the determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. for solving these ill-posed inverse problems, galerkin method based on sinc basis functions for space and time will be used. to solve the system of linear equation, a noise is imposed and tikhonove regularization is applied. by using a sensor located at a point in the domain of $x$, say $...

We consider Tikhonov and sparsity-promoting regularization in Banach spaces for inverse scattering from penetrable anisotropic media. To this end, we equip an admissible set of material parameters with the L-topology and use Meyers’ gradient estimate for solutions of elliptic equations to analyze the dependence of scattered fields and their Fréchet derivatives on the material parameter. This al...

Tikhonov regularization is applied to the inversion of EEG potentials. The discrete model of the inversion problem results from an analytic technique providing information about extended intracranial distributions, with separate current source and sink positions. A three-layered concentric sphere model is used for representing head geometry. The selected regularization parameter is the minimize...

The dielectric susceptibility measurements are usually interpreted in terms of the relaxation times of various dynamical processes. Using the simple examples of the simulated spectra it is shown how the distribution of these relaxation times can be obtained by means of the integral equations solved with the Tikhonov regularization technique, and the criteria for the choice of the regularization...

The purpose of this paper is to present to the Inverse Problems community some recent results regarding \nonsmooth", \edge preserving" regularization methods. Emphasis is placed on the penalized least squares (Tikhonov) regularization approach with penalty functionals of total variation type, although other nonquadratic penalty functionals are brieey discussed.