Abstracts

Reconstruction of scalar functions and vector fields from weighted V-line transforms with swinging branches

Rohit Kumar Mishra, Indian Institute of Technology, Gandhinagar

Weighted V-line transforms map a symmetric m-tensor field to its integrals along two rays emanating from a common vertex. The main question here is to invert these transforms in formally determined settings to reconstruct the unknown tensor field in 2-dimensional Euclidean space. The inversion and injectivity of these operators have been investigated under strict simplifying assumptions: equal integration weights along both branches and branch directions are constant or radial. In this talk, we present our recent work that relaxes these constraints for scalar functions and vector fields. Under significantly weaker conditions on branch directions, we successfully extend established results on kernel descriptions, injectivity, and exact inversion formulas to new, significantly more general configurations.