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

Abstract

Abstract-A new approach for position and shape reconstruction of both penetrable and impenetrable objects from the measurements of the scattered fields is introduced and described. The approach takes advantage of the fact that for perfect electric conductors the induced currents are localized on the boundary, and equivalent sources also placed on the surface of the scatterers can be considered in the case of dielectric targets by virtue of the equivalence theorem. Starting from these considerations, a new inversion approach is formulated in order to retrieve the location and the boundary of unknown objects. Examples with both numerical and experimental data are given to demonstrate and assess the effectiveness of the method.

Qualitative Methods for the Inverse Obstacle Problem: A Comparison on Experimental Data

“…In order to enforce this joint sparsity among the different scattering experiments, an auxiliary variable B can be defined as the common upper bound on the amplitude of the equivalent currents for the different scattering illumination conditions. Accordingly, the problem is recast as [15,16]:…”

Microwave Imaging of 3D Dielectric Structures by Means of a Newton-CG Method in lp Spaces

“…Under the twodimensional approximation, which assumes a particular form of the electromagnetic field (e.g., transverse-magnetic) and that the targets are invariant along one axis, the problem at hand can be significantly simplified [3]. Based on this 2D assumption, many inverse scattering techniques have been proposed [11][12][13][14][15][16] and subsequently exploited in experimental systems [17][18][19]. Among them, the family of the socalled Newton-based deterministic methods appears really valuable in the reconstruction process, providing accurate characterization results.…”

Micro-Doppler Effect Removal in ISAR Imaging by Promoting Joint Sparsity in Time-Frequency Domain

“…Nonetheless, minimizing the -norm leads to a combinatorial optimization problem [ 17 ] that is difficult to solve. In M. Bevacqua et al [ 18 ], the -norm of an auxiliary variable, defined as the common upper bound to the amplitudes of the electric currents, is utilized to replace the -norm so that the new problem is tractable. However, the difference between the -norm of the auxiliary variable and the original -norm is significant [ 19 ] because larger coefficients are penalized more heavily than smaller coefficients in the -norm.…”

“…Nonetheless, the -norm is a loose approximation to the original -norm and often leads to suboptimal solutions [ 22 ]. Different from the methods in M. Bevacqua et al, Y. Liu et al, and S. Sun et al [ 18 , 19 , 21 ], we propose a new objective function in this paper which can achieve tight approximation to the original -norm with proper parameters. The new objective function was minimized, similar to the smoothed (SL0) algorithm approach [ 23 ] which consisted of two steps, i.e., the steepest descend step and the projection step.…”