Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography

Wojciech Krauze; Piotr Makowski; Małgorzata Kujawińska; Arkadiusz Kuś

doi:10.1364/OE.24.004924

Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography

Wojciech Krauze, Piotr Makowski, Małgorzata Kujawińska, and Arkadiusz Kuś

Optics Express
Vol. 24,
Issue 5,
pp. 4924-4936
(2016)
•https://doi.org/10.1364/OE.24.004924

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Wojciech Krauze, Piotr Makowski, Małgorzata Kujawińska, and Arkadiusz Kuś, "Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography," Opt. Express 24, 4924-4936 (2016)

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Related Topics
Table of Contents Category
- Image Processing
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Inverse problems (100.3190)
- Tomographic image processing (100.6950)
- Cell analysis (170.1530)

About this Article
History
- Original Manuscript: December 30, 2015
- Revised Manuscript: February 4, 2016
- Manuscript Accepted: February 9, 2016
- Published: February 26, 2016

Accessible

Open Access

Abstract

Due to incompleteness of input data inherent to Limited Angle Tomography (LAT), specific additional constraints are usually employed to suppress image artifacts. In this work we demonstrate a new two-stage regularization strategy, named Generalized Total Variation Iterative Constraint (GTVIC), dedicated to semi-piecewise-constant objects. It has been successfully applied as a supplementary module for two different reconstruction algorithms: an X-ray type solver and a diffraction-wise solver. Numerical tests performed on a detailed phantom of a biological cell under conical illumination pattern show significant reduction of axial blurring in the reconstructed refractive index distribution after GTVIC is added. Analogous results were obtained with experimental data.

