SSP'05 -- Proceedings

	IEEE/SP 13th workshop on Statistical Signal Processing July, 17-20, 2005 - Bordeaux - France

Information regarding the paper

Title

A data-driven Haar-Fisz transform for multiscale variance stabilization

Author(s)

Piotr Fryzlewicz	Imperial College London, UK
Véronique Delouille	Royal Observatory of Belgium, Belgium

Get the paper in PDF format

To obtain Acrobat Reader (version 5 minimum required) necessary to his read.

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 competitors.