The Momentum Light Ray Transform

Abstract: In this article, we study Momentum Light Ray Transform (MLRT) on symmetric tensor fields. MLRT is an integral transform in time-space domain ($(t,x)\in \mathbb{R}^{1+n}$), which integrates a scalar function or a tensor field along the light rays with a polynomial type weight. We explore necessary and sufficient conditions for injectivity of MLRT, over general order tensors on space dimension $\geq 2$, from full and restricted measurements. Furthermore, we develop an inversion algorithm for MLRTs in the restricted measurement setting. To prove the results, we use tools from tensor tomography, geometry, and analysis.