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

Abstract

Abstract-We carefully investigate the structure of single-and multifrequency imaging functions, that are usually employed in inverse scattering problems. Based on patterns of the singular vectors of the Multi-Static Response (MSR) matrix, we establish a relationship between imaging functions and the Bessel function. This relationship indicates certain properties of imaging functions and the reason behind enhancement in the imaging performance by multiple frequencies. Several numerical simulations with a large amount of noisy data are performed in order to support our investigation.

Structural Behavior of the Music-Type Algorithm for Imaging Perfectly Conducting Cracks

“…However, due to the oscillation property of the Bessel function, some artifacts of small magnitude are displayed. (iv) According to the recent work [17], the last term of (12) can be negligible. Since Ψ(x; k 1 , k S ) reaches its maximum value 1 at x = 0 for any nonzero wavenumbers k 1 and k S , the map of W M F (z; S) has properties similar to those of W (z), except for less oscillation.…”

“…For this reason, various non-iterative shape reconstruction algorithms, such as linear sampling method [7,8,12,18], topological derivative [2,20,24,25], Kirchhoff and subspace migrations [3,16,17,22,23,27], SAR imaging technique [9,15,[32][33][34][35], and MUltiple SIgnal Classification (MUSIC) [4,5,11,26,28], have been investigated.…”

Performance analysis of multi-frequency topological derivative for reconstructing perfectly conducting cracks

“…, refer to [20]. Finally, by applying k F −→ ∞ in (13), we can immediately obtain the following result:…”

Linear sampling method for imaging an extended crack using limited-range far-field data

“…Moreover, iteration-based schemes need the calculation of Fréchet derivative, appropriate regularization terms, and a priori information about the unknown crack. To avoid these difficulties, alternative methods have been developed, for example, MUltiple SIgnal Classification [12], [13], [14], [15], [16], [17], [18], [19], [9], topological derivatives [20], [21], [22], [23], [24], [25], Kirchhoff and subspace migration [26], [27], [28], [29], [30], [31], [32], [33], [34], and linear sampling methods [35], [36], [37], [38], [39], [40]. Among them, the linear sampling methods have been successfully applied for reconstructing shapes of various inhomogeneities.…”