Simulations have shown that the best filtering approach for images containing Poisson noise with few events is the method based on the histogram autoconvolutions. This method allows one to give a probability that a wavelet coefficient is due to noise. No background model is needed, and simulations with different background levels have shown the reliability and the robustness of the method. Other noise models in the wavelet space lead to the problem of the significance of the wavelet coefficient. A ten sigma detection was not strong enough in our simulation to produce a good filtered image. In this case, only Monte Carlo simulations can allow one derivation of a good detection level, and then, a new problem appears of defining the correct background. The main advantage of the histograms based method is its independence of the background.
Acknowledgements
We wish to thank A. Bijaoui and E. Slezak for useful discussions and comments, and C. Delattre for his technical help.