The paper defines a distance between measures, gives an explicit recuperation operator, and proves that the resulting approximation error bounds are optimal for measures of finite total variation.
Exact Recovery of Discrete Measures from Wigner D-Moments
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abstract
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.
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math.FA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Super-resolution meets machine learning: approximation of measures
The paper defines a distance between measures, gives an explicit recuperation operator, and proves that the resulting approximation error bounds are optimal for measures of finite total variation.