2017/02/24 by Nuutti Hyvönen, Hyvönen, Nuutti, Lassi Païvärinta +3 · 1 citation
Earth and Planetary Sciences · Engineering · Environmental Science · Mathematics · #Electrical and Bioimpedance Tomography #FOS: Mathematics #Geophysical and Geoelectrical Methods #Groundwater flow and contamination studies #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1702.07531
openalex publication_date 2017/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a few ways of using conformal maps in the reconstruction of\ntwo-dimensional conductivities in electrical impedance tomography. First, by\nutilizing the Riemann mapping theorem, we can transform any simply connected\ndomain of interest to the unit disk where the D-bar method can be implemented\nmost efficiently. In particular, this applies to the open upper half-plane.\nSecond, in the unit disk we may choose a region of interest that is magnified\nusing a suitable M "obius transform. To facilitate the efficient use of\nconformal maps, we introduce input current patterns that are named conformally\ntransformed truncated Fourier basis; in practice, their use corresponds to\npositioning the available electrodes close to the region of interest. These\nideas are numerically tested using simulated continuum data in bounded domains\nand simulated point electrode data in the half-plane. The connections to\npractical electrode measurements are also discussed.\n