Calderón's inverse problem with a finite number of measurements II: independent data. Issue 10 (3rd July 2022)

• Record Type: Journal Article
• Authors: Alberti, Giovanni S.; Santacesaria, Matteo
• Is Part Of: Applicable analysis. Volume 101:Issue 10(2022)
• Page Start: 3636
• Page End: 3654
• Publication Date: 2022-07-03
• Subjects: Gel'fand-Calderón problem -- Calderón problem -- inverse conductivity problem -- electrical impedance tomography -- local uniqueness -- complex geometrical optics solutions -- Lipschitz stability -- reconstruction algorithm; 35R30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1745192
• Languages: English
• ISSNs: 0003-6811

Abstract

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 ∞ . 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.