Poisson Intensity Estimation Based on Wavelet Domain Hypothesis Testing

In this paper, we present the estimation of Poisson intensity based on hypothesis testing in the wavelet domain for any dimensional data. The testing framework for wavelet-based Poisson intensity estimation was first introduced by Kolaczyk, where a thresholding estimator, which realizes the hypothesis testing, is derived for Haar wavelet coefficients. Here we propose for the same wavelet a new thresholding estimator which is based on Fisher’s normal approximation. Furthermore, we have demonstrated that non-normalized biorthogonal Haar coefficients converge in distribution to non-normalized Haar coefficients as the scale increases. This allows us to directly apply the threshold in the biorthogonal Haar domain. Therefore we gain, by using this more regular wavelet, a reconstruction with less artifacts. Simulations show that on a wide range of intensity types, the proposed threshold combined with undecimated biorthogonal Haar transform gives one of the best estimation result compared with existing estimators of various kinds. Finally, potential applicability of our approach is illustrated on astronomical data. Index Terms Poisson intensity estimation, wavelet hypothesis testing, Fisher approximation, biorthogonal Haar wavelets