Multiscale Poisson data smoothing

This paper introduces a framework for nonlinear, multiscale decompositions of Poisson data with piecewise smooth intensity curves. The key concept is conditioning on the sum of the observations that are involved in the computation of a given coefficient. Within this framework, most classical wavelet thresholding schemes for data with additive, homoscedastic noise apply. Any family of wavelet transforms (orthogonal, biorthogonal, second generation) can be incorporated into this framework. The second contribution is a Bayesian shrinkage with an original prior for coefficients of this decomposition. As such, the method combines the advantages of the Fisz-wavelet transform and (Bayesian) Multiscale Likelihood models, with additional benefits, such as the extendibility towards arbitrary wavelet families. Simulations show an important reduction in mean squared error of the output, compared to the present techniques of Anscombe or Fisz variance stabilisation or Multiscale Likelihood Modelling.