We study the problem of reconstructing a positive discrete measure on a compact set $K\subseteq {\mathbb{R}}^n$ from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new quantitative estimates for approximate recovery and a new sum-of-squares based hierarchy for approximate super-resolution on compact semi-algebraic sets.

中文翻译：

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全方位的积极措施的近似超分辨率

我们研究在紧集上重建正离散测度的问题 $ķ\subseteq {\mathbb{[R}}^{ñ}$通过凸优化从一组有限的矩（可能只有大概的矩）中得出。我们给出了新的唯一性结果，新的近似估计的定量估计以及新的基于平方和的层次结构，用于紧凑半代数集上的近似超分辨率。