Optimization of Multi-Target EM Imaging Using Non–Line-Search Gradient Descent Methods

Abstract

Electromagnetic (EM) inverse scattering poses a significant computational challenge due to its large scale, inherited non-linearity, and ill-posed nature. Efficient and reliable reconstruction strategies are essential, especially in scenarios where complex structures of media are encountered. Non–line-search gradient-based methods offer reduced computational cost and improved convergence by exploiting curvature information without performing repeated line searches. This study presents a performance comparison of several prominent non–line-search optimization strategies, including fixed step, search based gradient descent, Barzilai–Borwein (BB) methods, Nesterov Accelerated Gradient (NAG), and the Heavy Ball Method (HBM), applied to nonlinear inverse scattering reconstruction of multiple targets with varying sizes. Numerical simulations are conducted using an Ultra wideband time-domain formulation covering frequencies up to 5 GHz, enabling a comprehensive evaluation of reconstruction accuracy and convergence behavior. Results demonstrate that the alternating Barzilai–Borwein strategy achieves the fastest convergence and highest reconstruction accuracy across single, and multi-target imaging configurations, consistently yielding the lowest mean squared error (MSE) values. The NAG and HBM methods maintain stable convergence, with NAG consistently outperforming HBM in both accuracy and speed. Although the steepest descent method produces accurate reconstructions, its computational efficiency is limited by the cost of line-search operations, while fixed step-size methods converge more slowly relatively yielding lower accuracy.