  If a functional in an inverse problem can be estimated with parametric rate,
then the minimax rate gives no information about the ill-posedness of the
problem. To have a more precise lower bound, we study semiparametric efficiency
in the sense of H\'ajek-Le Cam for functional estimation in regular indirect
models. These are characterized as models that can be locally approximated by a
linear white noise model that is described by the generalized score operator. A
convolution theorem for regular indirect models is proved. This applies to a
large class of statistical inverse problems, which is illustrated for the
prototypical white noise and deconvolution model. It is especially useful for
nonlinear models. We discuss in detail a nonlinear model of deconvolution type
where a L\'evy process is observed at low frequency, concluding an information
bound for the estimation of linear functionals of the jump measure.
