Inversion of the Momenta Doppler Transform in two dimensions

TL;DR

This paper presents a stable, analytic, and constructive method for inverting the Momenta Doppler transform in two dimensions, enabling accurate reconstruction of vector fields from Doppler data with demonstrated robustness.

Contribution

The paper introduces a new analytic and constructive inversion technique for the Momenta Doppler transform in 2D, improving stability and robustness over previous methods.

Findings

Numerical results show the method's robustness.

The inversion process is constructive and analytically stable.

Effective reconstruction of vector fields from Doppler data.

Abstract

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.