# Interference Suppression in EEG Dipole Source Localization through Reduced-Rank Beamforming
## 4 Discussion
However, the selection of the optimal level of rank-reduction is still an issue that requires to be solved. Therefore, in this paper we centered our comparisons around the original neural index proposed in [21], and we avoided directly entering in the problem of optimal rank selection for our own indices. Instead, we trusted the optimality conditions provided by the solution of the Wiener-Hopf for the calculation of the ABM. Yet, we recognize the issue requires further investigation, but it is out of the scope of this paper. With respect to our results using simulated data, they indicate that our proposed neural indices are not greatly affected by an increase in \(\eta_{b}\) and \(\eta_{m}\), while the performance of MAI degrades with the increase of noise. The consistency in the response of our proposed beamformers is due to their specific design, in which optimality is achieved in the estimation (and later cancellation) of the noise and interference components. Such affinity to the orthogonal space in the GSC of those undesired components is achieved both by the ABS and the rank-reduction based on the CSM. An strategy in which no rank-reduction is applied turns to be inefficient, as the results with \(P(W_{0})_{\text{min}}\), show. For the case of real data, we used brain sources related to SSVEP. Our results under those conditions show that our methods are capable of localizing brain sources in the visual cortices V1 and V2, which are expected for the SSVEP. In [30], by using functional magnetic resonance imaging (fMRI) and dipole modeling, they were able to analyze the neural generators of the SSVEP. They found that the primarily origin for these stimulus came from two concurrently active dipolar sources that were situated in medial and lateral occipital cortex, providing strong evidence that phase-locked neural activity in area V1 is a major contributor to the pattern-reversal SSVEP and in some of the single subjects fMRI also showed activity in area V2, but due to their close proximity these were included in the V1 sources. Our results are in agreement with those findings, as in both subjects we were able to map brain activation in V1 and V2. Nevertheless, our results have the uncertainty produced by fitting a head model that did not corresponded to the subjects. Still, our results make sense in term of the physiological event, even when they were estimated as average responses over only 15 processing windows. Although the mechanism of SSVEP is not quite clear, their generation via the visual pathway starts when the light projects on the rod cells or cone cells in the retina generating electronic signals then this signals are transferred to the ganglion cells to be pre-processed and transferred to the V1. There, the response of the neurons represents the integrated signals in an area or even a whole visual field. Finally, the signals integrated in the V1 are transferred to other areas in the brain for further processing. All the previous characterization is important because the neural networks associated to SSVEP can overlap with parts of the visual recognition network. Hence, some researchers believe that combining SSVEP extraction method with the superposition method is a valid way for elucidating the process of a recognition task over a long duration of time [31]. It is here where our proposed methods have the potential of helping, as our results show, due to the capacity of beamforming techniques to focalize the search in specific areas of interest. This is perhaps not fully demonstrated in our results given that we depended on a public database and we had limited access to information related to the frequencies of stimulation. For that reason, future work in this area will include a more exhaustive investigation with SSVEP data we plan to acquire ourselves.