Spectrum extrapolation by using combined root-Demidenko family of quasi-duration functionals

Spectrum extrapolation is widely used tools for improving presentation and preprocessing band-limited signals and images. In particular in the microwave engineering it can be useful for estimation of parameters of multi-layered dielectric materials and for estimation or synthesis of source distribution on antenna aperture. In case of known support of time or spatial signal solving problem of spectrum extrapolation have been obtained by methods based on functions with double orthogonality or Tartakovsky-Gerchberg-Papoulis iterative algorithms. A principle of minimal duration of solution means that spectrum extrapolation should be carried out so that the spatial extent of solution should be minimal. The present work is devoted to proper choice of form of quasi-duration that provides good compromise between demands of stability optimizing procedure and precision of the final results. We have used family of a quasi-duration functionals that combines the subfamily of the smoothed root functionals and subfamily of a generalized Demidenko functionals.