The Geodesic X-ray Transform with a GL (n, C)-Connection
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Monard, Francois
Paternain, Gabriel P
Abstract
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the absence of connection, then for any smooth enough connection multiplied by a complex parameter, the corresponding transform is injective for all values of that parameter outside a discrete set. Range characterizations are also provided, as well as numerical illustrations.
Description
Keywords
Geodesic X-ray transform, Connection, Scattering data
Journal Title
JOURNAL OF GEOMETRIC ANALYSIS
Conference Name
Journal ISSN
1050-6926
1559-002X
1559-002X
Volume Title
30
Publisher
Springer Science and Business Media LLC
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/M023842/1)