This paper investigates the source reconstruction problem in underwater mediums using a compressive Near-Field Electromagnetic Holography (NEH) approach. More specifically we investigate the use of ℓ1 regularization for the purpose of decomposing near-field magnetic and/or electric surface measurements into electric and magnetic dipole sources. Our study indicates that not only do ℓ1 decompositions enable much higher resolution of sources than traditional ℓ2 approaches, but important features of the dipoles are preserved in the reconstruction. Our hypothesis are supported by numerical experiments as well as underwater physical measurements obtained in an earth field simulator facility.
2. Balanis, C. A., Antenna Theory: Analysis and Design, Wiley-Interscience, 2005.
3. Beck, A. and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM Journal of Imaging Sciences, Vol. 2, 183-202, 2009.
doi:10.1137/080716542
4. Candes, E., "Compressive sampling," International Congress of Mathematics, 2006.
5. Candes, E., "The restricted isometry property and its implications for compressed sensing," Comptes Rendus Mathematique, Vol. 346, No. 9-10, 589-592, May 2008.
doi:10.1016/j.crma.2008.03.014
6. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, 1998.
doi:10.1007/978-3-662-03537-5
7. Donoho, D., "For most large underdetermined systems of linear equations, the minimal ell-1 norm solution is also the sparsest solution," Communications on Pure and Applied Mathematics, Vol. 59, 797-829, 2006.
doi:10.1002/cpa.20132
8. Hansen, P. C., Rank-deficient and Discrete Ill-posed Problems, SIAM, Philadelphia, 1998.
doi:10.1137/1.9780898719697
9. Harrington, R. F., Time-harmonic Electromagnetic Fields, Wiley-IEEE Press, 2001.
doi:10.1109/9780470546710
10. Holmes, J., Reduction of a Ship's Magnetic Field Signatures, Morgan & Claypool Publishers, 2008.
11. Izquierdo, J., J. Rubio, J. Corcoles, and R. Gomez-Alcala, "Efficient radiation antenna modeling via orthogonal matching pursuit in terms of infinitesimal dipoles," IEEE Antennas and Wireless Propagation Letters, 99:1-1, 2015.
12. Morgan, M. A., "Electromagnetic holography on cylindrical surfaces using k-space transformations," Progress In Electromagnetics Research, Vol. 42, 303-337, 2003.
doi:10.2528/PIER03020302
13. Natarajan, B. K., "Sparse approximate solutions to linear system," SIAM J. Comput., Vol. 24, No. 2, 227-234, 1995.
doi:10.1137/S0097539792240406
14. Bradley Nelson, J., T. C. Richards, M. Birsan, and C. Greene, "Rimpasse 2011 electromagnetic trials quick-look report," Technical Report, Defence R&D Canada-Atlantic, 2011.
15. Quijano, J. L. A. and G. Vecchi, "Field and source equivalence in source reconstruction on 3D surfaces," Progress In Electromagnetics Research, Vol. 103, 67-100, 2010.
doi:10.2528/PIER10030309
16. Valdivia, N., E. G. Williams, P. C. Herdic, and B. Houston, "Surface decomposition method for near-field acoustic holography," Journal of Acoustical Society of America, 2012.
17. Valdivia, N. P. and E. G. Williams, "The reconstruction of surface tangential components of the electromagnetic field from near-field measurements," Inverse Problems, Vol. 23, 2007.
doi:10.1088/0266-5611/23/2/018
18. Valdivia, N. P. and E. G. Williams, "Study of the comparison of the methods of equivalent sources and boundary element methods for near-field acoustic holography," The Journal of the Acoustical Society of America, Vol. 120, No. 6, 3694-3705, 2006.
doi:10.1121/1.2359284
19. Williams, E. G. and J. D. Maynard, "Holographic imaging without the wavelength resolution limit," Phys. Rev. Lett., Vol. 45, 554-557, Aug. 1980.
doi:10.1103/PhysRevLett.45.554
20. Williams, E. G., Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography, Academic Press, London, U.K., 1999.
21. Williams, E. G. and N. P. Valdivia, "Near-field electromagnetic holography in conductive media," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 4, 1181-1192, 2010.
doi:10.1109/TAP.2010.2042028
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