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A data-driven HAAR-FISZ transform for multiscale variance stabilization

By Piotr Fryzlewicz and V Delouille

Abstract

We propose a data-driven Haar Fisz transform (DDHFT): a fast, fully automatic, multiscale technique for approximately Gaussianising and stabilizing the variance of sequences of non-negative independent random variables whose variance is a non-decreasing (but otherwise unknown) function of the mean. We demonstrate the excellent performance of the DDHFT on Poisson data. We then use the DDHFT to denoise a solar irradiance time series recorded by the X-ray radiometer on board the GOES satellite: as the noise distribution is unknown, we first take the DDHFT, then use a standard wavelet technique for homogeneous Gaussian data, and then take the inverse DDHFT. The procedure is shown to significantly outperform its competitor

Topics: HA Statistics
Publisher: IEEE
Year: 2006
DOI identifier: 10.1109/SSP.2005.1628654
OAI identifier: oai:eprints.lse.ac.uk:30976
Provided by: LSE Research Online
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