Estimating the Signal-to-Noise Ratio

To compare the performance of each signal processing technique, it was beneficial to quantify the quality of the results. A simple yet effective way to do this was to calculate the signal-to-noise ratio (SNR) of the resulting output of each signal processing technique. The SNR quantified the amount of useful information in a signal relative to that of unwanted disturbances and was given by

where P _Signal was the power of the signal component and P _Noise was the power of the noise component. The power of a component is given by

where R(z) was the response data matrix with Z elements.

The issue with the IOS data however is that the true signal is not known, but rather the resulting output is a sum of the signal and the noise, whose power is given by P _Total. To deal with this situation, we took two equal size sets of imaging data from each mouse, labeled data1 and data2, and used these to estimate the values for signal and noise power. The reason behind using these two data sets was that the response signal should occur in both halves of the data. Any random noise would be different in each set, thus any component of the response which was the same in each half would be taken as signal. The noise power was calculated by

This calculation made the assumption of a zero mean additive noise present in the signal, thus the subtraction removed common signal and doubled the noise power. The power of the total signal could be taken as the power of data1 or data2, or their average. We opted to use the average:

Finally, the signal-to-noise ratio was estimated as

These calculations were performed on both the spatial and temporal output response for each animal for each signal processing technique.