Metamaterial apertures for coherent computational imaging on the physical layer |
JOSA A, Vol. 30, Issue 8, pp. 1603-1612 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001603
Acrobat PDF (1026 KB)
Abstract
We introduce the concept of a metamaterial aperture, in which an underlying
reference mode interacts with a designed metamaterial surface to produce a
series of complex field patterns. The resonant frequencies of the metamaterial
elements are randomly distributed over a large bandwidth (18–26 GHz), such that
the aperture produces a rapidly varying sequence of field patterns as a function
of the input frequency. As the frequency of operation is scanned, different
subsets of metamaterial elements become active, in turn varying the field
patterns at the scene. Scene information can thus be indexed by frequency, with
the overall effectiveness of the imaging scheme tied to the diversity of the
generated field patterns. As the quality (
© 2013 Optical Society of America
1. INTRODUCTION
2. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009). [CrossRef]
3. C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. 49, E67–E82 (2010). [CrossRef]
5. W. Freese, T. Kampfe, E. B. Kley, and A. Tunnermann, “Design of binary subwavelength multiphase level computer generated holograms,” Opt. Lett. 35, 676–678 (2010). [CrossRef]
7. S. Larouche, Y. J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11, 450–454 (2012). [CrossRef]
8. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006). [CrossRef]
18. J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef]
9. J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013). [CrossRef]
19. B. H. Fong, J. S. Colburn, J. J. Ottusch, J. L. Visher, and D. F. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58, 3212–3221 (2010). [CrossRef]
20. C. Rockstuhl, C. Menzel, S. Muhlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83, 245119 (2011). [CrossRef]
2. COHERENT IMAGING MODEL
3. MEASUREMENT MATRIX AND FIGURES OF MERIT
18. J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef]
22. E. J. Candesand and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005). [CrossRef]
23. E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef]
24. R. Calderbank, S. Howard, and S. Jafarpour, “Construction of a large class of deterministic sensing matrices that satisfy a statistical isometry property,” IEEE J. Sel. Top. Signal Process. 4, 358–374 (2010). [CrossRef]
25. J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009). [CrossRef]
26. M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55, 5695–5702 (2007). [CrossRef]
25. J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009). [CrossRef]
25. J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009). [CrossRef]
4. METAMATERIAL APERTURE
28. F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004). [CrossRef]
31. E. Jarauta, M. A. G. Laso, T. Lopetegi, F. Falcone, M. Beruete, J. D. Baena, A. Marcotegui, J. Bonache, J. Garcia, R. Marques, and F. Martin, “Novel microstrip backward coupler with metamaterial cells for fully planar fabrication techniques,” Microw. Opt. Technol. Lett. 48, 1205–1209 (2006). [CrossRef]
32. K. Afrooz, A. Abdipour, and F. Martin, “Broadband bandpass filter using open complementary split ring resonator based on metamaterial unit-cell concept,” Microw. Opt. Technol. Lett. 54, 2832–2835 (2012). [CrossRef]
33. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008). [CrossRef]
36. Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary metamaterials,” Appl. Phys. Lett. 95, 181901 (2009). [CrossRef]
20. C. Rockstuhl, C. Menzel, S. Muhlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83, 245119 (2011). [CrossRef]
37. T. H. Hand, J. Gollub, S. Sajuyigbe, D. R. Smith, and S. A. Cummer, “Characterization of complementary electric field coupled resonant surfaces,” Appl. Phys. Lett. 93, 212504 (2008). [CrossRef]
5. IMPROVING THE METAIMAGER μ g
39. B. E. Usevitch,” A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000,” IEEE Signal Process. Mag. 18(5), 22–35 (2001). [CrossRef]
40. R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010). [CrossRef]
