Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems

Abstract

Multi-frequency subspace migration imaging technique are usually adopted for the noniterative imaging of unknown electromagnetic targets such as cracks in the concrete walls or bridges, anti-personnel mines in the ground, etc. in the inverse scattering problems. It is confirmed that this technique is very fast, effective, robust, and can be applied not only full-but also limited-view inverse problems if suitable number of incident and corresponding scattered field are applied and collected. But in many works, the application of such technique is somehow heuristic. Under the motivation of such heuristic application, this contribution analyzes the structure of imaging functional employed in the subspace migration imaging technique in two-dimensional full-and limited-view inverse scattering when the unknown target is arbitrary shaped, arc-like perfectly conducting cracks located in the homogeneous two-dimensional space. Opposite to the Statistical approach based on the Statistical Hypothesis Testing, our approach is based on the fact that subspace migration imaging functional can be expressed by a linear combination of Bessel functions of integer order of the first kind. This is based on the structure of the Multi-Static Response (MSR) matrix collected in the far-field at nonzero frequency in either Transverse Magnetic (TM) mode (Dirichlet boundary condition) or Transverse Electric (TE) mode (Neumann boundary condition). Explored expression of imaging functionals gives us certain properties of subspace migration and an answer of why multi-frequency enhances imaging resolution. Particularly, we carefully analyze the subspace migration and confirm some properties of imaging when a small number of incident field is applied. Consequently, we simply introduce a weighted multi-frequency imaging functional and confirm that which is an improved version of subspace migration in TM mode. Various results of numerical simulations via the far-field data affected by large amount of random noise are well matched with the analytical results derived herein, and give some ideas of future studies.

Detection of small inhomogeneities via direct sampling method in transverse electric polarization

“…However, to successfully apply these schemes, one must begin the iteration procedure with a good initial guess that is close to the unknown inhomogeneities. Moreover, it is very difficult to identify multiple inhomogeneities simultaneously using iteration schemes To quickly identify multiple inhomogeneities, various techniques have been developed; these include MUltiple SIgnal Classification (MUSIC) [1,2,3], topological derivative [4,5,6], linear sampling method [7,8,9], and Kirchhoff and subspace migrations [10,11,12]. However, these techniques still require a significant amount of incident-field and corresponding scattered-field directional data to guarantee an acceptable result.…”

Real-time microwave imaging of unknown anomalies via scattering matrix

“…Then, the plot of F Full (r) is expected to exhibit peaks of magnitude 1 at r = r ∈ Σ and small magnitude at r / ∈ Σ. For a detailed discussion, we refer to [39,43].…”

Analysis and Improvement of Direct Sampling Method in the Monostatic Configuration

“…Among the various imaging methods, non-iterative-type algorithms are of interest due to expected numerical simplicity and low computational cost, for example, MUltiple SIgnal Classification (MUSIC), linear sampling method (LSM), topological derivative, Kirchhoff migration, direct sampling method (DSM), etc. Related works can be found in [14][15][16][17][18][19] and references therein. Even though these methods can provide good results with multi-static data, they may fail with mono-static ones the due to lack of information arising to great assumption from inherent limitation.…”