Non local means under Poisson noise with automatic setting based on risk minimization Moyennes non locales pour le bruit de Poisson avec réglage automatique fondé sur la minimisation du risque

An extension of the non local (NL) means is proposed for images damaged by Poisson noise. The proposed method is guided by the noisy image and a pre-filtered image and is adapted to the statistics of Poisson noise. The influence of both images can be tuned using two filtering parameters. We propose an automatic setting to select these parameters based on estimated mean square error (MSE) minimization. This selection uses an estimator of the MSE for NL means with Poisson noise and a Newton’s method to find the optimal parameters in few iterations. Index Terms Non local means, Poisson noise, mean square error, Newton’s method C. Deledalle et F. Tupin sont à l’Institut Telecom, Telecom ParisTech, CNRS LTCI, Paris, France, e-mail: [email protected] et [email protected]. L. Denis est à l’École Supérieure de Chimie Physique Électronique de Lyon et au Laboratoire Hubert Curien, CNRS UMR 5516, St-Étienne, France, e-mail: [email protected]. February 15, 2010