6. IMAGING OF A 2D SCENE
23. E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef]
41. E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006). [CrossRef]
42. D. L. Donoho, “For most large underdetermined systems of equations, the minimal l(1)-norm near-solution approximates the sparsest near-solution,” Commun. Pure Appl. Math. 59, 907–934 (2006). [CrossRef]
43. J. M. Bioucas-Dias and M. A. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007). [CrossRef]
39. B. E. Usevitch,” A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000,” IEEE Signal Process. Mag. 18(5), 22–35 (2001). [CrossRef]
7. IMAGING OF A 3D SCENE
8. CONCLUSIONS
ACKNOWLEDGMENTS
REFERENCES
1. | D. J. Brady, Optical Imaging and Spectroscopy (Wiley-OSA, 2009). |
2. | D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009). [CrossRef] |
3. | C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. 49, E67–E82 (2010). [CrossRef] |
4. | W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008). [CrossRef] |
5. | W. Freese, T. Kampfe, E. B. Kley, and A. Tunnermann, “Design of binary subwavelength multiphase level computer generated holograms,” Opt. Lett. 35, 676–678 (2010). [CrossRef] |
6. | U. Levy, H. C. Kim, C. H. Tsai, and Y. Fainman, “Near-infrared demonstration of computer-generated holograms implemented by using subwavelength gratings with space-variant orientation,” Opt. Lett. 30, 2089–2091 (2005). [CrossRef] |
7. | S. Larouche, Y. J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11, 450–454 (2012). [CrossRef] |
8. | H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006). [CrossRef] |
9. | J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013). [CrossRef] |
10. | W. Menzel, “New traveling-wave antenna in microstrip,” AEU Int. J. Electron. Commun. 33, 137–140 (1979). |
11. | A. Oliner and K. S. Lee, “Microstrip leaky wave strip antennas,” in IEEE International Antennas and Propagation Symposium Digest, Philadelphia, Pennsylvania, 1986, p. 443. |
12. | D. R. Jackson, C. Caloz, and T. Itoh, “Leaky-wave antennas,” Proc. IEEE 100, 2194–2206 (2012). [CrossRef] |
13. | A. Sutinjo, M. Okoniewski, and R. H. Johnston, “Radiation from fast and slow traveling waves,” IEEE Antennas Propag. Mag. 50(4), 175–181 (2008). [CrossRef] |
14. | C. A. Balanis, in Modern Antenna Handbook (Wiley, 2008), Chap. 7. |
15. | E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians, Madrid, August22–30, 2006 (invited lectures, 2006). |
16. | D. L. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006). [CrossRef] |
17. | R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007). [CrossRef] |
18. | J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef] |
19. | B. H. Fong, J. S. Colburn, J. J. Ottusch, J. L. Visher, and D. F. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58, 3212–3221 (2010). [CrossRef] |
20. | C. Rockstuhl, C. Menzel, S. Muhlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83, 245119 (2011). [CrossRef] |
21. | L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995). |
22. | E. J. Candesand and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005). [CrossRef] |
23. | E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef] |
24. | R. Calderbank, S. Howard, and S. Jafarpour, “Construction of a large class of deterministic sensing matrices that satisfy a statistical isometry property,” IEEE J. Sel. Top. Signal Process. 4, 358–374 (2010). [CrossRef] |
25. | J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009). [CrossRef] |
26. | M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55, 5695–5702 (2007). [CrossRef] |
27. | N. Landy, J. Hunt, and D. R. Smith, “Homogenization of guided wave metamaterials,” Photon. Nanostruct.—Fundam. Applic. (to be published). |
28. | F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004). [CrossRef] |
29. | F. Martin, J. Bonache, F. Falcone, M. Sorolla, and R. Marques, “Split ring resonator-based left-handed coplanar waveguide,” Appl. Phys. Lett. 83, 4652–4654 (2003). [CrossRef] |
30. | J. Martel, R. Marques, F. Falcone, J. D. Baena, F. Medina, F. Martin, and M. Sorolla, “A new LC series element for compact bandpass filter design,” IEEE Microw. Wirel. Compon. Lett. 14, 210–212 (2004). [CrossRef] |
