  The removal of blur from a signal, in the presence of noise, is readily
accomplished if the blur can be described in precise mathematical terms.
However, there is growing interest in problems where the extent of blur is
known only approximately, for example in terms of a blur function which depends
on unknown parameters that must be computed from data. More challenging still
is the case where no parametric assumptions are made about the blur function.
There has been a limited amount of work in this setting, but it invariably
relies on iterative methods, sometimes under assumptions that are
mathematically convenient but physically unrealistic (e.g., that the operator
defined by the blur function has an integrable inverse). In this paper we
suggest a direct, noniterative approach to nonparametric, blind restoration of
a signal. Our method is based on a new, ridge-based method for deconvolution,
and requires only mild restrictions on the blur function. We show that the
convergence rate of the method is close to optimal, from some viewpoints, and
demonstrate its practical performance by applying it to real images.
