A novel direct imaging method for passive inverse obstacle scattering problem

Figure 1.  In the passive imaging (Left), the incident sources are random and uncontrolled, but in the active imaging (Right), the incident sources are controlled and fixed

Figure 2.  The imaginary parts of $ C_{jm} $ and $ N^{s}_{jm} $ with $ \xi = 0.4 $ and $ \xi = 0.8 $ in the case of $ L = 64 $ for the kite (Top) and the peanut (Bottom). The first column displays the imaginary parts of $ C_{jm} $ with $ \xi = 0.4 $, the second column displays the imaginary parts of $ C_{jm} $ with $ \xi = 0.8 $ and the third column displays the imaginary parts of $ N^{s}_{jm} $

Figure 3.  Recoveries of $ \partial D $ by DCM with $ \xi = 0.4 $ and $ \xi = 0.8 $ in the case of $ L = 64 $ for the kite (Top) and the peanut (Bottom). The first column shows the exact boundary $ \partial D $ and $ L = 64 $ measurement points, the second column shows the reconstructed $ \partial D $ with $ \xi = 0.4 $ and the third column shows the reconstructed $ \partial D $ with $ \xi = 0.8 $

Figure 4.  The imaginary parts of $ C_{jm} $ and $ N^{s}_{jm} $ with $ \xi = 0.4 $ and $ \xi = 0.8 $ in the case of $ L = 256 $ for the kite (Top) and the peanut (Bottom). The first column displays the imaginary parts of $ C_{jm} $ with $ \xi = 0.4 $, the second column displays the imaginary parts of $ C_{jm} $ with $ \xi = 0.8 $ and the third column displays the imaginary parts of $ N^{s}_{jm} $

Figure 5.  Recoveries of $ \partial D $ by DCM with $ \xi = 0.4 $ and $ \xi = 0.8 $ in the case of $ L = 256 $ for the kite (Top) and the peanut (Bottom). The first column shows the exact boundary $ \partial D $ and $ L = 256 $ measurement points, the second column shows the reconstructed $ \partial D $ with $ \xi = 0.4 $ and the third column shows the reconstructed $ \partial D $ with $ \xi = 0.8 $

Figure 6.  The imaginary parts of $ C_{jm} $ and $ N^{s}_{jm} $ with $ k = 4\pi $ and $ k = 8\pi $ for the kite (Left) and the peanut (Right). The first row displays the imaginary parts of $ C_{jm} $ with $ k = 4\pi $, the second row displays the imaginary parts of $ N^{s}_{jm} $ with $ k = 4\pi $, the third row displays the imaginary parts of $ C_{jm} $ with $ k = 8\pi $ and the fourth row displays the imaginary parts of $ N^{s}_{jm} $ with $ k = 8\pi $

Figure 7.  Recoveries of $ \partial D $ by DCM with $ k = 4\pi $ and $ k = 8\pi $ for the kite (Top) and the peanut (Bottom). The first column shows the exact boundary $ \partial D $ and $ L = 256 $ measurement points, the second column shows the reconstructed $ \partial D $ with $ k = 4\pi $ and the third column shows the reconstructed $ \partial D $ with $ k = 8\pi $

Figure 8.  The imaginary parts of $ C^{\delta}_{jm} $ and $ N^{s}_{jm} $ with $ \delta = 0.2 $ and $ \delta = 0.4 $ for the kite (Top) and the peanut (Bottom). The first column displays the imaginary parts of $ C^{\delta}_{jm} $ with $ \delta = 0.2 $, the second column displays the imaginary parts of $ C^{\delta}_{jm} $ with $ \delta = 0.4 $ and the third column displays the imaginary parts of $ N^{s}_{jm} $

Figure 9.  Recoveries of $ \partial D $ by DCM with $ \delta = 0.2 $ and $ \delta = 0.4 $ for the kite (Top) and the peanut (Bottom). The first column shows the exact boundary $ \partial D $ and $ L = 256 $ measurement points, the second column shows the reconstructed $ \partial D $ with $ \delta = 0.2 $ and the third column shows the reconstructed $ \partial D $ with $ \delta = 0.4 $

Figure 10.  The imaginary parts of $ C^{\delta}_{jm} $ and $ N^{s}_{jm} $ with $ k = 2\pi $ (Top) and $ k = 4\pi $ (Bottom) for the resolution limit case. The first column displays the imaginary parts of $ C^{\delta}_{jm} $ with $ k = 2\pi $ and $ k = 4\pi $, and the second column displays the imaginary parts of $ N^{s}_{jm} $ with $ k = 2\pi $ and $ k = 4\pi $

Figure 11.  Recoveries of $ \partial D $ by DCM with $ k = 2\pi $ and $ k = 4\pi $ for the resolution limit. The first column shows the exact boundary $ \partial D $ and $ L = 256 $ measurement points, the second column shows the reconstructed $ \partial D $ with $ k = 2\pi $ and the third column shows the reconstructed $ \partial D $ with $ k = 4\pi $

Figure 12.  The imaginary parts of $ C^{\delta}_{jm} $ and $ N^{s}_{jm} $ with $ k = 4\pi $ (Top) and $ k = 8\pi $ (Bottom) for the multiscale case. The first column displays the imaginary parts of $ C^{\delta}_{jm} $ with $ k = 4\pi $ and $ k = 8\pi $, and the second column displays the imaginary parts of $ N^{s}_{jm} $ with $ k = 4\pi $ and $ k = 8\pi $

Figure 13.  Recoveries of $ \partial D $ by DCM with $ k = 4\pi $ and $ k = 8\pi $ for the multiscale case. The first column shows the exact boundary $ \partial D $ and $ L = 256 $ measurement points, the second column shows the reconstructed $ \partial D $ with $ k = 4\pi $ and the third column shows the reconstructed $ \partial D $ with $ k = 8\pi $