Current source density reconstruction from incomplete data

TL;DR

This paper introduces two methods for reconstructing current source density from incomplete voltage data, comparing their effectiveness and robustness through simulations and experiments.

Contribution

It presents two novel approaches—local averaging and least-squares fitting—for CSD estimation with missing data, analyzing their advantages and limitations.

Findings

LA method is more stable and robust.

LS method can be more accurate for specific distributions.

LA generally recommended for practical robustness.

Abstract

We propose two ways of estimating the current source density (CSD) from measurements of voltage on a Cartesian grid with missing recording points using the inverse CSD method. The simplest approach is to substitute local averages (LA) in place of missing data. A more elaborate alternative is to estimate a smaller number of CSD parameters than the actual number of recordings and to take the least-squares fit (LS). We compare the two approaches in the three dimensional case on several sets of surrogate and experimental data, for varying numbers of missing data points, and discuss their advantages and drawbacks. One can construct CSD distributions for which one or the other approach is better. However, in general, LA method is to be recommended being more stable and more robust to variations in the recorded fields.