Calderón's Inverse Problem with a Finite Number of Measurements II: Independent Data

Abstract

We prove a local Lipschitz stability estimate for Gel'fand-Calderón's inverse problem for the Schrödinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the unknown potential, provided it belongs to a known finite-dimensional subspace of $L^{\infty }$. A similar result for Calderón's problem is obtained as a corollary. This improves upon two previous results of the authors on several aspects, namely the number of measurements and the stability with respect to mismodeling errors. A new iterative reconstruction scheme based on the stability result is also presented, for which we prove exponential convergence in the number of iterations and stability with respect to noise in the data and to mismodeling errors.

arXiv comment19 pages

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Cited by in corpus (5)

• Infinite-dimensional inverse problems with finite measurements
• Inverse problems on low-dimensional manifolds
• Linearised Calderón problem: Reconstruction and Lipschitz stability for infinite-dimensional spaces of unbounded perturbations
• Series reversion for electrical impedance tomography with modeling errors
• Series reversion in Calderón's problem