Abstract #300644

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JSM 2003 Abstract #300644
Activity Number: 210
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #300644
Title: Thresholding Variance Stabilized Wavelet Coefficients for Poisson Noise
Author(s): Maarten Jansen*+
Companies: Tu Eindhoven
Address: PO Box 513, Eindhoven, , 5600 MB, Netherlands
Keywords: wavelet ; Poisson ; threshold ; smoothing ; variance stabilization
Abstract:

We present a variance stabilisation for a general wavelet transform of Poisson data. When applied to the Haar transform, this approach reduces to a method closely related to the Haar-Fisz transform (Fryzlewicz, Nason). Wavelet coefficients of Poisson data are highly heteroscedastic if the intermittent intensities show large fluctuations including intervals of low intensity. Some existing methods are therefore based on the assumption of a minimum intensity and the results are typically asymptotic w.r.t. this minimum value. Other methods are limited to the analogue of the Haar transform, or show considerable problems due to dependencies between coefficients. In principle, the method in this paper can adapt the benefits of any wavelet transform in the analysis of Poisson data of arbitrary intensities. The computations necessary for the stabilization are no bottleneck when compared to the fast wavelet transform. The stabilisation allows for the same, simple thresholding techniques as for coefficients with additive, homoscedastic noise.

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