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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 theproblem. To have a more precise lower bound, we study semiparametric efficiencyin the sense of H\'ajek-Le Cam for functional estimation in regular indirectmodels. These are characterized as models that can be locally approximated by alinear white noise model that is described by the generalized score operator. Aconvolution theorem for regular indirect models is proved. This applies to alarge class of statistical inverse problems, which is illustrated for theprototypical white noise and deconvolution model. It is especially useful fornonlinear models. We discuss in detail a nonlinear model of deconvolution typewhere a L\'evy process is observed at low frequency, concluding an informationbound for the estimation of linear functionals of the jump measure.

Information bounds for inverse problems with application to deconvolution and L\'evy models