On Bias and Its Reduction via Standardization in Discretized Electromagnetic Source Localization Problems

TL;DR

This paper provides a rigorous Bayesian analysis of the standardization technique to reduce bias in electromagnetic source localization, addressing its theoretical foundations, limitations, and noise robustness.

Contribution

It offers a mathematical foundation for standardization in source localization, clarifying its capabilities and limitations within a Bayesian framework.

Findings

Standardization reduces bias effectively in electromagnetic source localization.

The Bayesian analysis reveals the method's limitations under certain noise conditions.

The paper discusses the noise robustness of the standardization technique.

Abstract

In electromagnetic source localization problems stemming from linearized Poisson-type equation, the aim is to locate the sources within a domain that produce given measurements on the boundary. In this type of problem, biasing of the solution is one of the main causes of mislocalization. A technique called standardization was developed to reduce biasing. However, the lack of a mathematical foundation for this method can cause difficulties in its application and confusion regarding the reliability of solutions. Here, we give a rigorous and generalized treatment for the technique using the Bayesian framework to shed light on the technique's abilities and limitations. In addition, we take a look at the noise robustness of the method, which is widely reported in numerical studies. The paper starts by giving a gentle introduction to the problem and its bias and works its way toward standardization.