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This paper deals with the estimation of a probability measure on the realline from data observed with an additive noise. We are interested in rates ofconvergence for the Wasserstein metric of order $p\geq 1$. The distribution ofthe errors is assumed to be known and to belong to a class of supersmooth orordinary smooth distributions. We obtain in the univariate situation animproved upper bound in the ordinary smooth case and less restrictiveconditions for the existing bound in the supersmooth one. In the ordinarysmooth case, a lower bound is also provided, and numerical experimentsillustrating the rates of convergence are presented.

Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one