Wavelet denoising of Poisson-distributed data and applications

In experiments, observations are often modelled as a noisy signal. If the signal is embedded in an additive Gaussian noise, its estimation is often done by finding a wavelet basis that concentrates the signal energy over few coefficients and by thresholding the noisy coefficients. However, in many problems of physics, the recorded data are not modelled by Gaussian noise but as the realisation of a Poisson process. In this case, a method of general Poisson process filtering is used. This widens the Gaussian noise filtering and is operated by a kind of frequency-and-time hard thresholding of Haar wavelet coefficients. Not only the detail coefficients are thresholded but also the coefficients related to the rough approximation. Because of the distribution of the wavelet coefficients, a pair of thresholds is proposed for each coefficient. This filtering is illustrated with spectra from different experiments.