Weighted Divergent Beam Ray Transform: Reconstruction, Unique continuation and Stability

2024/12/01 by Shubham R. Jathar, Jathar, Shubham R., Manas Kar +5 · 3 citations
Computer Science · Engineering · Medicine · #35R11 #45Q05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Infrared Thermography in Medicine #Optical measurement and interference techniques #Photoacoustic and Ultrasonic Imaging #Primary 46F12

paper · pdf · doi:10.48550/arxiv.2412.00738

openalex publication_date 2024/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we establish that any symmetric m-tensor field can be recovered pointwise from partial data of the k-th weighted divergent ray transform for any k ∈ ℤ⁺ ∪\0\. Using the unique continuation property of the fractional Laplacian, we further prove the unique continuation of the fractional divergent beam ray transform for both vector fields and symmetric 2-tensor fields. Additionally, we derive explicit reconstruction formulas and stability results for vector fields and symmetric 2-tensor fields in terms of fractional divergent beam ray transform data. Finally, we conclude by proving a unique continuation result for the divergent beam ray transform for functions.

Cited by

• The Momentum Light Ray Transform
• The head-wave transform
• Reconstruction of scalar functions and vector fields from weighted V-line transforms with swinging branches

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