Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems

Abstract

The behavior of the multiple signal classification (MUSIC) algorithm is investigated when used to locate small dielectric cylinders of specific characteristics in noise-free and noisy scenarios using the TE incidence. We have made three observations regarding the performance of MUSIC in the two-dimensional TE scenario, which reveal the significance of the choice of signal subspace while employing MUSIC and the shortcoming of traditional MUSIC when used to detect degenerate cylinders (which might be so due to the material or geometry of the cylinders). The detailed analysis of the sources induced on a cylinder and their linear dependency on each other gives a distinct insight into the use of MUSIC algorithm to locate it. A non-iterative retrieval algorithm is provided that is based on the least squares method, which retrieves the electric and magnetic polarization tensors of the small cylinders. The algorithm proposed here is mathematically a simple and direct representation of the physical principles and is applicable to degenerate cylinders as well.

Interpretation of linear sampling method in terms of induced multipoles

“…This means that as long as the multipole expansion of the support at a point is such that the monopole is most prominent, the point will be detected as a scatterer. This interpretation is similar to the physical interpretation of MUSIC, which also uses the monopole radiation function as the imaging function for the given problem scenario [1].…”

“…Most often, knowledge of the presence, locations and shapes of scatterers is sufficient. Further, for problems requiring complete inverse solution, the information mentioned above may serve as a good initial guess and reduce the complexity of inverse problems considerably [1]- [6]. Qualitative imaging methods like Linear Sampling Method (LSM) and MUSIC [1], [2] serve as fast inversion tools towards gathering such information.…”

MUSIC Algorithms for Grid Diagnostics

“…, NM of the grid, and Φ(r n ) spans between zero and one: A zero value implies geometrical orthogonality, i.e., r = r p ∈ ; a unitary value means that the corresponding unitary vector belongs to ℵ. Note that different functionals, also relying on (5), can be used [6], [7]. The choice of P is a crucial question for succeeding while applying the MUSIC algorithm, as a wrong estimation can lead to degraded reconstructions.…”

“…Therefore, Multiple Signal Classification (MUSIC) algorithms are particularly suited to deal with it [5]. Indeed, it is shown that MUSIC algorithms provide high resolution in locating cylinders that scatter isotropically [5] and also nonisotropically, provided to properly take into account the polarization tensor rank deficiency (see [6] and [7] and references therein).…”

Shape Reconstruction via Equivalence Principles,constrained Inverse Source Problems and Sparsity Promotion

“…Among them, the most popular qualitative approaches are the multiple signal classification (MUSIC) for point-like targets [5][6][7], decomposition of time reversal operator (DORT) and time reversal (TR) based methods for small size objects [8,9], linear sampling method (LSM) [10][11][12], factorization method (FM) [13,14] and point source method [15] for generic scatterers. These methods rely on an indicator function computed on the (properly sampled) imaging domain through an auxiliary linear problem, whose values determine whether the tested point lies inside or outside the scatter.…”