2011/11/21 by Guillaume Bal, Gunther Uhlmann, Günther Uhlmann +2 · 3 citations
Earth and Planetary Sciences · Mathematics · Medicine · #35C99 #35J15 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Medical Imaging Techniques and Applications #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques #math.AP #msc:35C99 #msc:35J15 #msc:35R30
paper · pdf · doi:10.48550/arxiv.1111.5051
20 pages
arxiv created 2011/11/21 · openalex publication_date 2011/11/21 · arxiv updated 2011/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large number of solutions and for an open set of corresponding boundary conditions, all coefficients can be uniquely and stably reconstructed up to a well characterized gauge transformation. We also show that in some specific situations, a minimum number of such available solutions equal to In=\frac12n(n+3) is sufficient to uniquely and globally reconstruct the unknown coefficients. This theory finds applications in several coupled-physics medical imaging modalities including photo-acoustic tomography, transient elastography, and magnetic resonance elastography.