The biorthogonal decomposition (also referred to as the singular value decomposition) has recently emerged as a powerful tool for analysing and processing multichannel data. It is shown how this method can be used to enhance the signal-to-noise ratio of such data in a self-consistent way. Three applications to multichannel diagnostics that are routinely used on plasma devices, are presented: a soft X-ray camera, an XUV spectrometer and a microwave reflectometer. In each case, a physical interpretation of the enhancement is given. Furthermore, a robust criterion is presented, allowing data to be processed without making restrictive assumptions about their noise properties.