Abstract
We consider the direct sampling method (DSM) for the two-dimensional inverse scattering problem. Although DSM is fast, stable, and effective, some phenomena remain unexplained by the existing results. We show that the imaging function of the direct sampling method can be expressed by a Bessel function of order zero. We also clarify the previously unexplained imaging phenomena and suggest multi-frequency DSM to overcome traditional DSM. Our method is evaluated in simulation studies using both single and multiple frequencies.
Highlights
This study considers the imaging of two-dimensional electromagnetic inclusions within a homogeneous space
Τm with relatively small size or permittivity are very difficult to locate by this method
We derive the following representation of ISF(z; k) where the maximum value comes from the Holder inequality
Summary
This study considers the imaging of two-dimensional electromagnetic inclusions within a homogeneous space. According to [7, 8, 9], DSM has some merits: (i) it requires only one or a few incident waves for imaging the shapes and locations of unknown inclusions, (ii) it performs without any matrix operation (such as singular value decomposition), and (iii) it is highly tolerant to noise These advantages are tempered by several drawbacks: (i) the direction of propagation is crucial for identifying the shapes and locations of inclusions, (ii) there are many artifacts in the map of DSM, and (iii) an inclusion with significantly smaller size or permittivity than other inclusions is difficult to identify by DSM.
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