We revisit this issue in the case of radial piecewise constant conductivities, and prove that there are no local minimums in the case of two scalar unknowns with no measurement noise. We provide a partial proof in the general setting under a numerically verifiable assumption.

In electrical impedance tomography, one wishes to recover the conductivity of a medium from boundary current-voltage measurements. Calderón formalized this as an inverse problem for a PDE, whose goal is to estimate a coefficient of the PDE from measurements of its solution.

New preprint: "On the non-convexity issue in the radial Calderón problem" with Giovanni S. Alberti and Clarice Poon. We revisit the non-convexity issue for the least squares approach to the Calderón problem in the case of piecewise constant radial conductivities.

arxiv.org/abs/2507.03379