Regularizing parameter estimation for Poisson noisy image restoration

Deblurring images corrupted by Poisson noise is a challenging process which has devoted much research in many applications such as astronomical or biological imaging. This problem, among others, is an ill-posed problem which can be regularized by adding knowledge on the solution. Several methods have therefore promoted explicit prior on the image, coming along with a regularizing parameter to moderate the weight of this prior. Unfortunately, in the domain of Poisson deconvolution, only a few number of methods have been proposed to select this regularizing parameter which is most of the time set manually such that it gives the best visual results. In this paper, we focus on the use of l1-norm prior and present two methods to select the regularizing parameter. We show some comparisons on synthetic data using classical image delity measures.