Abstract

Optical diffraction tomography (ODT) using Born or Rytov approximation suffers from severe distortions in reconstructed refractive index (RI) tomograms when multiple scattering occurs or the scattering signals are strong. These effects are usually seen as a significant impediment to the application of ODT because multiple scattering is directly linked to an unknown object itself rather than a surrounding medium, and a strong scatter invalidates the underlying assumptions of the Born and Rytov approximations. The focus of this article is to demonstrate for the first time that multiple scattering and high material contrast, if handled aptly, can significantly improve the image quality of the ODT thanks to multiple scattering inside a sample. Experimental verification using various phantom and biological cells substantiates that we not only revealed the structures that were not observable using the conventional approaches but also resolved the long-standing problem of missing cones in the ODT.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

J. Yoo, Y. Jung, M. Lim, J. C. Ye, and A. Wahab, “A joint sparse recovery framework for accurate reconstruction of inclusions in elastic media,” SIAM J. Imag. Sci. 10(3), 1104–1138 (2017).
[Crossref]

2016 (1)

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Transactions on Computational Imaging 2(1), 59–70 (2016).
[Crossref]

2015 (6)

O. K. Lee, H. Kang, J. C. Ye, and M. Lim, “A non-iterative method for the electrical impedance tomography based on joint sparse recovery,” Inverse Probl. 31(7), 075002 (2015).
[Crossref]

J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Optics express 23(13), 16933–16948 (2015).
[Crossref] [PubMed]

H. Ammari and H. Zhang, “Super-resolution in high-contrast media,” Proc. R. Soc. A. 471(2178), 20140946 (2015).
[Crossref]

H. Ammari and H. Zhang, “A mathematical theory of super-resolution by using a system of sub-wavelength Helmholtz resonators,” Commun. Math. Phys. 337(1), 379–428 (2015).
[Crossref]

L. Su, L. Ma, and H. Wang, “Improved regularization reconstruction from sparse angle data in optical diffraction tomography,” Appl. Opt. 54(4), 859–868 (2015).
[Crossref] [PubMed]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

2014 (6)

Y. Kim, H. Shim, K. Kim, H. Park, J. Heo, J. Yoon, C. Choi, S. Jang, and Y. Park, “Common-path diffraction optical tomography for investigation of three-dimensional structures and dynamics of biological cells,” Opt. Express 22(9),10398–10407 (2014).
[Crossref] [PubMed]

K. Kim, Z. Yaqoob, K. Lee, J. Kang, Y. Choi, P. Hosseini, P. So, and Y. Park, “Diffraction optical tomography using a quantitative phase imaging unit,” Opt. Lett. 39(24), 6935–6938 (2014).
[Crossref] [PubMed]

A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
[Crossref]

L. Ma, H. Wang, L. Su, Y. Li, and H. Jin, “Digital holographic microtomography with few angle data-sets,” J. Mod. Opt. 61(14), 1140–1146 (2014).
[Crossref]

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
[Crossref]

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, and K. T. Nam, “Full-field subwavelength imaging using a scattering superlens,” Phys. Rev. Lett. 113, 113901 (2014).
[Crossref] [PubMed]

2013 (8)

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. C. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett.,  111(5), 053902 (2013).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photon. 7, 454–458 (2013).
[Crossref]

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13(23), 4512–4516 (2013).
[Crossref] [PubMed]

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7(2), 113–117 (2013).
[Crossref]

W. Deng, W. Yin, and Y. Zhang, “Group sparse optimization by alternating direction method,” Proc. SPIE 8858, 88580R (2013).
[Crossref]

S. Uttam, S. A. Alexandrov, R. K. Bista, and Y. Liu, “Tomographic imaging via spectral encoding of spatial frequency,” Opt. Express 21(6), 7488–7504 (2013).
[Crossref] [PubMed]

O. Lee and J. C. Ye, “Joint sparsity-driven non-iterative simultaneous reconstruction of absorption and scattering in diffuse optical tomography,” Opt. Express 21(22), 26589–26604 (2013).
[Crossref] [PubMed]

K. Kim, K. Kim, H. Park, J. Ye, and Y. Park, “Real-time visualization of 3-D dynamic microscopic objects using optical diffraction tomography,” Opt. Express 21(26), 32269–32278 (2013).
[Crossref]

2012 (5)

F. de Chaumont, S. Dallongeville, N. Chenouard, N. Hervé, S. Pop, T. Provoost, V. Meas-Yedid, P. Pankajakshan, T. Lecomte, Y. Le Montagner, T. Lagache, A. Dufour, and J.-C. Olivo-Marin, “Icy: an open bioimage informatics platform for extended reproducible research,” Nat. Methods 9(7), 690–696 (2012).
[Crossref] [PubMed]

