The Momentum Light Ray Transform

2025/10/21 by Sombuddha Bhattacharyya, Bhattacharyya, Sombuddha, Suman Kumar Sahoo +2
Mathematics · Physics and Astronomy · #44A12 #65R32 #Analysis of PDEs (math.AP) #Digital Holography and Microscopy #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2510.18450

openalex publication_date 2025/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

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)∈ ℝ¹⁺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 ≥ 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.

Citations

• The Light ray transform for pseudo-Euclidean metrics
• Weighted Divergent Beam Ray Transform: Reconstruction, Unique continuation and Stability
• Normal operators for momentum ray transforms, II: Saint Venant operator
• Inverse Problems For Third-Order Nonlinear Perturbations Of Biharmonic Operators
• Local data inverse problem for the polyharmonic operator with anisotropic perturbations
• A general support theorem for analytic double fibration transforms
• The linearized Calderón problem for polyharmonic operators
• The generalized Saint Venant operator and integral moment transforms
• Unique continuation results for certain generalized ray transforms of symmetric tensor fields
• Inverse problems for real principal type operators
• Momentum ray transforms
• Parametrices for the light ray transform on Minkowski spacetime
• X-ray transforms in pseudo-Riemannian geometry
• Support theorems for the Light Ray transform on analytic Lorentzian manifolds
• Limiting Carleman weights and anisotropic inverse problems
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

Related

• Momentum ray transforms
• A generalized Helmholtz-type decomposition of symmetric tensor fields and applications to ray transforms
• Normal operators for momentum ray transforms, II: Saint Venant operator
• Inversion of generalized Radon transform over symmetric m-tensor fields in ℝⁿ
• On solenoidal-injective and injective ray transforms of tensor fields on\n surfaces