Exact Recovery of Discrete Measures from Wigner D-Moments
Provides theoretical guarantees for exact recovery of discrete measures on SO(3) from moment data, which is relevant for applications in cryo-EM and robotics.
The paper proves that a sum of Dirac measures on SO(3) can be exactly recovered from low-degree Wigner D-moments if the support points are separated by at least 36/(N+1), with the measure being the unique solution to a total variation minimization.
In this paper, we show the possibility of recovering a sum of Dirac measures on the rotation group $SO(3)$ from its low degree moments with respect to Wigner D-functions only. The main Theorem of the paper states, that exact recovery from moments up to degree $N$ is possible, if the support set of the measure obeys a separation distance of $\frac{36}{N+1}$. In this case, the sought measure is the unique solution of a total variation minimization. The proof of the uniqueness requires localization estimates for interpolation kernels and corresponding derivatives on the rotation group $SO(3)$ with explicit constants.