Multiplexing and time averaging of signal are effective noise reduction protocols applied in many analytical measurement systems. The efficacy of these protocols may be reduced by random occurrences of high-magnitude noise that do not conform to the statistical distribution of noise for all other measurements in the data set. This high-magnitude noise, which may have an insignificant probability of occurrence for a single measurement, almost certainly affects data collected in a multichannel, multiplexed modality, such as Fourier transform infrared (FT-IR) spectroscopic imaging employing focal plane array detectors. To recover time-averaging advantages in these cases, we present a general coaddition method that uses two statistical measures, the mean and median of the ensemble of measurements of a signal, to obtain a better estimate of the true signal than that estimated by time averaging alone. This method, termed median filtered time averaging, is shown to be an effective noise removal procedure for FT-IR imaging data. The effects of noise removal on time averaging and multiplexing are examined theoretically and are demonstrated for hyperspectral infrared microspectroscopic imaging data obtained from human skin biopsies by using a rapid data acquisition procedure.