D. Gross, “Recovering low-rank matrices from few coefficients in any basis,” IEEE Trans. Inf. Theory 57, 1548–1566 (2011).

[CrossRef]

D. Pelliccia, A. Y. Nikulin, H. O. Moser, and K. A. Nugent, “Experimental characterization of the coherence properties of hard x-ray sources,” Opt. Express 19, 8073–8078 (2011).

[CrossRef]
[PubMed]

Y. Shechtman, Y. C. Eldar, A. Szameit, and M. Segev, “Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing,” Opt. Express 19, 14807–14822 (2011).

[CrossRef]
[PubMed]

E. J. Candès and T. Tao, “The power of convex relaxation: near-optimal matrix completion,” IEEE Trans. Inform. Theory 56, 2053–2080 (2010).

[CrossRef]

D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105, 150401 (2010).

[CrossRef]

E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Found. Comput. Math. 9, 717–772 (2009).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52, 489–509 (2006).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006).

[CrossRef]

C. Kurtsiefer, T. Pfau, and J. Mlynek, “Measurement of the Wigner function of an ensemble of Helium atoms,” Nature (London) 386, 150–153 (1997).

[CrossRef]

J. Tu, “Wave field determination using tomography of the ambiguity function,” Phys. Rev. E 55, 1946–1949 (1997).

[CrossRef]

U. Leonhardt, “Quantum–state tomography and discrete Wigner function,” Phys. Rev. Lett. 74, 4101–4105 (1995).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, and D. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244–1247 (1993).

[CrossRef]
[PubMed]

M. Beck, M. G. Raymer, I. A. Walmsley, and V. Wong, “Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses,” Opt. Lett. 18, 2041–2043 (1993).

[CrossRef]
[PubMed]

K. A. Nugent, “Wave field determination using three-dimensional intensity information,” Phys. Rev. Lett. 68, 2261–2264 (1992).

[CrossRef]
[PubMed]

K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).

[CrossRef]
[PubMed]

K.-H. Brenner, A. Lohmann, and J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).

[CrossRef]

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).

[CrossRef]

M. G. Raymer, M. Beck, and D. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

M. Beck, M. G. Raymer, I. A. Walmsley, and V. Wong, “Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses,” Opt. Lett. 18, 2041–2043 (1993).

[CrossRef]
[PubMed]

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244–1247 (1993).

[CrossRef]
[PubMed]

D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105, 150401 (2010).

[CrossRef]

K. Blum, Density Matrix Theory and Applications (Plenum Press, 1981).

K.-H. Brenner and J. Ojeda-Castañeda, “Ambiguity function and Wigner distribution function applied to partially coherent imagery,” Opt. Acta. 31, 213–223 (1984).

[CrossRef]

K.-H. Brenner, A. Lohmann, and J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).

[CrossRef]

J.-F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” ArXiv: 0810.3286 (2008).

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52, 489–509 (2006).

[CrossRef]

E. J. Candès and T. Tao, “The power of convex relaxation: near-optimal matrix completion,” IEEE Trans. Inform. Theory 56, 2053–2080 (2010).

[CrossRef]

E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Found. Comput. Math. 9, 717–772 (2009).

[CrossRef]

E. J. Candès, Y. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” ArXiv: 1109.0573 (2011).

J.-F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” ArXiv: 0810.3286 (2008).

E. J. Candès, T. Strohmer, and V. Voroninski, “Phaselift: exact and stable signal recovery from magnitude measurements via convex programming,” ArXiv: 1109.4499v1 (2011).

E. J. Candès and Y. Plan, “Matrix completion with noise,” ArXiv: 0903.3131 (2009).

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006).

[CrossRef]

D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105, 150401 (2010).

[CrossRef]

E. J. Candès, Y. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” ArXiv: 1109.0573 (2011).

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244–1247 (1993).

[CrossRef]
[PubMed]

D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105, 150401 (2010).

[CrossRef]

J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

D. Gross, “Recovering low-rank matrices from few coefficients in any basis,” IEEE Trans. Inf. Theory 57, 1548–1566 (2011).

[CrossRef]

D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105, 150401 (2010).

[CrossRef]

A. C. Kak and M. Slaney, Principle of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).

[CrossRef]

C. Kurtsiefer, T. Pfau, and J. Mlynek, “Measurement of the Wigner function of an ensemble of Helium atoms,” Nature (London) 386, 150–153 (1997).

[CrossRef]

U. Leonhardt, “Quantum–state tomography and discrete Wigner function,” Phys. Rev. Lett. 74, 4101–4105 (1995).

[CrossRef]
[PubMed]

D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105, 150401 (2010).

[CrossRef]

K.-H. Brenner, A. Lohmann, and J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).

[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

M. G. Raymer, M. Beck, and D. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

C. Kurtsiefer, T. Pfau, and J. Mlynek, “Measurement of the Wigner function of an ensemble of Helium atoms,” Nature (London) 386, 150–153 (1997).

[CrossRef]

D. Pelliccia, A. Y. Nikulin, H. O. Moser, and K. A. Nugent, “Experimental characterization of the coherence properties of hard x-ray sources,” Opt. Express 19, 8073–8078 (2011).

[CrossRef]
[PubMed]

C. Q. Tran, A. G. Peele, A. Roberts, K. A. Nugent, D. Paterson, and I. McNulty, “X-ray imaging: a generalized approach using phase-space tomography,” J. Opt. Soc. Am. A 22, 1691–1700 (2005).

[CrossRef]

K. A. Nugent, “Wave field determination using three-dimensional intensity information,” Phys. Rev. Lett. 68, 2261–2264 (1992).

