A phase and space coherent direct imaging method

Abstract

A direct imaging algorithm for point and extended targets are presented. The algorithm is based on a physical factorization of the response matrix of a transducer array. The factorization is used to transform a passive target problem to an active source problem and to extract principal components (tones) in a phase consistent way. TheMulti-tone imaging function that can superpose multiple tones (spatial diversity/aperture of the array) and frequencies (bandwidth of the probing signal) based on phase coherence. The method is a direct imaging algorithm which is simple and efficient since no forward solver or iteration is needed. Robustness of the algorithm with respect to noise is demonstrated via numerical examples.

Direct and Inverse Scattering Problems for Domains with Multiple Corners

“…There are two types of methods for solving the problem. The direct methods [2][3][4][5][6] are efficient but less accurate; the iterative methods [7][8][9][10][11][12][13][14][15] are accurate but more expensive. Typically the forward and adjoint problems have to be solved in each iteration.…”

“…However, for synthetic aperture data, which is more realistic in some applications, the results from the MUSIC algorithms degenerate. It is crucial to take advantage of phase coherence to overcome the challenge of lack of data [5]. We keep the phase information and use singular values as natural weight.…”

Non-Iterative Imaging of Thin Electromagnetic Inclusions From Multi-Frequency Response Matrix

“…. , M [3,17]. Since the first M columns of the matrix U(ω) and V(ω), {u 1 Thus, we can construct an image function at given frequency ω as:…”

A Topological Derivative Based Non-Iterative Electromagnetic Imaging of Perfectly Conducting Cracks

“…However, this method requires derivation of a complex Fréchet derivative, incurs large computational costs, and provides only a good initial guess regarding successful performance. Nevertheless, many practical experiments require starting with a good initial guess so alternative non-iterative imaging methods continue to be developed; e.g., the Multiple SIgnal Classification (MUSIC) algorithm [2], [3], linear sampling method [4], [5], and Kirchhoff migration [6], [7]. These appear to be fast and robust, and easily extend to the imaging of multiple cracks, but they still require a large number of incident fields with various directions and corresponding scattered field data.…”