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37(10), 1631–1633 (2012).
[Crossref] [PubMed]

M. E. Davies and Y. C. Eldar, “Rank awareness in joint sparse recovery,” IEEE Trans. Inf. Theory 58(2), 1135–1146 (2012).
[Crossref]

J. M. Kim, O.K. Lee, and J. C. Ye, “Compressive MUSIC: revisiting the link between compressive sensing and array signal processing,” IEEE Trans. Inf. Theory 58(1), 278–301 (2012).
[Crossref]

J. M. Kim, O. K. Lee, and J. C. Ye, “Improving noise robustness in subspace-based joint sparse recovery,” IEEE Trans. Signal Process. 60(11), 5799–5809 (2012).
[Crossref]

2011 (9)

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. on Medical Imaging 30(5), 1129–1142 (2011).
[Crossref] [PubMed]

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
[Crossref] [PubMed]

O. K. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: non-iterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imag. 30(5), 1129–1142 (2011).
[Crossref]

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[Crossref] [PubMed]

F. Lemoult, A. Ourir, J. de Rosny, A. Tourin, M. Fink, and G. Lerosey, “Time reversal in subwavelength-scaled resonant media: beating the diffraction limit,” Int. J. Microw. Sci. Technol. 2011, 425710 (2011).
[Crossref]

F. Lemoult, M. Fink, and G. Lerosey, “Acoustic resonators for far-field control of sound on a subwavelength scale,” Phys. Rev. Lett. 107(6), 064301 (2011).
[Crossref] [PubMed]

M. V. Afonso, J. M. Bioucas-Dias, and M. A. Figueiredo, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Trans. Image Process. 20(3), 681–695 (2011).
[Crossref]

Y. Sung and R. R. Dasari, “Deterministic regularization of three-dimensional optical diffraction tomography,” J. Opt. Soc. Am. A 28(8), 1554–1561 (2011).
[Crossref]

Z. Wang, D. L. Marks, P. S. Carney, L. J. Millet, M. U. Gillette, A. Mihi, P. V. Braun, Z. Shen, S. G. Prasanth, and G. Popescu, “Spatial light interference tomography (slit),” Opt. Express 19(21), 19907–19918 (2011).
[Crossref] [PubMed]

2010 (2)

F. Lemoult, G. Lerosey, J. de Rosny, and M. Fink, “Resonant metalenses for breaking the diffraction barrier,” Phys. Rev. Lett. 104(20), 203901 (2010).
[Crossref] [PubMed]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

2009 (4)

2008 (2)

M. Potcoava and M. Kim, “Optical tomography for biomedical applications by digital interference holography,” Meas. Sci. Technol. 19(7), 074010 (2008).
[Crossref]

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberlé, “Tomographic diffractive microscopy of transparent samples,” Eur. Phys. J. Appl. Phys. 44 (01), 29–35 (2008).
[Crossref]

2007 (2)

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315(5815), 1120–1122 (2007).
[Crossref] [PubMed]

D. P. Wipf and B. D. Rao, “An empirical Bayesian strategy for solving the simultaneous sparse approximation problem,” IEEE Trans. Signal Process. 55(7), 3704–3716 (2007).
[Crossref]

2006 (2)

J. Chena and X. Huo, “Theoretical results on sparse representations of multiple measurement vectors,” IEEE Trans. Signal Process. 54(12), 4634–4643 (2006).
[Crossref]

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B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberlé, “Tomographic diffractive microscopy of transparent samples,” Eur. Phys. J. Appl. Phys. 44 (01), 29–35 (2008).
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K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
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A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
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F. de Chaumont, S. Dallongeville, N. Chenouard, N. Hervé, S. Pop, T. Provoost, V. Meas-Yedid, P. Pankajakshan, T. Lecomte, Y. Le Montagner, T. Lagache, A. Dufour, and J.-C. Olivo-Marin, “Icy: an open bioimage informatics platform for extended reproducible research,” Nat. Methods 9(7), 690–696 (2012).
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M. E. Davies and Y. C. Eldar, “Rank awareness in joint sparse recovery,” IEEE Trans. Inf. Theory 58(2), 1135–1146 (2012).
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Engan, K.

S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors,” IEEE Trans. Signal Process. 53(7), 2477–2488 (2005).
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Feng, S.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
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F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13(23), 4512–4516 (2013).
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Figueiredo, M. A.