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References

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Publication

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[Crossref]
C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16(13), 9753–9764 (2008).
[Crossref] [PubMed]
B. Rappaz, B. Breton, E. Shaffer, and G. Turcatti, “Digital holographic microscopy: a quantitative label-free microscopy technique for phenotypic screening,” Comb. Chem. High Throughput Screen. 17(1), 80–88 (2014).
[Crossref] [PubMed]
G. Popescu, “Quantitative phase imaging of nanoscale cell structure and dynamics,” Methods Cell Biol. 90, 87–115 (2008).
[Crossref] [PubMed]
H. Ding, Z. Wang, X. Liang, S. A. Boppart, K. Tangella, and G. Popescu, “Measuring the scattering parameters of tissues from quantitative phase imaging of thin slices,” Opt. Lett. 36(12), 2281–2283 (2011).
[Crossref] [PubMed]
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 (2013).
[Crossref] [PubMed]
J. Kostencka, T. Kozacki, A. Kuś, M. Dudek, M. Kujawińska, and B. Kemper, “Holographic method for capillary induced aberration compensation for 3D tomographic measurements of living cells,” Proc. SPIE 8792, 879204 (2013).
[Crossref]
J. Kostencka, T. Kozacki, A. Kuś, and M. Kujawińska, “Accurate approach to capillary-supported optical diffraction tomography,” Opt. Express 23(6), 7908–7923 (2015).
[Crossref] [PubMed]
M. Kujawińska, W. Krauze, A. Kus, J. Kostencka, T. Kozacki, B. Kemper, and M. Dudek, “Problems and solutions in 3-D analysis of phase biological objects by optical diffraction tomography,” Int. J. Optomechatronics 8(4), 357–372 (2014).
[Crossref]
A. Kus, W. Krauze, and M. Kujawinska, “Active limited-angle tomographic phase microscope,” J. Biomed. Opt. 20(11), 111216 (2015).
[Crossref] [PubMed]
A. Kuś, W. Krauze, and M. Kujawińska, “Limited-angle, holographic tomography with optically controlled projection generation,” Proc. SPIE 9330, 933007 (2015).
[Crossref]
A. Kuś, W. Krauze, M. Kujawińska, and M. Filipiak, “Limited-angle hybrid diffraction tomography for biological samples,” Proc. SPIE 9132, 91320O (2014).
E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. Opt. Soc. Am. 25, 1772–1782 (2009).
Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]
S. Vertu, I. Yamada, J.-J. Delaunay, and O. Haeberlé, “Tomographic observation of transparent objects under coherent illumination and reconstruction by filtered backprojection and Fourier diffraction theorem,” Proc. SPIE 6861, 686103 (2008).
[Crossref]
T. Sato, S. J. Norton, M. Linzer, O. Ikeda, and M. Hirama, “Tomographic image reconstruction from limited projections using iterative revisions in image and transform spaces,” Appl. Opt. 20(3), 395–399 (1981).
[Crossref] [PubMed]
D. Wang, H. Qiao, X. Song, Y. Fan, and D. Li, “Fluorescence molecular tomography using a two-step three-dimensional shape-based reconstruction with graphics processing unit acceleration,” Appl. Opt. 51(36), 8731–8744 (2012).
[Crossref] [PubMed]
T. Humphries, A. Saad, A. Celler, G. Hamarneh, T. Möller, and M. Trummer, “Segmentation-based regularization of dynamic SPECT reconstruction,” in Nuclear Science Symposium Conference Record, (IEEE, 2009), 2849–2852.
D. Hyde, E. L. Miller, D. H. Brooks, and V. Ntziachristos, “Data specific spatially varying regularization for multimodal fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29(2), 365–374 (2010).
[Crossref] [PubMed]
X. Jin, L. Li, Z. Chen, L. Zhang, and Y. Xing, “Anisotropic total variation for limited-angle CT reconstruction,” in Nuclear Science Symposium Conference Record, (IEEE, 2010), 2232–2238.
[Crossref]
W. Krauze, A. Kuś, and M. Kujawinska, “Limited-angle hybrid optical diffraction tomography system with total-variation-minimization-based reconstruction,” Opt. Eng. 54(5), 054104 (2015).
[Crossref]
W. Krauze, P. Makowski, and M. Kujawińska, “Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures,” Proc. SPIE 9526, 95260Y (2015).
A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging,” J. Math. Imaging Vis. 40(1), 120–145 (2011).
[Crossref]
N. Otsu, “A threshold selection method from gray-level histograms,” Automatica 11, 23–27 (1975).
A. H. Andersen and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm,” Ultrason. Imaging 6(1), 81–94 (1984).
[Crossref] [PubMed]
A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society of Industrial and Applied Mathematics, 2001).
W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA Toolbox: A platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]
Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[Crossref] [PubMed]
K. Kim, K. S. Kim, H. Park, J. C. 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] [PubMed]
B. P. Medoff, W. R. Brody, M. Nassi, and A. Macovski, “Iterative convolution backprojection algorithms for image reconstruction from limited data,” J. Opt. Soc. Am. 73(11), 1493–1500 (1983).
[Crossref]
Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]
B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12(5), 054009 (2007).
[Crossref] [PubMed]
B. Kemper, L. Schmidt, S. Przibilla, C. Rommel, A. Vollmer, S. Ketelhut, J. Schnekenburger, and G. von Bally, “Influence of sample preparation and identification of subcelluar structures in quantitative holographic phase contrast microscopy,” Proc. SPIE 7715, 771504 (2010).
[Crossref]
C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16(1), 011005 (2011).
[Crossref] [PubMed]
Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002).
[Crossref]
P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms (Society of Industrial and Applied Mathematics, 2010).

2015 (6)

J. Kostencka, T. Kozacki, A. Kuś, and M. Kujawińska, “Accurate approach to capillary-supported optical diffraction tomography,” Opt. Express 23(6), 7908–7923 (2015).
[Crossref] [PubMed]

A. Kus, W. Krauze, and M. Kujawinska, “Active limited-angle tomographic phase microscope,” J. Biomed. Opt. 20(11), 111216 (2015).
[Crossref] [PubMed]

A. Kuś, W. Krauze, and M. Kujawińska, “Limited-angle, holographic tomography with optically controlled projection generation,” Proc. SPIE 9330, 933007 (2015).
[Crossref]

W. Krauze, A. Kuś, and M. Kujawinska, “Limited-angle hybrid optical diffraction tomography system with total-variation-minimization-based reconstruction,” Opt. Eng. 54(5), 054104 (2015).
[Crossref]

W. Krauze, P. Makowski, and M. Kujawińska, “Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures,” Proc. SPIE 9526, 95260Y (2015).

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA Toolbox: A platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

2014 (4)

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

A. Kuś, W. Krauze, M. Kujawińska, and M. Filipiak, “Limited-angle hybrid diffraction tomography for biological samples,” Proc. SPIE 9132, 91320O (2014).

