GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisz transform

We consider the stochastic mechanisms behind the data that were collected by the solar X-ray sensor (XRS) on board the GOES-8 satellite. We discover and justify a non-trivial mean-variance relationship within the XRS data. Transforming such data so that their variance is stable and its distribution is taken closer to the Gaussian distribution is the aim of many techniques (e.g. Anscombe and Box-Cox). Recently, new techniques based on the Haar-Fisz transform have been introduced that use a multiscale method to transform and stabilize data with a known mean-variance relationship. In many practical cases, such as the XRS data, the variance of the data can be assumed to increase with the mean, but other characteristics of the distribution are unknown. We introduce a method, the data-driven Haar-Fisz transform, which uses the Haar-Fisz transform but also estimates the mean-variance relationship. For known noise distributions, the data-driven Haar-Fisz transform is shown to be competitive with the fixed Haar-Fisz methods. We show how our data-driven Haar-Fisz transform method denoises the XRS series where other existing methods fail. Copyright 2007 Royal Statistical Society.