[CrossRef]
[PubMed]

K.-H. Brenner and J. Ojeda-Castañeda, “Ambiguity function and Wigner distribution function applied to partially coherent imagery,” Opt. Acta. 31, 213–223 (1984).

[CrossRef]

K.-H. Brenner, A. Lohmann, and J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).

[CrossRef]

C. Kurtsiefer, T. Pfau, and J. Mlynek, “Measurement of the Wigner function of an ensemble of Helium atoms,” Nature (London) 386, 150–153 (1997).

[CrossRef]

E. J. Candès and Y. Plan, “Matrix completion with noise,” ArXiv: 0903.3131 (2009).

M. G. Raymer, M. Beck, and D. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244–1247 (1993).

[CrossRef]
[PubMed]

M. Beck, M. G. Raymer, I. A. Walmsley, and V. Wong, “Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses,” Opt. Lett. 18, 2041–2043 (1993).

[CrossRef]
[PubMed]

E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Found. Comput. Math. 9, 717–772 (2009).

[CrossRef]

K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).

[CrossRef]
[PubMed]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52, 489–509 (2006).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

J.-F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” ArXiv: 0810.3286 (2008).

A. C. Kak and M. Slaney, Principle of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).

[CrossRef]

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244–1247 (1993).

[CrossRef]
[PubMed]

E. J. Candès, T. Strohmer, and V. Voroninski, “Phaselift: exact and stable signal recovery from magnitude measurements via convex programming,” ArXiv: 1109.4499v1 (2011).

E. J. Candès, Y. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” ArXiv: 1109.0573 (2011).

E. J. Candès and T. Tao, “The power of convex relaxation: near-optimal matrix completion,” IEEE Trans. Inform. Theory 56, 2053–2080 (2010).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52, 489–509 (2006).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

J. Tu, “Wave field determination using tomography of the ambiguity function,” Phys. Rev. E 55, 1946–1949 (1997).

[CrossRef]

K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).

[CrossRef]
[PubMed]

E. J. Candès, T. Strohmer, and V. Voroninski, “Phaselift: exact and stable signal recovery from magnitude measurements via convex programming,” ArXiv: 1109.4499v1 (2011).

E. J. Candès, Y. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” ArXiv: 1109.0573 (2011).

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

E. J. Candès and B. Recht, “Exact matrix completion via convex optimization,” Found. Comput. Math. 9, 717–772 (2009).

[CrossRef]

D. Gross, “Recovering low-rank matrices from few coefficients in any basis,” IEEE Trans. Inf. Theory 57, 1548–1566 (2011).

[CrossRef]

E. J. Candès and T. Tao, “The power of convex relaxation: near-optimal matrix completion,” IEEE Trans. Inform. Theory 56, 2053–2080 (2010).

[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory 52, 489–509 (2006).

[CrossRef]

C. Q. Tran, A. G. Peele, A. Roberts, K. A. Nugent, D. Paterson, and I. McNulty, “X-ray imaging: a generalized approach using phase-space tomography,” J. Opt. Soc. Am. A 22, 1691–1700 (2005).

[CrossRef]

M. J. Bastiaans, “New class of uncertainty relations for partially coherent light,” J. Opt. Soc. Am. A 1, 711–715 (1984).

[CrossRef]

K. Itoh and Y. Ohtsuka, “Fourier-transform spectral imaging: retrieval of source information from three-dimensional spatial coherence,” J. Opt. Soc. Am. A 3, 94–100 (1986).

[CrossRef]

M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3, 1227–1238 (1986).

[CrossRef]

C. Kurtsiefer, T. Pfau, and J. Mlynek, “Measurement of the Wigner function of an ensemble of Helium atoms,” Nature (London) 386, 150–153 (1997).

[CrossRef]

K.-H. Brenner and J. Ojeda-Castañeda, “Ambiguity function and Wigner distribution function applied to partially coherent imagery,” Opt. Acta. 31, 213–223 (1984).

[CrossRef]

K.-H. Brenner, A. Lohmann, and J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).

[CrossRef]

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).

[CrossRef]

D. Pelliccia, A. Y. Nikulin, H. O. Moser, and K. A. Nugent, “Experimental characterization of the coherence properties of hard x-ray sources,” Opt. Express 19, 8073–8078 (2011).

[CrossRef]
[PubMed]

Y. Shechtman, Y. C. Eldar, A. Szameit, and M. Segev, “Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing,” Opt. Express 19, 14807–14822 (2011).

[CrossRef]
[PubMed]

K. Vogel and H. Risken, “Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A 40, 2847–2849 (1989).

[CrossRef]
[PubMed]

J. Tu, “Wave field determination using tomography of the ambiguity function,” Phys. Rev. E 55, 1946–1949 (1997).

[CrossRef]

D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105, 150401 (2010).

[CrossRef]

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244–1247 (1993).

[CrossRef]
[PubMed]

U. Leonhardt, “Quantum–state tomography and discrete Wigner function,” Phys. Rev. Lett. 74, 4101–4105 (1995).

[CrossRef]
[PubMed]

K. A. Nugent, “Wave field determination using three-dimensional intensity information,” Phys. Rev. Lett. 68, 2261–2264 (1992).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, and D. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

K. Blum, Density Matrix Theory and Applications (Plenum Press, 1981).

J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

E. J. Candès and Y. Plan, “Matrix completion with noise,” ArXiv: 0903.3131 (2009).

J.-F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” ArXiv: 0810.3286 (2008).

A. C. Kak and M. Slaney, Principle of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).

[CrossRef]

E. J. Candès, T. Strohmer, and V. Voroninski, “Phaselift: exact and stable signal recovery from magnitude measurements via convex programming,” ArXiv: 1109.4499v1 (2011).

E. J. Candès, Y. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” ArXiv: 1109.0573 (2011).