Abstract

We present a method for inverse scattering that relies on intensity-only measurements of the scattered field on a single measurement plane. By collecting measurements from a suite of experiments in which the sample is illuminated using different incident fields, we create sufficient data diversity to overcome the limitations of the intensity-only measurements. We give an explicit procedure that uses an algebraic relation called the polarization identity to convert intensity measurements of scattered fields to interferometric measurements in which one of the scattered fields serves as the reference. By adjusting the multiple signal classification (MUSIC) method for these interferometric data, we effectively recover the location and shapes of multiple objects contained in the imaging region. This method is effective and robust to noise as long as there is sufficiently high data diversity and the fractional volume of the scattering objects is not too high. We present image reconstructions for several three-dimensional examples with simulated data computed using the Method of Fundamental Solutions that demonstrate the effectiveness of this imaging method.

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

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References

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2019 (1)

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1, 036003 (2019).
[Crossref]

2018 (4)

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
[Crossref]

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Robust multifrequency imaging with MUSIC,” Inverse Prob. 35, 015007 (2018).
[Crossref]

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9, 2130–2141 (2018).
[Crossref]

2017 (1)

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Multifrequency interferometric imaging with intensity-only measurements,” SIAM J. Imaging Sci. 10, 1005–1032 (2017).
[Crossref]

2016 (2)

M. Moscoso, A. Novikov, and G. Papanicolaou, “Coherent imaging without phases,” SIAM J. Imaging Sci. 9, 1689–1707 (2016).
[Crossref]

R. Horstmeyer, J. Chung, X. Ou, G. Zheng, and C. Yang, “Diffraction tomography with Fourier ptychography,” Optica 3, 827–835 (2016).
[Crossref]

2015 (2)

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscopy,” Optica 2, 104–111 (2015).
[Crossref]

A. Novikov, M. Moscoso, and G. Papanicolaou, “Illumination strategies for intensity-only imaging,” SIAM J. Imaging Sci. 8, 1547–1573 (2015).
[Crossref]

2014 (1)

A. Chai, M. Moscoso, and G. Papanicolaou, “Imaging strong localized scatterers with sparcity promoting optimization,” SIAM J. Imaging Sci. 7, 1358–1387 (2014).
[Crossref]

2013 (1)

2011 (1)

2010 (1)

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Prob. 27, 015005 (2010).
[Crossref]

2009 (2)

2008 (2)

2007 (4)

E. A. Marengo, R. D. Hernandez, and H. Lev-Ari, “Intensity-only signal-subspace-based imaging,” J. Opt. Soc. Am. A 24, 3619–3635 (2007).
[Crossref]

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. 29, 674–709 (2007).
[Crossref]

E. Iakovleva, S. Gdourra, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-D inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598–2609 (2007).
[Crossref]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[Crossref]

2005 (1)

H. Ammari, E. Iakovleva, and D. Lesselier, “A MUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency,” Multiscale Model. Simul. 3, 597–628 (2005).
[Crossref]

2004 (1)

F. K. Gruber, E. A. Marengo, and A. J. Devaney, “Time-reversal imaging with multiple signal classification considering multiple scattering between the targets,” J. Acoust. Soc. Am. 115, 3042–3047 (2004).
[Crossref]

2002 (1)

1999 (1)

1993 (1)

1992 (2)

M. H. Maleki, A. J. Devaney, and A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
[Crossref]

A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
[Crossref]

1985 (2)

G. Beylkin, “Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized radon transform,” J. Math. Phys. 26, 99–108 (1985).
[Crossref]

G. Beylkin, “Reconstructing discontinuities in multidimensional inverse scattering problems: smooth errors vs small errors,” Appl. Opt. 24, 4086–4088 (1985).
[Crossref]

1977 (1)

R. Mathon and R. L. Johnston, “The approximate solution of elliptic boundary-value problems by fundamental solutions,” SIAM J. Numer. Anal. 14, 638–650 (1977).
[Crossref]

1970 (1)

1935 (1)

P. Jordan and J. von Neumann, “On inner products in linear, metric spaces,” Ann. Math. 36, 719–723 (1935).
[Crossref]

Agarwal, G.

