Vol. 80
Latest Volume
All Volumes
PIERC 150 [2024] PIERC 149 [2024] PIERC 148 [2024] PIERC 147 [2024] PIERC 146 [2024] PIERC 145 [2024] PIERC 144 [2024] PIERC 143 [2024] PIERC 142 [2024] PIERC 141 [2024] PIERC 140 [2024] PIERC 139 [2024] PIERC 138 [2023] PIERC 137 [2023] PIERC 136 [2023] PIERC 135 [2023] PIERC 134 [2023] PIERC 133 [2023] PIERC 132 [2023] PIERC 131 [2023] PIERC 130 [2023] PIERC 129 [2023] PIERC 128 [2023] PIERC 127 [2022] PIERC 126 [2022] PIERC 125 [2022] PIERC 124 [2022] PIERC 123 [2022] PIERC 122 [2022] PIERC 121 [2022] PIERC 120 [2022] PIERC 119 [2022] PIERC 118 [2022] PIERC 117 [2021] PIERC 116 [2021] PIERC 115 [2021] PIERC 114 [2021] PIERC 113 [2021] PIERC 112 [2021] PIERC 111 [2021] PIERC 110 [2021] PIERC 109 [2021] PIERC 108 [2021] PIERC 107 [2021] PIERC 106 [2020] PIERC 105 [2020] PIERC 104 [2020] PIERC 103 [2020] PIERC 102 [2020] PIERC 101 [2020] PIERC 100 [2020] PIERC 99 [2020] PIERC 98 [2020] PIERC 97 [2019] PIERC 96 [2019] PIERC 95 [2019] PIERC 94 [2019] PIERC 93 [2019] PIERC 92 [2019] PIERC 91 [2019] PIERC 90 [2019] PIERC 89 [2019] PIERC 88 [2018] PIERC 87 [2018] PIERC 86 [2018] PIERC 85 [2018] PIERC 84 [2018] PIERC 83 [2018] PIERC 82 [2018] PIERC 81 [2018] PIERC 80 [2018] PIERC 79 [2017] PIERC 78 [2017] PIERC 77 [2017] PIERC 76 [2017] PIERC 75 [2017] PIERC 74 [2017] PIERC 73 [2017] PIERC 72 [2017] PIERC 71 [2017] PIERC 70 [2016] PIERC 69 [2016] PIERC 68 [2016] PIERC 67 [2016] PIERC 66 [2016] PIERC 65 [2016] PIERC 64 [2016] PIERC 63 [2016] PIERC 62 [2016] PIERC 61 [2016] PIERC 60 [2015] PIERC 59 [2015] PIERC 58 [2015] PIERC 57 [2015] PIERC 56 [2015] PIERC 55 [2014] PIERC 54 [2014] PIERC 53 [2014] PIERC 52 [2014] PIERC 51 [2014] PIERC 50 [2014] PIERC 49 [2014] PIERC 48 [2014] PIERC 47 [2014] PIERC 46 [2014] PIERC 45 [2013] PIERC 44 [2013] PIERC 43 [2013] PIERC 42 [2013] PIERC 41 [2013] PIERC 40 [2013] PIERC 39 [2013] PIERC 38 [2013] PIERC 37 [2013] PIERC 36 [2013] PIERC 35 [2013] PIERC 34 [2013] PIERC 33 [2012] PIERC 32 [2012] PIERC 31 [2012] PIERC 30 [2012] PIERC 29 [2012] PIERC 28 [2012] PIERC 27 [2012] PIERC 26 [2012] PIERC 25 [2012] PIERC 24 [2011] PIERC 23 [2011] PIERC 22 [2011] PIERC 21 [2011] PIERC 20 [2011] PIERC 19 [2011] PIERC 18 [2011] PIERC 17 [2010] PIERC 16 [2010] PIERC 15 [2010] PIERC 14 [2010] PIERC 13 [2010] PIERC 12 [2010] PIERC 11 [2009] PIERC 10 [2009] PIERC 9 [2009] PIERC 8 [2009] PIERC 7 [2009] PIERC 6 [2009] PIERC 5 [2008] PIERC 4 [2008] PIERC 3 [2008] PIERC 2 [2008] PIERC 1 [2008]
2017-12-02
Information Content in Inverse Source with Symmetry and Support Priors
By
Progress In Electromagnetics Research C, Vol. 80, 39-54, 2018
Abstract
This paper illustrates how inverse source problems are a ected by certain symmetry and support priors concerning the source space. The study is developed for a prototype con guration where the field radiated by square integrable strip sources is observed in far-zone. Three symmetry priors are considered: the source is a priori known to be a real or Hermitian or even (resp. odd) function. Instead, as spatial priors we assume that the source support consists of a single or multiple disjoint domains. The role of the aforementioned priors is assessed against some metrics commonly used to characterise inverse source problems such as the number of degrees of freedom, the point-spread function and the ``information content'' measured through the Kolmogorov entropy.
Citation
Raffaele Solimene, Maria Antonia Maisto, and Rocco Pierri, "Information Content in Inverse Source with Symmetry and Support Priors," Progress In Electromagnetics Research C, Vol. 80, 39-54, 2018.
doi:10.2528/PIERC17090903
References