M. Kujawińska, W. Krauze, A. Kus, J. Kostencka, T. Kozacki, B. Kemper, and M. Dudek, “Problems and solutions in 3-D analysis of phase biological objects by optical diffraction tomography,” Int. J. Optomechatronics 8(4), 357–372 (2014).
[Crossref]

B. Rappaz, B. Breton, E. Shaffer, and G. Turcatti, “Digital holographic microscopy: a quantitative label-free microscopy technique for phenotypic screening,” Comb. Chem. High Throughput Screen. 17(1), 80–88 (2014).
[Crossref] [PubMed]

2013 (4)

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 (2013).
[Crossref] [PubMed]

J. Kostencka, T. Kozacki, A. Kuś, M. Dudek, M. Kujawińska, and B. Kemper, “Holographic method for capillary induced aberration compensation for 3D tomographic measurements of living cells,” Proc. SPIE 8792, 879204 (2013).
[Crossref]

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

K. Kim, K. S. Kim, H. Park, J. C. 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] [PubMed]

2012 (1)

D. Wang, H. Qiao, X. Song, Y. Fan, and D. Li, “Fluorescence molecular tomography using a two-step three-dimensional shape-based reconstruction with graphics processing unit acceleration,” Appl. Opt. 51(36), 8731–8744 (2012).
[Crossref] [PubMed]

2011 (3)

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16(1), 011005 (2011).
[Crossref] [PubMed]

H. Ding, Z. Wang, X. Liang, S. A. Boppart, K. Tangella, and G. Popescu, “Measuring the scattering parameters of tissues from quantitative phase imaging of thin slices,” Opt. Lett. 36(12), 2281–2283 (2011).
[Crossref] [PubMed]

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

2010 (2)

B. Kemper, L. Schmidt, S. Przibilla, C. Rommel, A. Vollmer, S. Ketelhut, J. Schnekenburger, and G. von Bally, “Influence of sample preparation and identification of subcelluar structures in quantitative holographic phase contrast microscopy,” Proc. SPIE 7715, 771504 (2010).
[Crossref]

D. Hyde, E. L. Miller, D. H. Brooks, and V. Ntziachristos, “Data specific spatially varying regularization for multimodal fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29(2), 365–374 (2010).
[Crossref] [PubMed]

2009 (2)

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. Opt. Soc. Am. 25, 1772–1782 (2009).

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[Crossref] [PubMed]

2008 (3)

S. Vertu, I. Yamada, J.-J. Delaunay, and O. Haeberlé, “Tomographic observation of transparent objects under coherent illumination and reconstruction by filtered backprojection and Fourier diffraction theorem,” Proc. SPIE 6861, 686103 (2008).
[Crossref]

G. Popescu, “Quantitative phase imaging of nanoscale cell structure and dynamics,” Methods Cell Biol. 90, 87–115 (2008).
[Crossref] [PubMed]

C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16(13), 9753–9764 (2008).
[Crossref] [PubMed]

2007 (1)

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12(5), 054009 (2007).
[Crossref] [PubMed]

2002 (1)

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002).
[Crossref]

1997 (1)

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[Crossref]

1984 (1)

A. H. Andersen and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm,” Ultrason. Imaging 6(1), 81–94 (1984).
[Crossref] [PubMed]

1983 (1)

B. P. Medoff, W. R. Brody, M. Nassi, and A. Macovski, “Iterative convolution backprojection algorithms for image reconstruction from limited data,” J. Opt. Soc. Am. 73(11), 1493–1500 (1983).
[Crossref]

1981 (1)

T. Sato, S. J. Norton, M. Linzer, O. Ikeda, and M. Hirama, “Tomographic image reconstruction from limited projections using iterative revisions in image and transform spaces,” Appl. Opt. 20(3), 395–399 (1981).
[Crossref] [PubMed]

1975 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” Automatica 11, 23–27 (1975).

Altantzis, T.

Andersen, A. H.

A. H. Andersen and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm,” Ultrason. Imaging 6(1), 81–94 (1984).
[Crossref] [PubMed]

Badizadegan, K.

Bals, S.

Batenburg, K. J.

Bingham, P. R.

C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16(13), 9753–9764 (2008).
[Crossref] [PubMed]

Boppart, S. A.

Boss, D.

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

Bovik, A. C.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002).
[Crossref]

Bredebusch, I.

Breton, B.

Brody, W. R.

Brooks, D. H.

Celler, A.

T. Humphries, A. Saad, A. Celler, G. Hamarneh, T. Möller, and M. Trummer, “Segmentation-based regularization of dynamic SPECT reconstruction,” in Nuclear Science Symposium Conference Record, (IEEE, 2009), 2849–2852.

Chambolle, A.

