Generalized Radon transforms over symmetric m-tensor fields in Rn

We study the inverse problem of reconstructing symmetric m-tensor fields in Rn from generalized Radon transforms, which arise naturally in areas such as medical imaging, seismology, and tomography. We introduce longitudinal and transversal Radon transforms, along with their momentum variants, which extend classical Radon transforms to tensor fields. We provide explicit kernel characterizations and establish invertibility modulo these kernels. Furthermore, we show that symmetric m-tensor fields can be uniquely recovered from suitable combinations of introduced transforms. Our results provide a mathematical foundation for imaging of tensor-valued physical quantities, going beyond scalar tomography.