1. Soldovieri, F., C. Mola, R. Solimene, and R. Pierri, "Inverse source problem from the knowledge of radiated field over multiple rectilinear domains," Progress In Electromagnetics Research M, Vol. 8, 131-141, 2009.
doi:10.2528/PIERM09062607

2. Solimene, R., C. Mola, R. Pierri, and F. Soldovieri, "Inverse source problem: A comparison between the cases of electric and magnetic sources," Progress In Electromagnetics Research M, Vol. 20, 127-141, 2011.
doi:10.2528/PIERM11070502

3. Kantorovic, L. V. and G. P. Akilov, Functional Analysis, Pergamon Press, 1982.
doi:10.1016/B978-0-08-023036-8.50011-4

4. Bertero, M., "Linear inverse and ill-posed problems," Adv. Electron. Electron. Phys., Vol. 45, 1-120, 1989.

5. Den Dekker, A. and A. van den Bos, "Resolution: A survey," J. Opt. Soc. Am. A, Vol. 14, 547-557, 1997.
doi:10.1364/JOSAA.14.000547

6. Jagerman, D., "ε-entropy and approximation of bandlimitated functions," SIAM J. Appl. Math., Vol. 17, 362-377, 1969.
doi:10.1137/0117035

7. Toraldo di Francia, G., "Degrees of freedom of an image," J. Opt. Soc. Am., Vol. 59, 799-804, 1969.
doi:10.1364/JOSA.59.000799

8. Piestun, R. and D. A. B. Miller, "Electromagnetic degrees of freedom of an optical system," J. Opt. Soc. Am. A, Vol. 17, 892-902, 2000.
doi:10.1364/JOSAA.17.000892

9. Newsam, G. and R. Barakat, "Essential dimension as a well-defined number of degrees of freedom of finite-convolution operators appearing in optics," J. Opt. Soc. Am. A, Vol. 2, 2040-2045, 1985.
doi:10.1364/JOSAA.2.002040

10. Kolmogorov, F. M. and V. M. Tikhomirov, "ε-entropy and ε-capacity of sets in functional spaces," Am. Math. Soc. Transl., Vol. 17, 277-364, 1961.

11. Tikhonov, A. N. and V. I. Arsenine, Solution to Ill-posed Problems, Halsted, New York, 1977.

12. De Micheli, E. and G. A. Viano, "Fredholm integral equations of the first kind and topological information theory," Integr. Equ. Oper. Theory, Vol. 73, 553-571, 2012.
doi:10.1007/s00020-012-1970-z

13. De Micheli, E. and G. A. Viano, "Metric and probabilistic information associated with Fredholm integral equations of the first kind," J. Int. Eq. Appl., Vol. 14, 283-310, 2002.
doi:10.1216/jiea/1181074917

14. Slepian, D. and H. O. Pollak, "Prolate spheroidal wave function, Fourier analysis and uncertainty I," Bell Syst. Tech. J., Vol. 40, 43-63, 1961.
doi:10.1002/j.1538-7305.1961.tb03976.x

15. Hille, E. and J. Tamarkin, "On the characteristic values of linear integral equations," Acta Math., Vol. 57, 1-76, 1931.
doi:10.1007/BF02403043

16. Solimene, R., M. A. Maisto, and R. Pierri, "The role of diversity on the singular values of linear scattering operators: The case of strip objects," J. Opt. Soc. A, Vol. 30, 2266-2272, 2013.
doi:10.1364/JOSAA.30.002266

17. Landau, H. J., "Sampling, data transmission, and the Nyquist rate," IEEE Proc., Vol. 55, 1701-1706, 1967.
doi:10.1109/PROC.1967.5962

18. Beurling, A. and P. Malliavin, "On the closure of characters and the zeros of entire functions," Acta Math., Vol. 118, 79-93, 1967.
doi:10.1007/BF02392477

19. Landau, H. J., "Necessary density conditions for sampling and interpolation of certain entire functions," Acta Math., Vol. 117, 35-52, 1967.
doi:10.1007/BF02395039

20. Solimene, R. and R. Pierri, "Localization of a planar perfect-electric-conducting interface embedded in a half-space," J. Opt. A: Pure Appl. Opt., Vol. 8, 10-16, 2006.
doi:10.1088/1464-4258/8/1/002

21. Solimene, R., M. A. Maisto, and R. Pierri, "Inverse source in the presence of a reflecting plane for the strip case," J. Opt. Soc. Am. A, Vol. 31, 2814-2820, 2014.
doi:10.1364/JOSAA.31.002814

22. Solimene, R., M. A. Maisto, and R. Pierri, "Inverse scattering in the presence of a reflecting plane," J. Opt., Vol. 18, 025603, 2015.
doi:10.1088/2040-8978/18/2/025603

23. Solimene, R., C. Mola, G. Gennarelli, and F. Soldovieri, "On the singular spectrum of radiation operators in the non-reactive zone: The case of strip sources," J. Opt., Vol. 17, 025605, 2015.
doi:10.1088/2040-8978/17/2/025605

24. Riesz, F. and B. S. Nagy, Functional Analysis,, Dover Publications, 1990.