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Merońo Moreno, CristobalAuthorMaciá Lang, FabricioAuthorCastro Barbero, Carlos ManuelAuthorBarceló Ja, Castro C, Macià F, Meroño CjAuthorTHE BORN APPROXIMATION IN THE THREE-DIMENSIONAL CALDERON PROBLEM II: NUMERICAL RECONSTRUCTION IN THE RADIAL CASE
Publicated to:Inverse Problems And Imaging. 18 (1): 183-207 - 2024-02-01 18(1), DOI: 10.3934/ipi.2023029
Authors: Barceló JA; Castro C; Macià F; Meroño CJ
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Abstract
In this work we illustrate a number of properties of the Born approximation in the three-dimensional Calderón inverse conductivity problem by numerical experiments. The results are based on an explicit representation formula for the Born approximation recently introduced by the authors. We focus on the particular case of radial conductivities in the ball BR ⊂ R3 of radius R, in which the linearization of the Calderón problem is equivalent to a Hausdorff moment problem. We give numerical evidences that the Born approximation is well defined for L∞ conductivities, and present a novel numerical algorithm to reconstruct a radial conductivity from the Born approximation under a suitable smallness assumption. We also show that the Born approximation has depth-dependent uniqueness and approximation capabilities depending on the distance (depth) to the boundary ∂BR. We then investigate how increasing the radius R affects the quality of the Born approximation, and the existence of a scattering limit as R → ∞. Similar properties are also illustrated in the inverse boundary problem for the Schrödinger operator −∆ + q, and strong recovery of singularity results are observed in this case.
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Bibliometric impact. Analysis of the contribution and dissemination channel
The work has been published in the journal Inverse Problems And Imaging due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 109/343, thus managing to position itself as a Q2 (Segundo Cuartil), in the category Mathematics, Applied. Notably, the journal is positioned en el Cuartil Q2 para la agencia Scopus (SJR) en la categoría Discrete Mathematics and Combinatorics.
Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.
Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-07-26:
- Google Scholar: 2
- Scopus: 1
Impact and social visibility
Leadership analysis of institutional authors
There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (BARCELO VALCARCEL, JUAN ANTONIO) .