An Accelerated Nonlinear Contrast Source Inversion Scheme for Sparse Electromagnetic Imaging

Abstract

An efficient nonlinear contrast source inversion scheme for electromagnetic imaging of sparse two-dimensional investigation domains is proposed. To avoid generating a sequence of linear sparse optimization problems, the non-linearity is directly tackled using the nonlinear Landweber (NLW) iterations. A self-adaptive projected accelerated steepest descent (A-PASD) algorithm is incorporated to enhance the efficiency of the NLW iterations. The algorithm enforces the sparsity constraint by projecting the result of each steepest descent iteration into the $L_{1}$ -norm ball and selects the largest-possible iteration step without sacrificing from convergence. Numerical results, which demonstrate the proposed scheme’s accuracy, efficiency, and applicability, are presented.

Keywords

• Contrast source inversion
• electromagnetic imaging
• inverse problems
• Landweber iterations
• nonlinear inverse scattering
• sparse reconstruction