Simultaneous nonlinear reconstruction of two‐dimensional permittivity and conductivity

Abstract

A new inversion algorithm for the simultaneous reconstruction of permittivity and conductivity recasts the nonlinear inversion as the solution of a coupled set of linear equations. The algorithm is iterative and proceeds through the minimization of two cost functions. At the initial step the data are matched through the reconstruction of the radiating or minimum norm scattering currents; subsequent steps refine the nonradiating scattering currents and the material properties inside the scatterer. Two types of basis functions are constructed for the nonradiating currents: “invisible” (global) basis functions, which are appropriate for discrete measurements and nonradiating (local) basis functions, which are useful in studying the limit of continuous measurements. Reconstructions of square cylinders from multiple source receiver measurements at a single frequency show that the method can handle large contrasts in material properties.

Nonlinear Inversion of Multi-Frequency Microwave Fresnel Data Using the Multiplicative Regularized Contrast Source Inversion

“…where H (1) 0 denotes the first kind Hankel function of zero order. In the TE-case, the field quantities are two-components vectors representing the electric field components in the transversal plane of the cylindrical objects.…”

“…We discuss the performance of the Contrast Source Inversion (CSI) method [1,2], enhanced with a Multiplicative Regularization technique (MR-CSI) [3]. The MR-CSI method has been applied to invert the first set of data measured by the Institut Fresnel, Marseille, France [4].…”

Multi-Resolution Retrieval of Non-Measurable Equivalent Currents in Microwave Imaging Problems-Experimental Assessment

“…Many strategies in microwave imaging reformulate the arising inverse scattering problem as the solution of an equivalent inverse source problem to determine either the profiles [4] or the dielectric properties [2][3][4] of unknown objects embedded in an inaccessible region. Despite the linearity of the inverse source problem with respect to the unknown equivalent current density within the investigation domain [5][6][7], the problem still remains ill-posed in the sense of Hadamard [11]. As a matter of fact, the presence of nonradiating, or non-measurable contributions, causes the non-uniqueness of the equivalent source [9,10].…”

“…It is well known [6] that the equivalent current densities J v eq (x, y) can be expressed through the linear combination of two different contributions…”

Through-Wall Imaging: Application of Subspace-Based Optimization Method

“…Among the inverse scattering approaches, several numerical reconstruction methods have been applied for throughwall imaging. One such example is the contrast source inversion (CSI) [6][7][8][9][10]. Recently, subspace-based optimization method (SOM) has been proposed to solve inverse scattering problems [11][12][13][14][15][16].…”