Weighted divergent beam transform: reconstruction, unique continuation and stability

Abstract

In this article, we establish that any symmetric m-tensor field can be recovered pointwise from partial data of the k-weighted divergent beam transform for any . Using the unique continuation property of the fractional Laplacian, we further prove the unique continuation of the fractional divergent beam 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 transform data. Finally, we conclude by proving a unique continuation result for the k-weighted divergent beam transform for functions.