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

Chen, Z.

X. Jin, L. Li, Z. Chen, L. Zhang, and Y. Xing, “Anisotropic total variation for limited-angle CT reconstruction,” in Nuclear Science Symposium Conference Record, (IEEE, 2010), 2232–2238.
[Crossref]

Choi, W.

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16(1), 011005 (2011).
[Crossref] [PubMed]

Cotte, Y.

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

Dao, M.

Dasari, R. R.

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16(1), 011005 (2011).
[Crossref] [PubMed]

De Beenhouwer, J.

Delaunay, J.-J.

Depeursinge, C.

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

Diez-Silva, M.

Ding, H.

Domschke, W.

Dudek, M.

Fan, Y.

Fang-Yen, C.

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16(1), 011005 (2011).
[Crossref] [PubMed]

Feld, M. S.

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16(1), 011005 (2011).
[Crossref] [PubMed]

Filipiak, M.

A. Kuś, W. Krauze, M. Kujawińska, and M. Filipiak, “Limited-angle hybrid diffraction tomography for biological samples,” Proc. SPIE 9132, 91320O (2014).

Gureyev, T. E.

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[Crossref]

Haeberlé, O.

Hamarneh, G.

Hirama, M.

Holbrow, C. J.

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16(1), 011005 (2011).
[Crossref] [PubMed]

Humphries, T.

Hyde, D.

Ikeda, O.

Jang, S.

Jin, X.

Jourdain, P.

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

Kak, A. C.

A. H. Andersen and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm,” Ultrason. Imaging 6(1), 81–94 (1984).
[Crossref] [PubMed]

Kao, C.-M.

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. Opt. Soc. Am. 25, 1772–1782 (2009).

Kemper, B.

Ketelhut, S.

Kim, K.

Kim, K. S.

Kim, Y.

Kosmeier, S.

Kostencka, J.

J. Kostencka, T. Kozacki, A. Kuś, and M. Kujawińska, “Accurate approach to capillary-supported optical diffraction tomography,” Opt. Express 23(6), 7908–7923 (2015).
[Crossref] [PubMed]

Kozacki, T.

J. Kostencka, T. Kozacki, A. Kuś, and M. Kujawińska, “Accurate approach to capillary-supported optical diffraction tomography,” Opt. Express 23(6), 7908–7923 (2015).
[Crossref] [PubMed]

Krauze, W.

A. Kus, W. Krauze, and M. Kujawinska, “Active limited-angle tomographic phase microscope,” J. Biomed. Opt. 20(11), 111216 (2015).
[Crossref] [PubMed]

A. Kuś, W. Krauze, and M. Kujawińska, “Limited-angle, holographic tomography with optically controlled projection generation,” Proc. SPIE 9330, 933007 (2015).
[Crossref]

A. Kuś, W. Krauze, M. Kujawińska, and M. Filipiak, “Limited-angle hybrid diffraction tomography for biological samples,” Proc. SPIE 9132, 91320O (2014).

Kujawinska, M.

A. Kuś, W. Krauze, and M. Kujawińska, “Limited-angle, holographic tomography with optically controlled projection generation,” Proc. SPIE 9330, 933007 (2015).
[Crossref]

A. Kus, W. Krauze, and M. Kujawinska, “Active limited-angle tomographic phase microscope,” J. Biomed. Opt. 20(11), 111216 (2015).
[Crossref] [PubMed]

J. Kostencka, T. Kozacki, A. Kuś, and M. Kujawińska, “Accurate approach to capillary-supported optical diffraction tomography,” Opt. Express 23(6), 7908–7923 (2015).
[Crossref] [PubMed]

A. Kuś, W. Krauze, M. Kujawińska, and M. Filipiak, “Limited-angle hybrid diffraction tomography for biological samples,” Proc. SPIE 9132, 91320O (2014).

Kus, A.

A. Kus, W. Krauze, and M. Kujawinska, “Active limited-angle tomographic phase microscope,” J. Biomed. Opt. 20(11), 111216 (2015).
[Crossref] [PubMed]

A. Kuś, W. Krauze, and M. Kujawińska, “Limited-angle, holographic tomography with optically controlled projection generation,” Proc. SPIE 9330, 933007 (2015).
[Crossref]

J. Kostencka, T. Kozacki, A. Kuś, and M. Kujawińska, “Accurate approach to capillary-supported optical diffraction tomography,” Opt. Express 23(6), 7908–7923 (2015).
[Crossref] [PubMed]

A. Kuś, W. Krauze, M. Kujawińska, and M. Filipiak, “Limited-angle hybrid diffraction tomography for biological samples,” Proc. SPIE 9132, 91320O (2014).

