Signal-to-noise ratio · Grey Matter

The signal-to-noise ratio is how large the brain's own signal is at a sensor compared with everything else the sensor picks up, and it decides what a recording can resolve long before the electronics or the decoder do.

Signal-to-noise ratio. The signal-to-noise ratio is how large the brain's own signal is at a sensor compared with everything else the sensor picks up, and it decides what a recording can resolve long before the electronics or the decoder do.

Brain signals are faint and fall off fast with distance. A spike measured by an electrode within about 50 µm of a neuron can reach a few hundred microvolts; a few hundred micrometres away it is lost among the spikes of many other cells. At the scalp, the summed synaptic currents of several square centimetres of cortex arrive as tens of microvolts in EEG and as tens to hundreds of femtotesla in MEG. Against them stand the noise of the sensor itself (thermal noise in the electrode and amplifier, which grows with electrode impedance), the slow drift and 1/f background of the brain and the hardware, and larger signals from outside: the eyes, the jaw and neck muscles, the heart, the mains wiring and, for MEG, every moving piece of metal nearby.

Distance is the main loss. The field of a current dipole falls roughly with the square of distance, and the skull spreads what is left, so the signal of one neuron that an implanted electrode reads clearly is far below the noise at the scalp.

Averaging buys signal with time. Repeating a stimulus and averaging the responses lowers random noise by the square root of the number of repetitions, which is how evoked potentials are measured, and which is useless for a thought that happens once.

Synchrony is what survives. Only activity shared by many cells adds up faster than the noise, which is why non-invasive methods see rhythms and large events well and single cells not at all.

Noise sets the smallest thing worth recording.

Better sensors lower the floor, but the brain's signal at a distance falls faster than any sensor can improve, so the cheapest gain is always to get closer.

Questions: How small is the brain's signal at the scalp compared with the noise around it? Scalp EEG is measured in tens of microvolts, and it already reflects several square centimetres of cortex firing in step; a single neuron contributes nothing measurable at that distance. Blinks, eye movements, jaw and neck muscles and the heart produce signals of similar or larger size, and mains wiring adds interference at 50 or 60 Hz, so much of EEG practice is about recognising and removing those artefacts. The noise does not shrink as fast as the brain's signal does with distance, which is why recording closer to the source improves signal more than any better amplifier. If consumer EEG is so noisy, how much can it reveal about its user? Enough to matter, because noise is beaten by repetition. In a 2012 study, software connected to a cheap EEG headset flashed images of banks, digits and places and read the brain's recognition response to each, narrowing down which bank a user had, digits of a PIN and where they lived better than chance. A single noisy trial says little, but many trials averaged by an app that runs for hours say more, which is why privacy advocates treat even low-quality consumer recordings as sensitive neural data.