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A direct imaging method for the half-space inverse scattering problem with phaseless data

  • * Corresponding author: Guanghui Huang

    * Corresponding author: Guanghui Huang
The first author was supported in part by the China NSF under the grant 113211061.
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  • We propose a direct imaging method based on the reverse time migration method for finding extended obstacles with phaseless total field data in the half space. We prove that the imaging resolution of the method is essentially the same as the imaging results using the scattering data with full phase information when the obstacle is far away from the surface of the half-space where the measurement is taken. Numerical experiments are included to illustrate the powerful imaging quality.

    Mathematics Subject Classification: Primary: 65N30; Secondary: 78A45, 35Q60.


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  • Figure 1.  Examples 6.1: Imaging results of penetrable obstacles with different shapes from left to right. The top results are imaged with phaseless data by our RTM algorithm, and the bottom one are imaing results with full phase data. The probe wave number is $k=4\pi$, and $N_s=512$, $N_r=512$

    Figure 2.  Example 6.2: Imaging results of an elliptic obstacle with boundary conditions as sound soft, sound hard and impedance boundary with $\lambda=1$, respectively. The probe wave number $k=4\pi$, and $N_s=512$, $N_r=512$

    Figure 3.  Examples 6.3 (first test): Imaging results of a penetrable obstacle with noise levels $\mu=0.1, 0.2, 0.3, 0.4$ (from left to right). The top row is imaged with single frequency data, and the bottom row is imaged with multi-frequency data

    Figure 4.  Example 6.3 (second test): Imaging results of two sound soft obstacles. All the parameters are the same as that in Figure 3

    Figure 5.  Example 6.4: Imaging results of two sound soft obstacles overlaid with the true obstacle model. The left column is imaged with the single frequency data, and the right one is imaged with the multi-frequency data

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