Langehanenberg, P.

Li, D.

Li, L.

Liang, X.

Linzer, M.

Macovski, A.

Magistretti, P.

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

Makowski, P.

Mann, C. J.

C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16(13), 9753–9764 (2008).
[Crossref] [PubMed]

Marquet, P.

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

Medoff, B. P.

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Supplementary Material (3)

Name	Description
» Visualization 1: AVI (11515 KB)	Comparison of y-z cross-sections of reconstructions calculated with and without GTVIC support
» Visualization 2: AVI (5988 KB)	Comparison of x-z cross-sections of reconstructions calculated with and without GTVIC support
» Visualization 3: AVI (2981 KB)	Comparison of x-y cross-sections of reconstructions calculated with and without GTVIC support

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Fig. 1 Flow diagram of GTVIC strategy. M1: module 1, where 3D mask is generated; M2: module 2, where an arbitrary solver for LAT is utilized.

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Fig. 2 (a) Refractive index distribution of a synthetic phantom model of a Paramecium cell; the cell structure includes cytoplasm, a nucleus and a vacuole. (b) Schematic of the conical projection geometry used for synthetic sinogram generation (α = 45°).

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Fig. 3 Biological cell phantom reconstructions by GDRA solver (straight line propagation model, unwrapped phase projections). Left: GDRA algorithm with 180 auxiliary projection planes. Right: same GDRA algorithm supplemented by the GTVIC strategy; (a) cross-sections of the refractive index images (immersion subtracted), cropped to 0.75 of original output size; (b) reconstruction quality progress curves: Quality Index in XZ plane inside the phantom (circles) and RMS in full cube (triangles); (c) quality index for 3 sets of cross-section planes, rotated in ± 90° range around X, Y, Z axes respectively.

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Fig. 4 Biological cell phantom reconstructions by the diffraction-wise FTRA solver (Rytov approximation, amplitude-phase projections). Left: FTRA acting alone. Right: FTRA supplemented by GTVIC strategy. (a) reconstruction quality progress curves: Quality Index in XZ plane inside the phantom (circles) and RMS in full cube (triangles); (b) cross-sections of the reconstructed RI images, cropped to 0.75 of original output size; (c) quality index for 3 sets of cross-section planes, rotated in ± 90° range around X, Y, Z axes respectively.

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Fig. 5 Two comparisons of one-dimensional cross-sections of the reconstructions presented in Figs. 3 and 4. The cross-sections are parallel to Z axis and run through the center of the vacuole. Figure 5(a) presents comparison between phantom data and two reconstructions: one calculated with GDRA and GTVIC strategy (shown in Fig. 3(d)), and one calculated with GDRA only (Fig. 3(a)). Figure 5(b) presents analogical comparison, but with FTRA-based reconstructions (Figs. 4(d) and 4(a)).

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Fig. 6 Fourier-based reconstruction in Rytov approximation from complex projections with equalized amplitude patterns.

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Fig. 7 Quality of reconstructions by FTRA( + GTVIC) solver fed by different projection subsets of the original sinogram (360 views in conical pattern). In (a) the adaptive RI masks for GTVIC were calculated from the full sinogram and in (b) from corresponding limited subset of projections (realistic scenario); the dotted curves correspond to an alternative projection subset chosen from the same full sinogram in a pattern shifted azimuthally by 1°.

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Fig. 8 Experimental reconstruction of a C2C12 muscle cell by means of the iterative Fourier Transform solver; (a)-(b) K-space representation of input data (180 projections), (c)-(f) reconstruction by means of FTRA with Non-Negativity Constraint (50 iterations in 4 minuses), (g)-(j) reconstruction by means of FTRA with NNC + GTVIC (GTVIC mask generation and 5 FTRA + GTVIC iterations in 11 minutes). Animations with all Y-Z, X-Z, and X-Y cross-sections are presented in Visualization 1, Visualization 2 and Visualization 3, respectively.

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Equations (2)

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\min {‖ A x - B ‖}_{2} + λ {‖ x ‖}_{T V}

Q I = \frac{4 σ_{x y} \bar{x} \cdot \bar{y}}{(σ_{x}^{2} + σ_{y}^{2}) ({\bar{x}}^{2} + {\bar{y}}^{2})}