Titel
On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere
Autor*in
Abstract
Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e. the magnetization is described by a scalar susceptibility and the dipole direction). Here, we investigate the situation under the additional constraint that the susceptibility is either spatially localized in a subregion of the sphere or that it is band-limited. If the dipole direction is known, then the susceptibility is uniquely determined under the spatial localization constraint while it is only determined up to a constant under the assumption of band-limitedness. If the dipole direction is not known, uniqueness is lost again. However, we show that all dipole directions that could possibly generate the measured magnetic potential need to be zeros of a certain polynomial which can be computed from the given potential. We provide examples of non-uniqueness of the dipole direction and examples on how to find admissible candidates for the dipole direction under the spatial localization constraint.
Stichwort
Inverse magnetization problemdecomposition of spherical vector fieldsuniquenessmagnetic dipolessusceptibility
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Inverse Problems in Science and Engineering
Seitenanfang
1
Seitenende
24
Publication
Informa UK Limited
Erscheinungsdatum
2018
Zugänglichkeit
Rechteangabe
© 2018 The Author(s)
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