  Assume that an unknown integral operator living in some known subspace is
observed indirectly, by evaluating its action on a few Dirac masses at unknown
locations. Is this information enough to recover the operator and the impulse
responses locations stably? We study this question and answer positively under
realistic technical assumptions. We illustrate the well-foundedness of this
theory on two challenging optical imaging problems: blind super-resolution and
deconvolution. This provides a simple, practical and theoretically grounded
approach to solve these long resisting problems.
