Volume 14, Issue 6

We consider an inverse problem which arises in the framework of identification of doping profiles for semiconductor devices, based on current measures for varying voltage. We set formally the inverse problem, and study and discuss the main properties of the resulting problem.

The restoring of the pollutant release history makes use of transfer functions (TFs) usually known by analytical formulation. In many cases the computation of an analytical TF is not possible; this fact limits the application of the inverse procedures to very simple conditions or it forces to drastic simplifications of complicated problems. In this paper a new procedure, useful to compute the numerical transfer functions in transport problems with no analytical solution, is outlined. This method, analogous to the computation of the Instantaneous Unit Hydrograph (IUH) in surface hydrology, makes use of mathematical modelling.

In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein type operator equation in Hilbert spaces. The proposed Newton–Lavrentiev method is a combination of Lavrentiev regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result.

In this paper we investigate reconstruction methods for the treatment of ill-posed inverse problems. These methods are based on a data estimation operator S λ followed by a classical regularization operator R α T α,λ = R α S λ . As a particular example of such a two-step regularization method we investigate in detail the combination of a wavelet shrinkage operator S λ followed by Tikhonov regularization R α . The nonlinear shrinkage operator is applied to noisy data and partially recovers the smoothness properties of the exact data. We prove order optimality for the proposed scheme and confirm the theoretical results with an example from medical imaging.

In this work, an inverse problem for the time-independent vector transfer equation for polarized radiation in isotropic medium is examined. In the problem, it is required to find the attenuation factor from known solution of the equation at the medium boundary. A formula is derived that relates the Radon transform of the attenuation factor with the radiation-flux density at the boundary. The uniqueness theorem for the solution of the tomography problem is proved.

In this paper, we consider the optimal-control problem for a system whose behavior is governed by a nonlinear elliptic-type equation in the absence of constraints that guarantee unique solvability of the boundary-value problem. The nonlinear term in the equation is assumed to be nonlinear. Insolvability of the optimization problem is admitted. Using the penalty method with smooth approximation of the system operator, and also the Tikhonov method, we pass to some solvable variational problem, for which necessary extremum conditions are established. We show that the solution of the obtained problem presents, in a sense, an approximate solution to the initial problem.

In this paper we address the tomographic imaging of the electrical resistivity of material bodies by means of static or low frequency electromagnetic fields. The problem is treated in the framework of a recently proposed imaging method based on a monotonicity of the operator mapping a given resistivity distribution into the measured data. The monotonicity holds for elliptic problems such as Electrical Resistance Tomography (ERT). Here we prove that it is possible to extend the monotonicity to parabolic problems such as Magnetic Induction Tomography (MIT). Specifically, we prove that it is possible to construct a proper observable having the same monotonicity of ERT. In addition, a method for measuring this observable from time-domain MIT data is presented.