Explicit inversion formulas for normal operators of momentum ray transforms

Venue: Ground Floor Auditorium (006)

Abstract: The inversion of the ray transform serves as an important mathematical tool for investigating object properties from external measurements with extensive applications spanning medical imaging to geophysics. However, the inversion of the ray transform on symmetric tensor fields is constrained by the presence of an infinite dimensional null space. One natural question is whether we can utilize supplementary data in the form of higher order moments of the ray transform for the explicit recovery of the entire tensor field. In this talk, we will focus our attention on normal operators associated to momentum ray transforms (the composition of the transform with its formal L^2 adjoint), and introduce an approach for the explicit reconstruction of entire symmetric m tensor field from this data.