  An optimal algorithm is described for solving the deconvolution problem of
the form ${\bf k}u:=\int_0^tk(t-s)u(s)ds=f(t)$ given the noisy data $f_\delta$,
$||f-f_\delta||\leq \delta.$ The idea of the method consists of the
representation ${\bf k}=A(I+S)$, where $S$ is a compact operator, $I+S$ is
injective, $I$ is the identity operator, $A$ is not boundedly invertible, and
an optimal regularizer is constructed for $A$. The optimal regularizer is
constructed using the results of the paper MR 40#5130.
