Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency

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:…”

“…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.…”

Structure Analysis of Single- And 2 Multi-Frequency Subspace Migrations in 3 Inverse Scattering Problems

“…To find a good initial guess, alternative non-iterative reconstruction algorithms have been developed, such as the MUltiple SIgnal Classification (MUSIC)-type algorithm [5,23,25], linear sampling method [8,12], topological derivative strategy [3,6,18,21,22], linear-δ, vector and multipolarized approaches [29,30], and the multifrequency based algorithm such as Kirchhoff and subspace migrations [2,4,15,19,20,24]. Among them, although the multi-frequency based subspace migration has exhibited potential as a non-iterative imaging technique, a mathematical identification of its structure needs to be performed for its heuristical applications, which is the motivation behind.…”