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Most EEG machines use a system based upon differential amplifiers to enhance the signal, a basic differential amplifier has 2 inputs and one output. the device takes 2 signals and outputs the difference between them (see this video). In short, the output is the difference between 2 signals and the differential amplifier discards the rest of the signal. But I think that possibly the current way of recording EEG could be encouraging loss of data due to ONLY looking for difference within EEG signals instead of analytical evaluation of absolute signals?

Why do we use relative signals and not absolute signals with EEG? Have there been any attempts to use absolute signals?

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A voltage is by definition a potential difference between 2 electrodes.

Nonetheless, to record a signal on 1 electrode that is hardly affected by the other reference electrode a distant electrode can be used, referred to as monopolar recording. By contrast, when 2 electrodes are placed close together on the site of interest it is referred to as a bipolar recording. In EEGs, it has everything to do with differential amplifiers and common mode rejection, which you already hint at in the question.

Without going into the technical details of opamps, I can say that differential amplifiers, ideally, reject the common signal on the electrodes and keep the differential voltage. In effect, most of the artifacts are rejected, while the signal is maintained. Artifacts are often widespread across the scalp, such as muscular artifacts, and are shared across electrodes, while the signal of interest is mostly confined to local areas on the scalp.

In EEG monopolar recordings are typically used, basically because sufficient artifact is rejected yet the signal is least distorted. In addition, and not least important, standard EEG electrode montages allow for the arithmetic deduction of bipolar recordings from monopolar recordings, whereas the reverse is not possible (Saab, 2009).

However, many electrophysiological signals, even those closely related to EEG, are often recorded using bipolar recordings, because either the signal is too low to be recordable, or the artifact is otherwise too large (e.g., Diez et al, 2010; Stronks et al., 2009; Stronks et al., 2013).

References
- Diez et al., Annu Int Conf IEEE Eng Med Biol Soc (2010): 5803-6
- Saab, Biofeedback (2009); 36(4): 128–33
- Stronks et al.,IOVS (2013); 54:3891–901
- Stronks et al., Doc Ophthalmol (2016); 132:1–15

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EEG measures voltage. By definition, voltage is an electric potential difference. There is no meaning of an "absolute" voltage, it's always a difference.

Yes, people "attempt" to measure a voltage with only one contact all the time, it happens whenever there is a broken channel or a failure of a ground wire. The result is an amplification of whatever other environmental signals can be picked up, dominated by AC current ("60/50-cycle noise"), radio waves, and other electromagnetic interference. A good ground wire is necessary to measure the small signals from the brain; something like an "Earth ground" would not be anywhere near sufficient.

You can get more local measures of voltage using electrodes in close proximity and measuring the potential between them rather than each against some other "ground". Usually these are depth electrodes in the brain.

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