Deconvolution in white noise with a random blurring function

Details Deconvolution in white noise with a random blurring function Deconvolution in white noise with a random blurring function

2005-05-09

arxiv.org/abs/math/0505142v1

Mathematics

Statistics Theory

Scientific paper

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.

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