Soft Shrinkage Thresholding Algorithm for Nonlinear Microwave Imaging

6th International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Zaimaga, Hidayet^1 ; Lambert, Marc^2

Laboratoire des Signaux et Systèmes-CNRS UMR8506, CentraleSupélec-Univ.Paris-Sud, Université Paris-Saclay, France^1

GeePs - Group of Electrical Engineering - Paris, UMR CNRS 8507, CentraleSupélec, Univ. Paris-Sud, Université Paris-Saclay, Sorbonne Universités, UPMC Univ Paris 06, France^2

关键词: Dielectric contrasts;    Iterative algorithm;    Nonlinear iterations;    Nonlinear microwaves;    Sparsity constraints;    Step size selection;    Thresholding algorithms;    Tikhonov functional;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/756/1/012011/pdf
DOI  :  10.1088/1742-6596/756/1/012011

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

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.