Weighted Divergent Beam Transform: Reconstruction, Unique continuation and Stability

In this article, we establish that any symmetric m-tensor field can be recovered pointwise from partial data of the k-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.