  We address the question of estimating Kullback-Leibler losses rather than
squared losses in recovery problems where the noise is distributed within the
exponential family. Inspired by Stein unbiased risk estimator (SURE), we
exhibit conditions under which these losses can be unbiasedly estimated or
estimated with a controlled bias. Simulations on parameter selection problems
in applications to image denoising and variable selection with Gamma and
Poisson noises illustrate the interest of Kullback-Leibler losses and the
proposed estimators.
