2025/04/24 by Gaoming Chen, Chen, Gaoming, Fadil Santosa +3
Decision Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Probabilistic and Robust Engineering Design #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2504.17592
openalex publication_date 2025/04/24 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
Professor Pierre Sabatier contributed much to the study of inverse problems in theory and practice. Two of these contributions were a focus on theory that actually supports practice, and the identification of well-posed aspects of inverse problems that may quite ill-posed. This paper illustrates these two themes in the context of Electrical Impedance Tomography (EIT), which is both very ill-posed and very practical. We show that for a highly constrained version of this inverse problem, in which a small elliptical inclusion in a homogeneous background is to be identified, optimization of the experimental design (that is, electrode locations) vastly improves the stability of the solution.