M. V. Afonso, J. M. Bioucas-Dias, and M. A. Figueiredo, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Trans. Image Process. 20(3), 681–695 (2011).
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F. Lemoult, A. Ourir, J. de Rosny, A. Tourin, M. Fink, and G. Lerosey, “Time reversal in subwavelength-scaled resonant media: beating the diffraction limit,” Int. J. Microw. Sci. Technol. 2011, 425710 (2011).
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Frank, W. Y.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
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B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberlé, “Tomographic diffractive microscopy of transparent samples,” Eur. Phys. J. Appl. Phys. 44 (01), 29–35 (2008).
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O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
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S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. C. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett.,  111(5), 053902 (2013).
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Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37(10), 1631–1633 (2012).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
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O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
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C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, and K. T. Nam, “Full-field subwavelength imaging using a scattering superlens,” Phys. Rev. Lett. 113, 113901 (2014).
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J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photon. 7, 454–458 (2013).
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F. de Chaumont, S. Dallongeville, N. Chenouard, N. Hervé, S. Pop, T. Provoost, V. Meas-Yedid, P. Pankajakshan, T. Lecomte, Y. Le Montagner, T. Lagache, A. Dufour, and J.-C. Olivo-Marin, “Icy: an open bioimage informatics platform for extended reproducible research,” Nat. Methods 9(7), 690–696 (2012).
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Huo, X.

J. Chena and X. Huo, “Theoretical results on sparse representations of multiple measurement vectors,” IEEE Trans. Signal Process. 54(12), 4634–4643 (2006).
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S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
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Jang, S.

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J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Optics express 23(13), 16933–16948 (2015).
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J. Yoo, Y. Jung, M. Lim, J. C. Ye, and A. Wahab, “A joint sparse recovery framework for accurate reconstruction of inclusions in elastic media,” SIAM J. Imag. Sci. 10(3), 1104–1138 (2017).
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M. Azimi and A. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging 2(4), 176–195 (1983).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Transactions on Computational Imaging 2(1), 59–70 (2016).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
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Kim, M.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, and K. T. Nam, “Full-field subwavelength imaging using a scattering superlens,” Phys. Rev. Lett. 113, 113901 (2014).
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S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, “Sparse solutions to linear inverse problems with multiple measurement vectors,” IEEE Trans. Signal Process. 53(7), 2477–2488 (2005).
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A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
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Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7(2), 113–117 (2013).
[Crossref]

Tuchin, V.

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
[Crossref] [PubMed]

Unser, M.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Transactions on Computational Imaging 2(1), 59–70 (2016).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
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Uttam, S.

Vishnyakov, G. N.

G. G. Levin, G. N. Vishnyakov, S. C. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, “Three-dimensional limited-angle microtomography of blood cells: experimental results,” in BiOS’98 International Biomedical Optics Symposium (International Society for Optics and Photonics1998), pp. 159–164.

Vollmer, A.

A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
[Crossref]

Vonesch, C.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Transactions on Computational Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Wahab, A.

J. Yoo, Y. Jung, M. Lim, J. C. Ye, and A. Wahab, “A joint sparse recovery framework for accurate reconstruction of inclusions in elastic media,” SIAM J. Imag. Sci. 10(3), 1104–1138 (2017).
[Crossref]

Wang, H.

L. Su, L. Ma, and H. Wang, “Improved regularization reconstruction from sparse angle data in optical diffraction tomography,” Appl. Opt. 54(4), 859–868 (2015).
[Crossref] [PubMed]

L. Ma, H. Wang, L. Su, Y. Li, and H. Jin, “Digital holographic microtomography with few angle data-sets,” J. Mod. Opt. 61(14), 1140–1146 (2014).
[Crossref]

Wang, Z.

Wanson, E. A.

Wattellier, B.

Wicker, K.

Willsky, A. S.

D. Malioutov, M. Cetin, and A. S. Willsky, “A sparse signal reconstruction perspective for source localization with sensor arrays,” IEEE Trans. Signal Process. 53(8), 3010–3022 (2005).
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D. P. Wipf and B. D. Rao, “An empirical Bayesian strategy for solving the simultaneous sparse approximation problem,” IEEE Trans. Signal Process. 55(7), 3704–3716 (2007).
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M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. (CUP Archive, 1999).
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Yaqoob, Z.

Ye, J.

