A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

Y. Shechtman, S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse images carried by incoherent light,” Opt. Lett. 35(8), 1148–1150 (2010).

[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(15), 150401 (2010).

[CrossRef]
[PubMed]

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).

[CrossRef]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).

[CrossRef]
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).

[CrossRef]
[PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).

[CrossRef]
[PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).

[CrossRef]
[PubMed]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).

[CrossRef]
[PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).

[CrossRef]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).

[CrossRef]
[PubMed]

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 A spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13(3), 227–231 (1984).

[CrossRef]

E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237(5357), 510–512 (1972).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237(5357), 510–512 (1972).

[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(15), 150401 (2010).

[CrossRef]
[PubMed]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).

[CrossRef]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

[CrossRef]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).

[CrossRef]
[PubMed]

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).

[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).

[CrossRef]

D. Gross, Y. K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105(15), 150401 (2010).

[CrossRef]
[PubMed]

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).

[CrossRef]

Y. Shechtman, S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse images carried by incoherent light,” Opt. Lett. 35(8), 1148–1150 (2010).

[CrossRef]
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[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(15), 150401 (2010).

[CrossRef]
[PubMed]

Y. Shechtman, S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse images carried by incoherent light,” Opt. Lett. 35(8), 1148–1150 (2010).

[CrossRef]
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).

[CrossRef]
[PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).

[CrossRef]

D. Gross, Y. K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105(15), 150401 (2010).

[CrossRef]
[PubMed]

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 A spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13(3), 227–231 (1984).

[CrossRef]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).

[CrossRef]
[PubMed]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).

[CrossRef]
[PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).

[CrossRef]
[PubMed]

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 A spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13(3), 227–231 (1984).

[CrossRef]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).

[CrossRef]
[PubMed]

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 A spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13(3), 227–231 (1984).

[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).

[CrossRef]

D. Gross, Y. K. Liu, S. T. Flammia, S. Becker, and J. Eisert, “Quantum state tomography via compressed sensing,” Phys. Rev. Lett. 105(15), 150401 (2010).

[CrossRef]
[PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 A spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13(3), 227–231 (1984).

[CrossRef]

E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237(5357), 510–512 (1972).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

[CrossRef]

Y. Shechtman, S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse images carried by incoherent light,” Opt. Lett. 35(8), 1148–1150 (2010).

[CrossRef]
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).

[CrossRef]
[PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).

[CrossRef]
[PubMed]

Y. Shechtman, S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse images carried by incoherent light,” Opt. Lett. 35(8), 1148–1150 (2010).

[CrossRef]
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).

[CrossRef]
[PubMed]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).

[CrossRef]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).

[CrossRef]
[PubMed]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).

[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).

[CrossRef]
[PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).

[CrossRef]
[PubMed]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).

[CrossRef]
[PubMed]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

[CrossRef]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).

[CrossRef]
[PubMed]

E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237(5357), 510–512 (1972).

[CrossRef]
[PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).

[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).

[CrossRef]
[PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009).

[CrossRef]
[PubMed]

Y. Shechtman, S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse images carried by incoherent light,” Opt. Lett. 35(8), 1148–1150 (2010).

[CrossRef]
[PubMed]

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (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(15), 150401 (2010).

[CrossRef]
[PubMed]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106(10), 100401 (2011).

[CrossRef]
[PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).

[CrossRef]
[PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).

[CrossRef]
[PubMed]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991).

[CrossRef]
[PubMed]

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).

[CrossRef]

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 A spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13(3), 227–231 (1984).

[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

A. Szameit, Y. Shechtman, H. Dana, S. Steiner, S. Gazit, T. Cohen-Hyams, E. Bullkich, O. Cohen, Y. C. Eldar, S. Shoham, E. B. Kley, and M. Segev, “Far-field microscopy of sparse subwavelength objects,” arXiv:1010.0631 [physics.optics] (2010).

J. W. Goodman, Statistical Optics (Wiley, 1985).

M. Fazel, H. Hindi, and S. Boyd, “Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices,” in Proceedings of Am. Control Conf. (2003).

E. J. Candes (Departments of Mathematics and of Statistics, Stanford University, Stanford CA 94305), Y. C. Eldar, T. Strohmer, and V. Voroninski are preparing a manuscript to be called “Phase retrieval via matrix completion.”