Ammari, H.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. 29, 674–709 (2007).
[Crossref]

H. Ammari, E. Iakovleva, and D. Lesselier, “A MUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency,” Multiscale Model. Simul. 3, 597–628 (2005).
[Crossref]

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[Crossref]

Belkebir, K.

Beylkin, G.

G. Beylkin, “Reconstructing discontinuities in multidimensional inverse scattering problems: smooth errors vs small errors,” Appl. Opt. 24, 4086–4088 (1985).
[Crossref]

G. Beylkin, “Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized radon transform,” J. Math. Phys. 26, 99–108 (1985).
[Crossref]

Brady, D. J.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
[Crossref]

Cang, J.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

Cao, L.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

Carney, P. S.

Chai, A.

A. Chai, M. Moscoso, and G. Papanicolaou, “Imaging strong localized scatterers with sparcity promoting optimization,” SIAM J. Imaging Sci. 7, 1358–1387 (2014).
[Crossref]

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Prob. 27, 015005 (2010).
[Crossref]

Chen, X.

Choi, K.

Choi, W.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[Crossref]

Chung, J.

Crocco, L.

D’Urso, M.

Dasari, R. R.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[Crossref]

Devaney, A. J.

F. K. Gruber, E. A. Marengo, and A. J. Devaney, “Time-reversal imaging with multiple signal classification considering multiple scattering between the targets,” J. Acoust. Soc. Am. 115, 3042–3047 (2004).
[Crossref]

M. H. Maleki and A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).
[Crossref]

M. H. Maleki, A. J. Devaney, and A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
[Crossref]

A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
[Crossref]

Doicu, A.

T. Wriedt, A. Doicu, and Y. Eremin, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, 2000).

Eremin, Y.

T. Wriedt, A. Doicu, and Y. Eremin, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, 2000).

Fang-Yen, C.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[Crossref]

Feld, M. S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[Crossref]

Fienup, J. R.

Gbur, G.

Gdourra, S.

E. Iakovleva, S. Gdourra, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-D inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598–2609 (2007).
[Crossref]

Goy, A.

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
[Crossref]

Gruber, F. K.

F. K. Gruber, E. A. Marengo, and A. J. Devaney, “Time-reversal imaging with multiple signal classification considering multiple scattering between the targets,” J. Acoust. Soc. Am. 115, 3042–3047 (2004).
[Crossref]

Hernandez, R. D.

Horisaki, R.

Horstmeyer, R.

Iakovleva, E.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. 29, 674–709 (2007).
[Crossref]

E. Iakovleva, S. Gdourra, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-D inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598–2609 (2007).
[Crossref]

H. Ammari, E. Iakovleva, and D. Lesselier, “A MUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency,” Multiscale Model. Simul. 3, 597–628 (2005).
[Crossref]

Isernia, T.

Jin, G.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

Johnston, R. L.

R. Mathon and R. L. Johnston, “The approximate solution of elliptic boundary-value problems by fundamental solutions,” SIAM J. Numer. Anal. 14, 638–650 (1977).
[Crossref]

Jordan, P.

P. Jordan and J. von Neumann, “On inner products in linear, metric spaces,” Ann. Math. 36, 719–723 (1935).
[Crossref]

Kamilov, U. S.

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1, 036003 (2019).
[Crossref]

Kolner, C.

Lee, H.

Lesselier, D.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. 29, 674–709 (2007).
[Crossref]

E. Iakovleva, S. Gdourra, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-D inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598–2609 (2007).
[Crossref]

H. Ammari, E. Iakovleva, and D. Lesselier, “A MUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency,” Multiscale Model. Simul. 3, 597–628 (2005).
[Crossref]

Lev-Ari, H.

Lim, J.

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
[Crossref]

Lim, S.

Lin, H.-Y.

Ling, R.

Litman, A.

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[Crossref]

Maleki, M. H.

Marengo, E. A.

