Oberseminar Mathematische Strömungsmechanik

Tensor tomography: Momentum ray transforms by Suman-Kumar Sahoo

The central question in tensor tomography is to recover a symmetric m-th tensor field from its ray trans from (I⁰). The ray transform I⁰ was studied by several authors since it had many tomographic applications. It is well known that, any tensor field can be decompose into solenoidal part and potential part. Potential part lies in the kernel of the ray transform I0, so only solenoidal part can be recovered from the ray transform (I⁰) (Vladimir A. Sharafutdinov, Integral geometry of tensor fields, Inverse and Illposed Problems Series. VSP, Utrecht, 1994). In this talk, we discuss an algorithm for recovering f from the first m+1 momentum ray transform. Moreover, we obtain a stability estimate for m = 1 and  m = 2.