MUSIC-type imaging of perfectly conducting cracks in limited-view inverse scattering problems

MUSIC Algorithm Without Diagonal Elements of Scattering Matrix

“…However, if one uses , there is only one nonzero singular value so that only the first left-singular vector is needed to generate the projection operator. Notice that based on several works [6,8,11,12], total number of nonzero singular value is same as the total number of small anomalies. Thus, by eliminating diagonal elements, we can examine similar phenomenon.…”

“…Among them, MUSIC algorithm has shown its feasibilities of imaging performance. Related works can be found in [5][6][7][8][9][10][11][12][13][14] and references therein. Notice that most of researches assumed that diagonal elements of scattering matrix are dependent on the existence of anomaly and independent of the dipole antennas.…”

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.…”

Object Locating of Electromagnetic Inclusions in Anisotropic Permeable Background Using Music Algorithm

“…This approach cannot reconstruct the exact contour of large cylindrical scatterers, but it provides some information of them, such as the number of cylinders and their approximate location. In [8] and [9], this approach is used for imaging of the perfect conductor cracks; however, shape of the inclusions cannot be reconstructed. The MUSIC algorithm is also used to detect an inhomogeneous thin dielectric structure in a two-dimensional homogeneous space in [10] and electromagnetic structure in [11].…”