Geometry of imaging configuration. The targets are embedded in a semi-infinite host medium with a flat interface. The imaging system is constituted of 81 transmitters and receivers placed on a two-dimensional lattice with square mesh. The antennas array is located at two wavelengths above the flat surface of the host medium. The typical size of the targets is about one incident wavelength.
Intensity map within W domain of the electric field deduced from the eigenvectors corresponding to the first ((a) and (c)) and the third ((b) and (d)) eigenvalue. (a) in the (x,y) plane for . (b) in the (x,y) plane for . (c) and (d) in the (x,z) plane for . Circles represent the actual boundary profiles of targets, while the dashed box represents the investigating domain Ω to be used in the inversion procedure.
Permittivity reconstruction obtained by HDORTM when the targets are placed in a homogeneous semi-infinite medium. (a) Cut along the (x,z) plane for when sole the data corresponding to are used. (b) Same as (a), but the frequency hopping procedure has been applied. (c) Plot of the relative permittivity along a vertical line passing through the target close to the interface (corresponding to and ).The solid curve indicates the actual permittivity profiles, the red line indicates the reconstruction obtained with the frequency hopping procedure, the dark green dashed line indicates the reconstruction obtained with the data only. (d) same as (c) but the line passes through the target far from the interface at and .
Reconstructed permittivity using either the HDORTM approach or the HM. Both techniques are applied with the frequency-hopping procedure. The targets are buried in a quasi-uncorrelated cluttered medium with correlation length and standard variation yielding a CSR of 102%. Except indicated otherwise, the clutter is generated in a domain W of size . (a) cut along the (x,z) plane at using the HDORTM. (b) same as (a) using the HM. (c) Iso-surface of the reconstructed permittivity profile at using HDORTM. (d) same as (c) using HM. (e) same as (c) but the clutter is generated in a larger domain of size . (f) Evolution of the cost function (log-scale representation) versus the iteration step using HDORTM (dashed curve) and HM (solid curve).
Iso-surface of the reconstructed permittivity profile at using HDORTM for the same configuration as that used in Fig. 4 (c); (a) The antennas are oriented along the x direction and the scattered field is detected along the x direction only. (b) The antennas are oriented along the y direction and the scattered field is detected along the y direction only.
Same as Figs. 4(a) and 4(b) , but the clutter standard variation is increased to yielding a CSR of 148%.
(a) Strength of the clutter scattered intensity, SC, versus for the half-space configuration (solid line) and for the homogeneous configuration (dashed line). (b)–(d) Reconstructed permittivity obtained with HDORTM and a frequency hopping procedure using only and . The clutter is defined by a correlation length and a standard deviation (b) Cut in the (x,z) plane for . (c) Reconstructed permittivity with respect to z at and . The blue solid curve denotes the actual permittivity of the targets, the red dashed line corresponds to the reconstructed profile obtained with HDORTM and a frequency hopping procedure restricted to and . The black line indicates the reconstruction obtained when the data obtained at for the two incident DORT fields focusing on the target close to the interface are included in the frequency hopping procedure. (d) same as (c) but and . Note that the black line (not shown) is superposed to the red one.
Reconstructed permittivity obtained with HDORTM when the clutter correlation length is and standard variation when three, and , or six wavelengths are used in the frequency hopping procedure. (a) Cut along the (x,z) plane for of the reconstructed permittivity obtained when three wavelengths are used in the frequency hopping procedure. (b) same as (a) but six wavelengths are used in the frequency hopping procedure. (c) and (d) plot of the relative permittivity versus (c) z for and ; (d) z for and . The blue solid line denotes the actual profiles of the targets. The dark green dashed lines indicate the reconstruction obtained with three wavelengths. The red solid lines indicate the reconstruction obtained with six wavelengths.
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