Venky Krishnan | Explicit inversion formulas for normal operators of momentum ray transforms

Days on Diffraction 2024. Mini-symposium “Inverse Problems”. Monday, 10 June, 2024
Shubham R. Jathar (Computational Engineering, School of Engineering Sciences),
Manas Kar (Indian Institute of Science Education and Research (IISER)),
Venky P. Krishnan (Centre for Applicable Mathematics, Tata Institute of Fundamental Research),
Vladimir A. Sharafutdinov (Sobolev Institute of Mathematics)
Explicit inversion formulas for normal operators of momentum ray transforms

We study certain weighted ray transforms of symmetric tensor fields called momentum ray transforms. In the absence of weights, the ray transform reduces to the standard ray transform of symmetric tensor fields, and full inversion of the ray transform recovering the symmetric tensor field is
not possible due to the presence of an infinite dimensional null space. The supplementary data in the form of higher order moments of the ray transform leads to explicit recovery of the entire tensor field. In this talk, instead of the momentum ray transforms, we will focus our attention on normal operators associated to momentum ray transforms (the composition of the transform with its formal adjoint), and introduce an approach for the explicit reconstruction of the entire symmetric tensor field from this data.