  We consider the problem of denoising a function observed after a convolution
with a random filter independent of the noise and satisfying some mean
smoothness condition depending on an ill posedness coefficient. We establish
the minimax rates for the Lp risk over balls of periodic Besov spaces with
respect to the level of noise, and we provide an adaptive estimator achieving
these rates up to log factors. Simulations were performed to highlight the
effects of the ill posedness and of the distribution of the filter on the
efficiency of the estimator.
