Nuutti Hyvönen

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In electrical impedance tomography one tries to recover the spatial admittance distribution inside a body from boundary measurements. In theoretical considerations it is usually assumed that the boundary data consists of the Neumann-to-Dirichlet map; when conducting realworld measurements, the obtainable data is a linear finite-dimensional operator mapping(More)
In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The(More)
In this talk we extend the concept of the convex scattering support to the case of electrostatics in a bounded domain. Furthermore, we apply this approach to devise a new reconstruction algorithm in electric impedance tomography. The convex scattering support was developed by Stephen Kusiak and John Sylvester, cf. [3],[4], and is meant to be the smallest(More)
This thesis presents mathematical analysis of optical and electrical impedance tomography. We introduce papers [I–III], which study these diffusive tomography methods in the situation where the examined object is contaminated with inclusions that have physical properties differing from the background. AMS subject classifications: 35R30, 35Q60, 35J25, 31A25,(More)
In the paper [1] we have claimed (in the concluding remarks) that the same arguments that we have used in the rest of the paper for insulating cavities can also be applied to establish that two (simply connected) perfectly conducting inclusions with the same backscatter data of impedance tomography are necessarily the same. Unfortunately, while our(More)