J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Optics express 23(13), 16933–16948 (2015).
[Crossref] [PubMed]

K. Kim, K. Kim, H. Park, J. Ye, and Y. Park, “Real-time visualization of 3-D dynamic microscopic objects using optical diffraction tomography,” Opt. Express 21(26), 32269–32278 (2013).
[Crossref]

Ye, J. C.

J. Yoo, Y. Jung, M. Lim, J. C. Ye, and A. Wahab, “A joint sparse recovery framework for accurate reconstruction of inclusions in elastic media,” SIAM J. Imag. Sci. 10(3), 1104–1138 (2017).
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O. K. Lee, H. Kang, J. C. Ye, and M. Lim, “A non-iterative method for the electrical impedance tomography based on joint sparse recovery,” Inverse Probl. 31(7), 075002 (2015).
[Crossref]

O. Lee and J. C. Ye, “Joint sparsity-driven non-iterative simultaneous reconstruction of absorption and scattering in diffuse optical tomography,” Opt. Express 21(22), 26589–26604 (2013).
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J. M. Kim, O. K. Lee, and J. C. Ye, “Improving noise robustness in subspace-based joint sparse recovery,” IEEE Trans. Signal Process. 60(11), 5799–5809 (2012).
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O. K. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: non-iterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imag. 30(5), 1129–1142 (2011).
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J. C. Ye and S. Y. Lee, “Non-iterative exact inverse scattering using simultaneous orthogonal matching pursuit (S-OMP),” in IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE2008), pp. 2457–2460.

Yin, W.

W. Deng, W. Yin, and Y. Zhang, “Group sparse optimization by alternating direction method,” Proc. SPIE 8858, 88580R (2013).
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Yoo, J.

J. Yoo, Y. Jung, M. Lim, J. C. Ye, and A. Wahab, “A joint sparse recovery framework for accurate reconstruction of inclusions in elastic media,” SIAM J. Imag. Sci. 10(3), 1104–1138 (2017).
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Yoon, H.

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
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Yoon, J.

Yu, H.

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, and K. T. Nam, “Full-field subwavelength imaging using a scattering superlens,” Phys. Rev. Lett. 113, 113901 (2014).
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H. Ammari and H. Zhang, “Super-resolution in high-contrast media,” Proc. R. Soc. A. 471(2178), 20140946 (2015).
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Zhang, Y.

W. Deng, W. Yin, and Y. Zhang, “Group sparse optimization by alternating direction method,” Proc. SPIE 8858, 88580R (2013).
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Zhernovaya, O.

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56(13), 4013–4021 (2011).
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H. Ammari and H. Zhang, “A mathematical theory of super-resolution by using a system of sub-wavelength Helmholtz resonators,” Commun. Math. Phys. 337(1), 379–428 (2015).
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M. E. Davies and Y. C. Eldar, “Rank awareness in joint sparse recovery,” IEEE Trans. Inf. Theory 58(2), 1135–1146 (2012).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Transactions on Computational Imaging 2(1), 59–70 (2016).
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O. K. Lee, H. Kang, J. C. Ye, and M. Lim, “A non-iterative method for the electrical impedance tomography based on joint sparse recovery,” Inverse Probl. 31(7), 075002 (2015).
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J. Biomed. Opt. (2)

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
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J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photon. 7, 454–458 (2013).
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Nature Photon. (1)

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7(2), 113–117 (2013).
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O. Lee and J. C. Ye, “Joint sparsity-driven non-iterative simultaneous reconstruction of absorption and scattering in diffuse optical tomography,” Opt. Express 21(22), 26589–26604 (2013).
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Supplementary Material (1)

NameDescription
» Code 1       Source Code: Reconstruction algorithm

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Figures (6)

Fig. 1
Fig. 1 (a) Resolution enhancement from engineered resonant medium. (b) Resolution enhancement from medium induced sub-wavelength resonance modes.
Fig. 2
Fig. 2 Experimental results of microsphere RI tomograms obtained with (a) Rytov approximation and (b) proposed method. The white dotted lines represent the slices of the complementary figures. All scale bars are 2μm.
Fig. 3
Fig. 3 Experimental results of multiple 0.2-μm-diameter fused silica microspheres RI tomograms obtained with (a) Rytov approximation and (b) proposed method. The white dotted lines and squares represent the slices of the complementary figures. All scale bars are 2μm.
Fig. 4
Fig. 4 Experimental results of RBC RI tomograms obtained with (a) Rytov approximation and (b) proposed method. The white dotted lines represent the slices of the complementary figures. All scale bars are 3μm.
Fig. 5
Fig. 5 Experimental results of hepatocyte RI tomograms obtained with (a) Rytov approximation and (b) proposed method. The white dotted lines and squares represent the slices of the complementary figures. All scale bars are 5μm.
Fig. 6
Fig. 6 Cropped images of experimental results of hepatocyte RI tomograms in Fig. 5; (a),(c) : Rytov approximation, (b),(d) : proposed method. (c) and (d) are 3-D volume rendering images of the volume containing 3 slices in x-axis.