E. A. Marengo, R. D. Hernandez, and H. Lev-Ari, “Intensity-only signal-subspace-based imaging,” J. Opt. Soc. Am. A 24, 3619–3635 (2007).
[Crossref]

F. K. Gruber, E. A. Marengo, and A. J. Devaney, “Time-reversal imaging with multiple signal classification considering multiple scattering between the targets,” J. Acoust. Soc. Am. 115, 3042–3047 (2004).
[Crossref]

Marks, D. L.

Mathon, R.

R. Mathon and R. L. Johnston, “The approximate solution of elliptic boundary-value problems by fundamental solutions,” SIAM J. Numer. Anal. 14, 638–650 (1977).
[Crossref]

Moscoso, M.

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Robust multifrequency imaging with MUSIC,” Inverse Prob. 35, 015007 (2018).
[Crossref]

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Multifrequency interferometric imaging with intensity-only measurements,” SIAM J. Imaging Sci. 10, 1005–1032 (2017).
[Crossref]

M. Moscoso, A. Novikov, and G. Papanicolaou, “Coherent imaging without phases,” SIAM J. Imaging Sci. 9, 1689–1707 (2016).
[Crossref]

A. Novikov, M. Moscoso, and G. Papanicolaou, “Illumination strategies for intensity-only imaging,” SIAM J. Imaging Sci. 8, 1547–1573 (2015).
[Crossref]

A. Chai, M. Moscoso, and G. Papanicolaou, “Imaging strong localized scatterers with sparcity promoting optimization,” SIAM J. Imaging Sci. 7, 1358–1387 (2014).
[Crossref]

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Prob. 27, 015005 (2010).
[Crossref]

Novikov, A.

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Robust multifrequency imaging with MUSIC,” Inverse Prob. 35, 015007 (2018).
[Crossref]

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Multifrequency interferometric imaging with intensity-only measurements,” SIAM J. Imaging Sci. 10, 1005–1032 (2017).
[Crossref]

M. Moscoso, A. Novikov, and G. Papanicolaou, “Coherent imaging without phases,” SIAM J. Imaging Sci. 9, 1689–1707 (2016).
[Crossref]

A. Novikov, M. Moscoso, and G. Papanicolaou, “Illumination strategies for intensity-only imaging,” SIAM J. Imaging Sci. 8, 1547–1573 (2015).
[Crossref]

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[Crossref]

Ou, X.

Papanicolaou, G.

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Robust multifrequency imaging with MUSIC,” Inverse Prob. 35, 015007 (2018).
[Crossref]

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Multifrequency interferometric imaging with intensity-only measurements,” SIAM J. Imaging Sci. 10, 1005–1032 (2017).
[Crossref]

M. Moscoso, A. Novikov, and G. Papanicolaou, “Coherent imaging without phases,” SIAM J. Imaging Sci. 9, 1689–1707 (2016).
[Crossref]

A. Novikov, M. Moscoso, and G. Papanicolaou, “Illumination strategies for intensity-only imaging,” SIAM J. Imaging Sci. 8, 1547–1573 (2015).
[Crossref]

A. Chai, M. Moscoso, and G. Papanicolaou, “Imaging strong localized scatterers with sparcity promoting optimization,” SIAM J. Imaging Sci. 7, 1358–1387 (2014).
[Crossref]

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Prob. 27, 015005 (2010).
[Crossref]

Perrusson, G.

E. Iakovleva, S. Gdourra, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-D inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598–2609 (2007).
[Crossref]

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. 29, 674–709 (2007).
[Crossref]

Pham, T.-A.

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
[Crossref]

Psaltis, D.

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
[Crossref]

Schatzberg, A.

Soubies, E.

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
[Crossref]

Soulez, F.

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
[Crossref]

Tahir, W.

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1, 036003 (2019).
[Crossref]

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9, 2130–2141 (2018).
[Crossref]

Tian, L.

Tsogka, C.

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Robust multifrequency imaging with MUSIC,” Inverse Prob. 35, 015007 (2018).
[Crossref]

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Multifrequency interferometric imaging with intensity-only measurements,” SIAM J. Imaging Sci. 10, 1005–1032 (2017).
[Crossref]

Unser, M.

