  This paper considers the deconvolution problem in the case where the target
signal is multidimensional and no information is known about the noise
distribution. More precisely, no assumption is made on the noise distribution
and no samples are available to estimate it: the deconvolution problem is
solved based only on the corrupted signal observations. We establish the
identifiability of the model up to translation when the signal has a Laplace
transform with an exponential growth smaller than $2$ and when it can be
decomposed into two dependent components. Then, we propose an estimator of the
probability density function of the signal without any assumption on the noise
distribution. As this estimator depends of the lightness of the tail of the
signal distribution which is usually unknown, a model selection procedure is
proposed to obtain an adaptive estimator in this parameter with the same rate
of convergence as the estimator with a known tail parameter. Finally, we
establish a lower bound on the minimax rate of convergence that matches the
upper bound.
