Chapter 3: Vehicle-Mounted GPR System for Landmine Detection

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36 3. Vehicle-Mounted GPR System for Landmine Detection 3.3 Image Reconstruction In this system, well-established and fast imaging algorithms are implemented in order to satisfy the time limitation. The followings are the processing flow of the acquired data as summarized in Fig. 3.10 (Feng and Sato, 2004): data D ( r, ω) acquired at a certain position r = {, x yz ,} includes direct coupling components D c ( ω) . The components can be acquired prior to a measurement pointing the antennas to the air space and is subtracted from the measured data. S (, r ω) = D (, r ω) −D c ( ω) (3.1) Then inverse Fourier transform is taken to construct time domain signals. 1 s(,) r t = F − ⎡ S ⎣ (, r ω) ⎤ ⎦ (3.2) Signals acquired by different antennas have different amplitudes. Their amplitudes should take a balance to make the weights equal for CMP stacking. The balanced traces can be obtained by weighting the original traces, and the weighting factor is calculated from the averaged amplitudes. First, a time average of a trace by an antenna combination is calculated as 1 Qn() r = dt sn(,) t n= 1, , N T ∫ r , (3.3) where N denotes the number of antenna combinations, N = 3 in the system, and T is a length of the time window. Then the averaged amplitude for all combinations is calculated as Frequency domain data Direct coupling subtraction IFT Trace balancing NMO CMP Migration 3D image Fig. 3.10: Processing flow chart in SAR-GPR.
3.3 Image Reconstruction 37 N 1 Q() r = ∑Qn () r . (3.4) N n = 1 According to Eqs. (3.3) and (3.4), the weighting factor is defined as the ratio Q() r Wn () r = Q () r n (3.5) With the weighting factor, the balanced traces sˆ( r ,) t are calculated as sˆ (,) r t = s (,) r t ⋅W () r . (3.6) n n n Next, these traces for each antenna combination are stacked to reduce incoherent clutter and noise. Since these traces have different offset (antenna separation), their time axes are not the same. To compensate the axes, normal move out (NMO) is performed, and then the traces are stacked. where s (,) r t = ∑ sˆ (, r τ ), (3.7a) CMP n n n= 1 N air soil ⎛Ln L ⎞ n τ n = 2⎜ + ⎟, (3.7b) ⎝ c 1 ε ⎠ air L and L soil are the path lengths in the air and soil, respectively. c is the velocity of the electromagnetic wave in the air, and ε is a permittivity of the soil. This process virtually constructs a monostatic radar signal measured at the CMP position from bistatic signals as illustrated in Fig. 3.11. Then migration is performed for the stacked signals. Here diffraction stacking is used as a migration technique. The amplitude at a position r ′ = { x′ , y′ , z′ } in the three-dimensional image is given by where i( r′ ) dxdys ( r , τ ′), (3.8a) = ∫∫ CMP 2 ′ − τ ′ = r r , (3.8b) 1 ε and r = { x, yz , } is the position signal acquired, i.e., the CMP position.
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Chapter 3: Vehicle-Mounted GPR System for Landmine Detection

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