Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution inside a medium from measurements made on its surface. The impedance distribution reconstruction in EIT is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods are often used in solving inverse pro...

Tikhonov regularization of linear discrete ill-posed problems often is applied with a finite difference regularization operator that approximates a low-order derivative. These operators generally are represented by banded rectangular matrices with fewer rows than columns. They therefore cannot be applied in iterative methods that are based on the Arnoldi process, which requires the regularizati...

This article describes a new approach to reconstruction of the conductivity eld in electrical impedance tomography. Our goal is to improve the trade-oo between the quality of the images and the numerical complexity of the reconstruction method. In order to reduce the computational load, we adopt a linearized approximation to the forward problem that describes the relationship between the unknow...

We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional Gα based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikh...

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix. In this sense the method can be referred to as an iterative refinement process. Numerical experiments arising from integral equati...

– Ultrasound tomography based on inverse scattering has the capability to resolve structures which are smaller than the wavelength of the incident wave, as opposed to conventional ultrasound imaging using echo method. Some material properties such as sound contrast are very useful to detect small objects. Born Iterative Method (BIM) based on first-order Born approximation has been introduced as...

The total least squares (TLS) method is a successful approach for linear problems when not only the right-hand side but the system matrix as well are contaminated by some noise. For ill-posed TLS problems regularization is necessary to stabilize the computed solution. In this paper we present a new approach for computing an approximate solution of the Tikhonov-regularized large-scale total leas...

A new method of extracting the relaxation matrix directly from absorption spectral data is formulated and applied to R-branch line mixing in HCN. The formulation makes use of a general iterative inversion algorithm based upon first-order sensitivity analysis and Tikhonov regularization. The recovered relaxation matrices describe line mixing much better than those derived from the fitting laws c...