MUSIC-type imaging of a thin penetrable inclusion from its multi-static response matrix

Abstract

The imaging of a thin inclusion, with dielectric and/or magnetic contrasts with respect to the embedding homogeneous medium, is investigated. A MUSIC-type algorithm operating at a single time-harmonic frequency is developed in order to map the inclusion (that is, to retrieve its supporting curve) from scattered field data collected within the multi-static response matrix. Numerical experiments carried out for several types of inclusions (dielectric and/or magnetic ones, straight or curved ones), mostly single inclusions and also two of them close by as a straightforward extension, illustrate the pros and cons of the proposed imaging method.

Non-Iterative Imaging of Thin Electromagnetic Inclusions From Multi-Frequency Response Matrix

“…. , M , at each segment is expected to contribute to the image space of the response matrix K [2,18,24,25].…”

“…, M f and of small magnitude at x ∈ R 2 \Γ. A suitable number of M f for each frequency ω f can be found via careful thresholding, see [24,25] for instance. It is worth mentioning that (9) is an improved version of an important Kirchhoff migration:…”

“…Comparisons of imaging results will be exhibited in the next section (see Figures 3 and 4). By virtue of [25], we briefly introduce a MUSIC-type image function at a single frequency ω. Let us define a corresponding projection onto the null (or noise) subspace…”

“…For obtaining the number of nonzero singular values M f at each frequency ω f , a 0.01-threshold scheme (choosing first j singular values s j (ω f ) such that s j (ω f ) s 1 (ω f ) ≥ 0.01) is adopted. A more detailed discussion of thresholding can be found in [24,25]. The search domain Ω is defined as Ω = [−1, 1] × [−1, 1].…”

“…From the results in [24,25], it has been shown that this algorithm is fast, effective and robust. However, in the imaging of thin inclusion of both dielectric and magnetic contrast with respect to the embedding homogeneous space R 2 case, one obtains a poor result so that an improvement is required.…”