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arXiv · 2504.17592

Well-posed Questions for Ill-posed Inverse Problems: a Note in Memory of Pierre Sabatier

Gaoming Chen·Fadil Santosa·William W. Symes
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Abstract

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.

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Gaoming Chen, Fadil Santosa, William W. Symes. 2025-04-24. Well-posed Questions for Ill-posed Inverse Problems: a Note in Memory of Pierre Sabatier. https://arxiv.org/abs/2504.17592

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