. (a) The schematic of the experimental setup with illustrations showing the preprocessing procedures for phase-space deconvolution. Different spatial frequency components (marked with different colors) are extracted from LFM raw data into higher dimensions, followed with an up-sampling interpolation for high-resolution reconstruction. (b) The axial slice (at z = 5 μm) of the traditional point spread function (PSF) used in 3D deconvolution for LFM, with a cross-section profile to show its large size and periodic patterns. (c) The axial slices (at z = 5 μm) of the PSFs after realignment used in phase-space deconvolution for two typical spatial frequency components, with the cross-section profiles to show the small size and smooth property. Scale bar, 10 μm.
Fig. 2
Fig. 2 Pipeline of the phase-space deconvolution algorithm. (a) The procedures to calculate the PSFs used for phase-space deconvolution, with typical examples of the output for each step. (b) The pre-processing procedures applied to the captured light field image with typical outputs for each step. We first realign the pixels according to the coordinates defined in phase space and then up-sampling the phase-space measurements with sub-aperture filtering to apply the smooth prior in phase space. (c) The procedures of the iterative reconstruction with typical outputs for each step. Within each iteration, we update the volume with different spatial frequency components sequentially by the corresponding PSFs and preprocessed measurements.
Fig. 3
Fig. 3 Numerical simulations for quantitative analysis of reconstruction performance and convergence speed. (a) Different axial slices (arranged from left to right with depth marked on the top) reconstructed by the traditional 3D RL deconvolution (first row), the traditional 3D RL deconvolution with TV regularization (second row), the phase-space deconvolution (third row), and the phase-space deconvolution with TV regularization (fourth row) at highest SNR, together with the ground truth for comparison (fifth row). Scale bar, 10 μm. (b) The SNR-versus-iteration curve illustrates that the phase-space deconvolution has much faster convergence speed and more robust performance than the traditional 3D RL deconvolution for LFM reconstruction. And TV regularization improves reconstructed SNR slightly with better robustness to overfitting. (c) The SNR-versus-time curve shows an ~11 times reduction in computation cost for the phase-space deconvolution (with or without TV regularization) compared with the traditional 3D RL deconvolution, taking 6dB SNR (dashed line) for reference. And the advanced optimization method with TV regularization will slow down both algorithms similarly.
Fig. 4
Fig. 4 Performance comparison on the GFP-labeled B16 cell. The orthogonal maximum intensity projections (MIP) of the reconstructed LFM volume with the 3D RL deconvolution using 2 iterations and 20 iterations are shown in (a) and (b) respectively. (c) The orthogonal MIPs of the reconstructed LFM volume with our phase-space deconvolution (2 iterations), showing no artifacts and more subcellular structures. (d) The orthogonal MIPs of the reconstructed volume by the wide-field deconvolution microscopy with axial scanning (300 iterations). Different axial slices close to the native object plane at different depths from the reconstructed volume are shown on the right for all the methods. Both deconvolution algorithms show the optical sectioning ability of LFM, while our phase-space deconvolution has no artifacts and achieves much higher contrast than the traditional 3D RL deconvolution. Scale bars, 10 μm.
Fig. 5
Fig. 5 The dynamics of a freely-moving histone-labeled C. elegans imaged at 50 volumes per second. The reconstructed orthogonal MIPs at one time stamp by the 3D RL deconvolution using 2 iterations and 20 iterations are shown in (a) and (b) respectively. Zoom-in views of the marked yellow box at different time stamps are shown on the right. Reconstruction by traditional 3D RL deconvolution with low iteration numbers has a low spatial resolution, while higher iteration numbers will induce more artifacts. (c) The reconstructed orthogonal MIPs by the phase-space deconvolution (2 iterations). The zoom-in views in the same area are shown on the right. Higher image contrast in both xy and xz planes can be observed with no artifacts and much less computation time. Scale bars, 10 μm.
Fig. 6
Fig. 6 Contrast comparison by imaging a USAF-1951 resolution chart. The resolution chart is placed at different axial planes away from the native object plane (z = 0 μm) and imaged using the LFM with a 10 × 0.3NA dry objective. (a-c) The reconstructed in-focus plane (z = −150 μm) by 3D RL deconvolution with 2 iterations, with 5 iterations, and phase-space deconvolution with 2 iterations, respectively. (d-f) The reconstructed in-focus plane (z = 0 μm) by 3D RL deconvolution algorithm with 2 iterations, with 5 iterations, and phase-space deconvolution with 2 iterations, respectively. The cross-section profiles of the marked yellow lines in a-f are shown on the right. (g) The modulation transfer function (MTF) of the line pairs (group 5 line 6) in the resolution chart placed at different axial positions. Scale bar, 100 μm.
Fig. 7
Fig. 7 Performance comparison on the GFP-labeled B16 tumor spheroid with strong background fluorescence. (a-c) The orthogonal maximum intensity projections (MIPs) of the reconstructed volume by the 3D RL deconvolution with 2 iterations, with 20 iterations, and phase-space deconvolution with 2 iterations, respectively. (d-f) Different axial slices of the reconstructed volumes with the depths marked at the bottom and the algorithms in the left. Scale bars, 10 μm.

Equations (15)

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h p (x,p,z,u)= ω xx K z F ω x-x { U z (xp)t(xx) }s(u) 2 2 d ω xx ,
U z (xp)= M f obj 2 λ 2 exp( i 2π λ z ) 0 α cosθ exp( i 4πz sin 2 (θ/2) λ ) J 0 ( 2πsin( θ ) λ ( x 1 p 1 ) 2 + ( x 1 p 2 ) 2 )sin( θ )dθ,
h p (x,p,z,u)= xx K z { U z (xp)t(xx) } F x-x -1 ( s(u) ) 2 2 d( xx ) x=x-x _ _ K z x { U z (x+xp)t(x) } F x -1 ( s(u) ) 2 2 dx,
LF( x )= z p g( p,z ) | h l (x+u,p,z) | 2 dpdz ,
WDF( x,u )=cubic( WD F L ( x,u ) )filte r u ,
WDF( x,u )= z p g( p,z ) | h p (x,p,z,u) | 2 dpdz .
H i,j,k = β i ( α j γ k | h p ( x,p,z,u ) | 2 dudx )dpdz ,
Y j,k = α j γ k WDF( x,u )dudx ,
X i = β i g(p,z)dpdz .
Y j,k = i X i H i,j,k , k={ Ω| ( k 1 , k 2 )Ω },
Y ˜ j,k =Pois( i X i H i,j,k ),
X i (k,iter) ( 1-c w k ) X i (k-1,iter) +c w k X i (k-1,iter) ( j ( Y ˜ j,k ./( i X i (k-1,iter) H i,j,k ) ) H i, N j -j,k )./ ( j 1 H i, N j -j,k ) ,
w k = i H i,k 1 kΩ i H i,k 1 .
10 log 10 ||X| | 2 2 ||XY| | 2 2 ,

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