## 4 ESI Challenges and Limitations  
During the last decade, significant advancements have been made regarding ESI methodologies, both in computational time as well as in the accuracy of solutions for the EEG inverse problem. However, the very nature of the inverse problem, given its underdetermined properties, is a major obstruction. Despite the fact that recent approaches have successfully alleviated several limitations, a number of challenges that need to be addressed are still present. The greatest drawback of EEG, and by extension source localization calculations, is its sensitivity to signal noise, which can consist of background noise, distortions and movement artifacts. These interferences affect greatly the accuracy of the inverse solution, producing ghost sources, or even displace the predicted brain activity areas completely [92]. In this context, the corresponding results can be misleading and might present safety risks, especially regarding presurgical planning and evaluation. Several methods for specific signal processing have been proposed to tackle these problems, like Independent Component Analysis [93] for artifacts removal and Faraday/empty room recordings, in order to resolve background and instrument noise. However, unrelated signal noise from inhibitory brain functions can be still present, while critical signal properties could be embedded in the identified artifact-related independent components and thus be removed alongside them [9, 94]. The number of electrodes and the number of dipoles defined by the source model creation is also crucial. As described in the previous sections, the number of source points vastly exceeds the number of electrodes and, thus, the solution is never unique and can be only estimated using priors (spatial, mathematical or anatomical). Furthermore, a very high number of source points would increase the resolution of the ESI solution, but would also increase the complexity of the process. More specifically, a small number of dipoles would result in lower spatial resolution and location accuracy, evidently making the produced solution more prone to misinterpretations, but require less memory and computational time to calculate. On the other hand, a higher number of source points leads to solutions with higher spatial resolution with smaller sparsity of the brain activity around each computed point, due to the larger number of neighboring points [9]. The main reason for the increased accuracy is that the Leadfield matrix is more complete and is calculated more thoroughly, indubitably requiring additional resources. As such, there is a fine balance on the computational cost and the ESI output where one has to consider minimizing the cortical activity sparsity (i.e., the extent of the source localization activation in terms of brain area surface) at the expense of high computational complexity. Leadfield calculation is also dependent on the number of electrode channels. The actual number of electrodes contributes significantly in the accuracy of the ESI, with limited channel number leading to the mislocalization of sources [40]. However, even if Low-Density ESI (LD-ESI) is less accurate compared to High-Density ESI (HD-ESI), LD-ESI is far more accessible and it could provide enough information given the appropriate recording time. Specifically, in hospital settings where High-Density EEG is unavailable, methods that could harness the power of a smaller number of electrodes could boost the usability of ESI. In Figure 2, different paradigms of electrode and source point numbers are displayed. Figure 2: Examples of how the number of electrodes and dipoles (source points) affect the ESI output. In each panel the calculated Leadfield matrix (heat map) depends on the electrode channels and the source points corresponding to a specific brain surface. In turn, the EEG recordings deriving from the different sensor settings are combined with the Leadfield matrix to estimate the locations of activity in the brain.