31. | E. Jarauta, M. A. G. Laso, T. Lopetegi, F. Falcone, M. Beruete, J. D. Baena, A. Marcotegui, J. Bonache, J. Garcia, R. Marques, and F. Martin, “Novel microstrip backward coupler with metamaterial cells for fully planar fabrication techniques,” Microw. Opt. Technol. Lett. 48, 1205–1209 (2006). [CrossRef] |
32. | K. Afrooz, A. Abdipour, and F. Martin, “Broadband bandpass filter using open complementary split ring resonator based on metamaterial unit-cell concept,” Microw. Opt. Technol. Lett. 54, 2832–2835 (2012). [CrossRef] |
33. | R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008). [CrossRef] |
34. | Q. Cheng, R. P. Liu, J. J. Mock, T. J. Cui, and D. R. Smith, “Partial focusing by indefinite complementary metamaterials,” Phys. Rev. B 78, 121102 (2008). [CrossRef] |
35. | R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009). [CrossRef] |
36. | Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary metamaterials,” Appl. Phys. Lett. 95, 181901 (2009). [CrossRef] |
37. | T. H. Hand, J. Gollub, S. Sajuyigbe, D. R. Smith, and S. A. Cummer, “Characterization of complementary electric field coupled resonant surfaces,” Appl. Phys. Lett. 93, 212504 (2008). [CrossRef] |
38. | C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989). |
39. | B. E. Usevitch,” A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000,” IEEE Signal Process. Mag. 18(5), 22–35 (2001). [CrossRef] |
40. | R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010). [CrossRef] |
41. | E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006). [CrossRef] |
42. | D. L. Donoho, “For most large underdetermined systems of equations, the minimal l(1)-norm near-solution approximates the sparsest near-solution,” Commun. Pure Appl. Math. 59, 907–934 (2006). [CrossRef] |
43. | J. M. Bioucas-Dias and M. A. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007). [CrossRef] |
44. | R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002). |
45. | M. A. Richards, Fundamentals of Radar Signal Processing (McGraw-Hill, 2005). |
OCIS Codes
(100.3190) Image processing : Inverse problems
(110.1220) Imaging systems : Apertures
(110.2970) Imaging systems : Image detection systems
(110.1758) Imaging systems : Computational imaging
(160.3918) Materials : Metamaterials
ToC Category:
Imaging Systems
History
Original Manuscript: April 2, 2013
Manuscript Accepted: May 13, 2013
Published: July 19, 2013
Virtual Issues
August 9, 2013 Spotlight on Optics
Citation
Guy Lipworth, Alex Mrozack, John Hunt, Daniel L. Marks, Tom Driscoll, David Brady, and David R. Smith, "Metamaterial apertures for coherent computational imaging on the physical layer," J. Opt. Soc. Am. A 30, 1603-1612 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-8-1603
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References
- D. J. Brady, Optical Imaging and Spectroscopy (Wiley-OSA, 2009).
- D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009). [CrossRef]
- C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. 49, E67–E82 (2010). [CrossRef]
- W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008). [CrossRef]
- W. Freese, T. Kampfe, E. B. Kley, and A. Tunnermann, “Design of binary subwavelength multiphase level computer generated holograms,” Opt. Lett. 35, 676–678 (2010). [CrossRef]
- U. Levy, H. C. Kim, C. H. Tsai, and Y. Fainman, “Near-infrared demonstration of computer-generated holograms implemented by using subwavelength gratings with space-variant orientation,” Opt. Lett. 30, 2089–2091 (2005). [CrossRef]
- S. Larouche, Y. J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11, 450–454 (2012). [CrossRef]
- H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006). [CrossRef]
- J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339, 310–313 (2013). [CrossRef]
- W. Menzel, “New traveling-wave antenna in microstrip,” AEU Int. J. Electron. Commun. 33, 137–140 (1979).
- A. Oliner and K. S. Lee, “Microstrip leaky wave strip antennas,” in IEEE International Antennas and Propagation Symposium Digest, Philadelphia, Pennsylvania, 1986, p. 443.
