Fryzlewicz, Piotr, Delouille, V´eronique and Nason, Guy P.
GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisz transform.
Journal of the Royal Statistical Society: Series C, 56
We consider the stochastic mechanisms behind the data collected by the solar X-ray sensor (XRS) on board the the GOES-8 satellite. We discover and justify a non-trivial mean-variance relationship within the XRS data. Transforming such data so that its variance is stable and its distribution is taken closer to the Gaussian is the aim of many techniques (e.g. Anscombe, 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 meanvariance 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 (DDHFT), which uses Haar-Fisz but also estimates the mean-variance relationship. For known noise distributions, the DDHFT is shown to be competitive with the fixed Haar-Fisz methods. We show how our DDHFT method denoises the XRS series where other existing methods fail.
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