Introduction:
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The subject of this special session is focused on the new developments in the fields of microlocal analysis and inverse conductivity problems. We aim to bring together both leading experts in these fields, as well as young researchers.
Microlocal analysis has a great impact on inverse scattering theory, where its techniques can be used to recover images. Inverse problems to which microlocal analysis is particularly well-suited include those of seismology, Synthetic Aperture Radar (SAR) and Single Photon Emitted Computed Tomography (SPECT). In these problems, the forward operator which maps the image to the data is typically known and the goal is to invert it by applying to it the backprojection operator. In doing so, artifacts appear and the focus is to describe these artifacts, understand their strength and diminish their strength.
The inverse conductivity problem is the problem of recovering the conductivity of the interior of a body from knowledge of currents and voltages applied to its surface. Such problem appears in geophysics, where the method is used in prospecting, in archaeology, in industrial process tomography and in medical imaging, where it is also known as Electrical Impedance Tomography (EIT). The mathematical problem consists in finding the conductivity function on a domain D (the body under inspection), from the knowledge of the so-called Dirichlet-to-Neumann map which describes measurements of boundary voltages and currents densities. In the context of EIT, different tissues inside the human body present different conductivities so that a map of the conductivity in the human body provides unique information about tissues and organs that no other medical imaging technique would provide. |
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