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
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W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

Zhang, W.

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

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Adv. Photonics (1)

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1, 036003 (2019).
[Crossref]

Ann. Math. (1)

P. Jordan and J. von Neumann, “On inner products in linear, metric spaces,” Ann. Math. 36, 719–723 (1935).
[Crossref]

Appl. Opt. (2)

Biomed. Opt. Express (2)

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9, 2130–2141 (2018).
[Crossref]

T.-A. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez, D. Psaltis, and M. Unser, “Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering,” Biomed. Opt. Express 26, 2749–2763 (2018).
[Crossref]

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E. Iakovleva, S. Gdourra, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-D inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598–2609 (2007).
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M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Robust multifrequency imaging with MUSIC,” Inverse Prob. 35, 015007 (2018).
[Crossref]

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Prob. 27, 015005 (2010).
[Crossref]

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F. K. Gruber, E. A. Marengo, and A. J. Devaney, “Time-reversal imaging with multiple signal classification considering multiple scattering between the targets,” J. Acoust. Soc. Am. 115, 3042–3047 (2004).
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H. Ammari, E. Iakovleva, and D. Lesselier, “A MUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency,” Multiscale Model. Simul. 3, 597–628 (2005).
[Crossref]

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Opt. Express (1)

Opt. Lett. (1)

Optica (2)

Phys. Rev. Lett. (1)

W. Zhang, L. Cao, D. J. Brady, H. Zhang, J. Cang, H. Zhang, and G. Jin, “Twin-image-free holography: a compressive sensing approach,” Phys. Rev. Lett. 121, 093902 (2018).
[Crossref]

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A. Chai, M. Moscoso, and G. Papanicolaou, “Imaging strong localized scatterers with sparcity promoting optimization,” SIAM J. Imaging Sci. 7, 1358–1387 (2014).
[Crossref]

A. Novikov, M. Moscoso, and G. Papanicolaou, “Illumination strategies for intensity-only imaging,” SIAM J. Imaging Sci. 8, 1547–1573 (2015).
[Crossref]

M. Moscoso, A. Novikov, and G. Papanicolaou, “Coherent imaging without phases,” SIAM J. Imaging Sci. 9, 1689–1707 (2016).
[Crossref]

M. Moscoso, A. Novikov, G. Papanicolaou, and C. Tsogka, “Multifrequency interferometric imaging with intensity-only measurements,” SIAM J. Imaging Sci. 10, 1005–1032 (2017).
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H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. 29, 674–709 (2007).
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T. Wriedt, A. Doicu, and Y. Eremin, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, 2000).

A. D. Kim, “IntensityOnlyImagingwMUSIC,” https://github.com/arnolddkim/IntensityOnlyImagingwMUSIC .

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Figures (5)

Fig. 1.
Fig. 1. Spherical scattering object plotted in blue with radius $ a = 632\, \,\textrm{nm} $ and relative refractive index $ {n_1}/{n_0} = 1.4 $ and an isosurface corresponding to $ {I_k} = 0.1 $ of the reconstructed image plotted in red.
Fig. 2.
Fig. 2. Three spherical scattering objects plotted in blue, each with radius $ a = 632\,\, \textrm{nm} $ and relative refractive index $ {n_1}/{n_0} = 1.4 $ and an isosurface corresponding to $ {I_k} = 0.1 $ of the reconstructed image plotted in red.
Fig. 3.
Fig. 3. Eight spherical scattering objects plotted in blue, each with radius $ a = 632\, \,\textrm{nm} $ and relative refractive index $ {n_1}/{n_0} = 1.4 $ and an isosurface corresponding to $ {I_k} = 0.1 $ of the reconstructed image plotted in red.
Fig. 4.
Fig. 4. An ellipsoidal scattering object plotted in blue with principal semi-axes: $ a = 632\,\, \textrm{nm} $ , $ b = 948\,\, \textrm{nm} $ , and $ c = 474\,\, \textrm{nm} $ , and relative refractive index $ {n_1}/{n_0} = 1.4 $ . The isosurface corresponding to $ {I_k} = 0.1 $ of the reconstructed image plotted in red.
Fig. 5.
Fig. 5. Eight ellipsoidal scattering objects plotted in blue with principal semi-axes: $ a = 500\, \,\textrm{nm} $ , $ b = 400\,\, \textrm{nm} $ , and $ c = 300\, \,\textrm{nm} $ , and relative refractive index $ {n_1}/{n_0} = 1.4 $ . The orientations of these ellipsoidal scattering objects have been chosen randomly. The isosurface corresponding to $ {I_k} = 0.1 $ of the reconstructed image plotted in red.

