# Cross-correlated Contrast Source Inversion

## TL;DR

This paper introduces a cross-correlated contrast source inversion method that enhances robustness and accuracy in electromagnetic imaging by interrelating state and data errors, demonstrated through 2-D benchmark problems.

## Contribution

It proposes a novel cross-correlated cost functional for CSI, improving robustness and accuracy without significant computational overhead.

## Key findings

- Better robustness and higher inversion accuracy than classical CSI and MR-CSI.
- Effective in 2-D benchmark problems with transverse magnetic and electric waves.
- Gradient calculation remains computationally efficient.

## Abstract

In this paper, we improved the performance of the contrast source inversion (CSI) method by incorporating a so-called cross-correlated cost functional, which interrelates the state error and the data error in the measurement domain. The proposed method is referred to as the cross-correlated CSI. It enables better robustness and higher inversion accuracy than both the classical CSI and multiplicative regularized CSI (MR-CSI). In addition, we show how the gradient of the modified cost functional can be calculated without significantly increasing the computational burden. The advantages of the proposed algorithms are demonstrated using a 2-D benchmark problem excited by a transverse magnetic wave as well as a transverse electric wave, respectively, in comparison to classical CSI and MR-CSI.