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

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