Numerical comparative study between regularized Gauss-Newton and Conjugate-Gradient methods in the context of microwave tomography

TL;DR

This paper compares regularized Gauss-Newton and Conjugate-Gradient methods for microwave tomography, analyzing their resolution, speed, and robustness to noise, and finds that each has advantages depending on data noisiness.

Contribution

It provides a numerical comparison of two iterative schemes in microwave tomography, highlighting their respective strengths and suitability for different noise conditions.

Findings

Gauss-Newton has better resolution and convergence with noiseless data.

Conjugate-Gradient is faster per iteration and more suitable for noisy data.

Both methods perform similarly on noisy data, with Conjugate-Gradient being more autonomous.

Abstract

The reconstruction of relative permittivity and conductivity in microwave tomography is carried out using regularized Gauss-Newton and Conjugate-Gradient iterative schemes. These two approaches are numerically tested and compared in terms of resolution, speed of convergence and robustness to noise. The numerical results show that for noiseless data, the regularized Gauss-Newton iterative scheme has a better resolution and a higher convergence rate, while the Conjugate-Gradient iterative scheme remains the fastest in terms of calculation time per iteration. For noisy data, both approaches give almost the same results, making the Conjugate-Gradient approach the most suitable for inverting experimental data for its autonomy and ease of implementation.