A unified weighted minimum norm solution for the reference inverse problem in EEG

Abstract

A well known problem in EEG recordings deals with the unknown potential of the reference electrode. In the last years several authors presented comparisons among the most popular solutions, the global conclusion being that the traditional Average Reference (AR) and the Reference Standardization Technique (REST) are the best approximations (Nunez, 2010; Kayser and Tenke, 2010; Liu et al., 2015; Chella et al., 2016). In this work we do not aim to further compare these techniques but to support the fact that both solutions can be derived from a general inverse problem formalism for reference estimation (Hu et al., 2019; Hu et al., 2018; Salido-Ruiz et al., 2011). Using the alternative approach of least squares, our findings are consistent with the theoretical findings in Hu et al. (2019) and Hu et al. (2018) showing that the AR is the minimum norm solution, while REST is a weighted minimum norm including some approximate propagation model. AR is thus a particular case of REST, which itself uses a particular formulation of the source estimation inverse problem. With a different derivation, we provide the additional powerful evidences to reinforce the cited findings.