4 - La transformation de Fisz pour l'estimation de l'image des intensités d'un bruit Poissonien dans le domaine des ondelettes
Jalal M. Fadili, Mathieu, Jérôme, Michel Desvignes · HAL (Le Centre pour la Communication Scientifique Directe) · 2004
A novel wavelet-based Poisson-intensity estimator of images is presented. This method is based on the asymptotic normality of a certain function of the Haar wavelet and scaling coefficients called the Fisz transformation. Some asymptotic results such as normality and decorrelation of the transformed image samples are extended to the 2D case. This Fisz-transformed image is then treated as if it was independent and gaussian variables. Then we apply a novel Bayesian denoiser that we have recently developed. In the latter, a prior model is imposed on the wavelet coefficients designed to capture the sparseness of the wavelet expansion. Seeking probability models for the marginal densities of the wavelet coefficients, the new family of Bessel K forms densities are shown to fit very well to the observed histograms. Exploiting this prior, we designed a Bayesian nonlinear denoiser and a closed-form for its expression was derived. Our Fisz-transformation based Bayesian denoiser compares very favorably to variance stabilizing transformation methods in both smooth and piece-wise constant intensities. It clearly outperforms the other denoising methods especially in the low-count setting. Combining the Fisz transform and the BKF Bayesian denoiser yields the best performance.