Abstract
We consider the integral geometry problem of finding a symmetric 2-tensor field in a unit disk provided that the ray transforms of this field are known. We construct singular value decompositions of the operators of longitudinal, transversal, and mixed ray transforms that are the integrals of projections of a field onto the line where they are computed. We essentially use the results on decomposition of tensor fields and their representation in terms of potentials. The singular value decompositions are constructive and can be used for creating an algorithm for recovering a tensor field from its known ray characteristics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have