5 research outputs found
Inversion of the Momenta Doppler Transform in two dimensions
We introduce an analytic method which stably reconstructs both components of
a (sufficiently) smooth, real valued, vector field compactly supported in the
plane from knowledge of its Doppler transform and its first moment Doppler
transform. The method of proof is constructive. Numerical inversion results
indicate robustness of the method.Comment: 18 pages, 12 figure
On the inversion of the momenta ray transform of symmetric tensors in the plane
We present a reconstruction method which stably recovers some sufficiently
smooth, real valued, symmetric tensor fields compactly supported in the
Euclidean plane, from knowledge of their non/attenuated momenta ray transform.
The reconstruction method extends Bukhgeim's -analytic theory from an
equation to a system.Comment: 20 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:2307.1075