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

[CrossRef]

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]

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]

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, “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]

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).

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

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]

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, “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]

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

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. 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. 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]

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

[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]

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, “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. 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]

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).

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

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

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).

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).

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

[CrossRef]