Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 485-502

BOUNDARY RECONSTRUCTION FOR THE BROKEN RAY TRANSFORM

Joonas Ilmavirta

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; joonas.ilmavirta 'at' jyu.fi

Abstract. We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the values of the function itself we obtain the usual geodesic ray transform, but for derivatives this transform has to be weighted by powers of the second fundamental form. The problem studied here is related to Calderón's problem with partial data.

2010 Mathematics Subject Classification: Primary 53C65, 78A05; Secondary 35R30, 58J32.

Key words: Broken ray transform, X-ray transform, Calderón's problem, inverse problems.

Reference to this article: J. Ilmavirta: Boundary reconstruction for the broken ray transform. Ann. Acad. Sci. Fenn. Math. 39 (2014), 485-502.

Full document as PDF file

doi:10.5186/aasfm.2014.3935