Abstract
In this paper, we analyze a sparse nonlinear inverse scattering problem arising in microwave imaging and numerically solved it for retrieving dielectric contrast from measured fields. In sparsity reconstruction, contrast profiles are a priori assumed to be sparse with respect to a certain base. We proposed an approach which is motivated by a Tikhonov functional incorporating a sparsity promoting l1-penalty term. The proposed iterative algorithm of soft shrinkage type enforces the sparsity constraint at each nonlinear iteration. The scheme produces sharp and good reconstruction of dielectric profiles in sparse domains by adapting Barzilai and Borwein (BB) step size selection criteria and positivity by maintaining its convergence during the reconstruction.
Highlights
Development of efficient reconstruction methods and techniques that exploit sparseness regularized formulations have been widely emerged for solving inverse electromagnetic scattering problems in recent years
Soft iterative thresholding is used to solve the 2-D electromagnetic inverse scattering problem based on l1 norm penalty term
Taking advantage of Barzilai and Borwein (BB) method for step size selection and adding projection enhance the effectiveness of proposed method
Summary
Development of efficient reconstruction methods and techniques that exploit sparseness regularized formulations have been widely emerged for solving inverse electromagnetic scattering problems in recent years. High demand of such methods in various applications such as material characterization, subsurface prospecting, remote sensing, and non-destructive testing and evaluation [1, 2] enforces the importance and the need of effective and accurate methods. Innovative sparseness-regularized formulations have recently emerged as an effective recipe to overcome the non-uniqueness and/or numerical instability of the inversion process [6, 7] The reason behind this is that many images have sparse representations with respect to their expansion basis in the wavelet domain and this yields new developing approaches that minimize the cost functions with zeroth/first norm penalty terms
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