Noise is a persistent feature in seismic data and poses a particular challenge for microseismic monitoring where events are often at or below the noise level of individual recordings. This work introduces a statistics-driven noise suppression technique that whitens noise through the calculation and removal of the noise's covariance. Using the Aquistore CO2 storage site as an example, the technique is shown to reduce the noise energy by a factor of 3.5 whilst having negligible effect on the seismic wavelet. This opens up the opportunity to identify and image events below current detection levels. Furthermore, while the technique has been discussed with respect to a microseismic monitoring application, it is applicable to any situation where noise may be considered as a multivariate Gaussian distribution, including other exploration, global and hazard monitoring scenarios.