- D. R. Jackson, C. Caloz, and T. Itoh, “Leaky-wave antennas,” Proc. IEEE 100, 2194–2206 (2012). [CrossRef]
- A. Sutinjo, M. Okoniewski, and R. H. Johnston, “Radiation from fast and slow traveling waves,” IEEE Antennas Propag. Mag. 50(4), 175–181 (2008). [CrossRef]
- C. A. Balanis, in Modern Antenna Handbook (Wiley, 2008), Chap. 7.
- E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians, Madrid, August22–30, 2006 (invited lectures, 2006).
- D. L. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006). [CrossRef]
- R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007). [CrossRef]
- J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef]
- B. H. Fong, J. S. Colburn, J. J. Ottusch, J. L. Visher, and D. F. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58, 3212–3221 (2010). [CrossRef]
- C. Rockstuhl, C. Menzel, S. Muhlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B 83, 245119 (2011). [CrossRef]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
- E. J. Candesand and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005). [CrossRef]
- E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef]
- R. Calderbank, S. Howard, and S. Jafarpour, “Construction of a large class of deterministic sensing matrices that satisfy a statistical isometry property,” IEEE J. Sel. Top. Signal Process. 4, 358–374 (2010). [CrossRef]
- J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009). [CrossRef]
- M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55, 5695–5702 (2007). [CrossRef]
- N. Landy, J. Hunt, and D. R. Smith, “Homogenization of guided wave metamaterials,” Photon. Nanostruct.—Fundam. Applic. (to be published).
- F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marques, F. Martin, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93, 197401 (2004). [CrossRef]
- F. Martin, J. Bonache, F. Falcone, M. Sorolla, and R. Marques, “Split ring resonator-based left-handed coplanar waveguide,” Appl. Phys. Lett. 83, 4652–4654 (2003). [CrossRef]
- J. Martel, R. Marques, F. Falcone, J. D. Baena, F. Medina, F. Martin, and M. Sorolla, “A new LC series element for compact bandpass filter design,” IEEE Microw. Wirel. Compon. Lett. 14, 210–212 (2004). [CrossRef]
- E. Jarauta, M. A. G. Laso, T. Lopetegi, F. Falcone, M. Beruete, J. D. Baena, A. Marcotegui, J. Bonache, J. Garcia, R. Marques, and F. Martin, “Novel microstrip backward coupler with metamaterial cells for fully planar fabrication techniques,” Microw. Opt. Technol. Lett. 48, 1205–1209 (2006). [CrossRef]
- K. Afrooz, A. Abdipour, and F. Martin, “Broadband bandpass filter using open complementary split ring resonator based on metamaterial unit-cell concept,” Microw. Opt. Technol. Lett. 54, 2832–2835 (2012). [CrossRef]
- R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008). [CrossRef]
- Q. Cheng, R. P. Liu, J. J. Mock, T. J. Cui, and D. R. Smith, “Partial focusing by indefinite complementary metamaterials,” Phys. Rev. B 78, 121102 (2008). [CrossRef]
- R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 073506 (2009). [CrossRef]
- Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary metamaterials,” Appl. Phys. Lett. 95, 181901 (2009). [CrossRef]
- T. H. Hand, J. Gollub, S. Sajuyigbe, D. R. Smith, and S. A. Cummer, “Characterization of complementary electric field coupled resonant surfaces,” Appl. Phys. Lett. 93, 212504 (2008). [CrossRef]
- C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
- B. E. Usevitch,” A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000,” IEEE Signal Process. Mag. 18(5), 22–35 (2001). [CrossRef]
- R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010). [CrossRef]
- E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006). [CrossRef]
- D. L. Donoho, “For most large underdetermined systems of equations, the minimal l(1)-norm near-solution approximates the sparsest near-solution,” Commun. Pure Appl. Math. 59, 907–934 (2006). [CrossRef]
- J. M. Bioucas-Dias and M. A. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007). [CrossRef]
- R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).
- M. A. Richards, Fundamentals of Radar Signal Processing (McGraw-Hill, 2005).
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