Equations (30)

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| z 1 + z 2 | 2 = | z 1 | 2 + | z 2 | 2 + 2 Re [ z 1 z 2 ] ,
| z 1 + i z 2 | 2 = | z 1 | 2 + | z 2 | 2 + 2 Im [ z 1 z 2 ] ,
z 1 z 2 = 1 2 [ | z 1 + z 2 | 2 | z 1 | 2 | z 2 | 2 ] + i 1 2 [ | z 1 + i z 2 | 2 | z 1 | 2 | z 2 | 2 ] .
u 1 s ( r ) u m s ( r ) = 1 2 [ | u 1 s ( r ) + u m s ( r ) | 2 | u 1 s ( r ) | 2 | u m s ( r ) | 2 ] + i 1 2 [ | u 1 s ( r ) + i u m s ( r ) | 2 | u 1 s ( r ) | 2 | u m s ( r ) | 2 ] , m = 2 , , M .
b ( r ) = ( u 1 s ( r ) u 1 s ( r ) , u 1 s ( r ) u 2 s ( r ) , , u 1 s ( r ) u M s ( r ) ) .
B = [ b ( r 1 ) | b ( r 2 ) | | b ( r N ) ] ,
u m s ( r n ) = k = 1 K u m i ( ρ k ) G 0 ( r n , ρ k ) X k ,
G 0 ( r , r ) = e i k 0 | r r | 4 π | r r | ,
b n = b ( r n ) = u 1 s ( r n ) [ u 1 s ( r n ) u 2 s ( r n ) u M s ( r n ) ] ,
A Λ n x = b n .
[ A ] m k = u m i ( ρ k ) .
[ Λ n ] k k = u 1 s ( r n ) G 0 ( r n , ρ k ) ,
A [ Λ 1 x | Λ 2 x | | Λ N x ] = B ,
P = I M U ~ U ~ H ,
I k = η min η k , k = 1 , , K .
u m i ( r ) = e i k 0 s ^ r , m = 1 , , M ,
s ^ i j = ( sin θ i cos φ j , sin θ i sin φ j , cos θ i ) , i = 1 , , 25 , j = 1 , , 25.
( 2 + k 0 2 ) u s = 0 , in E ,
( 2 + k 1 2 ) U q = 0 , in Ω q for q = 1 , , Q ,
U q u s = u i on Ω q for q = 1 , , Q ,
ν U q ν u s = ν u i on Ω q for q = 1 , , Q ,
G j ( r r ) = e i k j | r r | 4 π | r r | , j = 0 , 1
( 2 + k j 2 ) G j ( r r ) = δ ( r r ) , j = 0 , 1
r q p int = r q p + ν q p , p = 1 , , P ,
r q p s = r q p ν q p , p = 1 , , P .
u s ( r ) q = 1 Q p = 1 P c q p s G 0 ( r r q p s ) , r E ,
U q ( r ) p = 1 P c q p int G 1 ( r r q p int ) , r Ω q ,
p = 1 P c q p int G 1 ( r q p r q p int ) q = 1 Q p = 1 P c q p s G 0 ( r q p r q p ext ) = u i ( r q p ) , q = 1 , , Q , p = 1 , , P
p = 1 P c q p int ν G 1 ( r q p r q p int ) q = 1 Q p = 1 P c q p s ν G 0 ( r q p r q p ext ) = ν u i ( r q p ) , q = 1 , , Q , p = 1 , , P
x 2 a 2 + y 2 b 2 + z 2 c 2 = 1.

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