Equations (31)

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n ( r ) = [ 1 + χ e ( r ) ] [ 1 + χ m ( r ) ] , r 3 .
Δ U s ( r ) + κ 2 U s ( r ) = τ κ 2 f ( r ) U ( r ) , r 3 ,
f ( r ) = 1 τ ( n ( r ) 2 n 0 2 1 ) χ D ( r ) , r 3 ,
τ : = max r D { | n ( r ) | } n 0 .
U s ( r ) = τ K D [ U ] ( r ) : = τ D κ 2 f ( r ) G ( r , r ) U ( r ) d r , r Ω ¯ ,
K D [ φ ] ( r ) : = D κ 2 f ( r ) G ( r , r ) φ ( r ) d r , r 3 , φ L 2 ( D ) .
{ u 0 ( r ) + κ 2 u 0 ( r ) = s ( r ) , r 3 , u 0 ( r ) satisfies the Sommerfeld radiation condition as | r | + ,
Δ u ( r ) + κ 2 u ( r ) + τ κ 2 f ( r ) χ D ( r ) u ( r ) = s ( r ) ,
u s ( r ) = τ K D [ u ] ( r ) = τ K D [ u s ] ( r ) + τ K D [ u 0 ] ( r ) , r 3 ,
σ ( K D ) = { 0 , λ 1 , λ 2 , , λ n , } , where | λ 1 | | λ 2 | , and λ n 0 .
{ ( Δ + κ 2 ) v ( r ) = κ 2 λ f ( r ) v ( r ) , r D , ( Δ + κ 2 ) v ( r ) = 0 , 3 \ D , v ( r ) satisfies the Sommerfeld radiation condition as | r | + .
L 2 ( D ) = i = 1 i ¯ .
u s ( r ) = i a i ( 1 / τ K D ) 1 K D [ φ i ] ( r ) = i a i λ i 1 / τ λ i φ i ( r ) , r D ,
U s ( r ) K D [ U 0 ] ( r ) , r Ω ¯ .
U s ( r ) = τ κ 2 D G ( r , r ) I ( r ) d r , r Γ .
U ^ ( r ) = U 0 ( r ) + τ κ 2 D ^ G ( r , r ) I ^ ( r ) d r , r D ,
I ^ ( r ) = U ^ ( r ) f ( r ) , r D ^ ,
U s ( r ) = τ κ 2 D ^ G ( r , r ) U ^ ( r ) f ( r ) d r , r Γ .
{ U s ( m ) ( r ) = τ κ 2 D G ( r , r ) I ( m ) ( r ) d r , r Γ I ( m ) ( r ) = f ( r ) U ( m ) ( r ) , m = 1 , , M ,
𝒴 = 𝒢 ,
I ˜ ( m ) ( r ) : = { I ( m ) ( r ) , r D , 0 , r Ω \ D .
min 0 , subject to 𝒴 𝒢 F .
e i κ | r r | 4 π | r r | = e i κ | r | | r | { G ( r ^ , r ) + O ( 1 | r | ) } , as | r | + and r is fixed .
U s , ( m ) ( r ^ ) = τ κ 2 4 π { I D ( m ) } ( r ^ ) ,
U ( r ) = U 0 ( r ) e ϕ s ( r ) ,
U s ( r ) = U ( r ) U 0 ( r ) = U 0 ( r ) ( e ϕ s ( r ) 1 ) U 0 ( r ) ϕ s ( r ) ,
A = τ κ 2 4 π [ ] , x = [ I ( 1 ) I ( 2 ) I ( M ) ] , y = [ U s , ( 1 ) U s , ( 2 ) U s , ( M ) ] .
min x x w , 2 , 1 = i = 1 N w i x g i 2 such that A x = y ,
min f m = 1 M I ^ ( m ) U ^ ( m ) f 2 2 + α 𝒟 f 2 2 ,
( B m f ) ( r ) = τ κ 2 D ^ f ( r ) U ^ ( m ) ( r ) G ( r , r ) d r , r Γ ,
min f 1 2 m = 1 M B m f U s ( m ) 2 2 + α 𝒟 f 2 2 + ι 𝒞 ( f ) ,

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