This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm exactly recovers the true spikes if they are sufficiently separated, and the samples are sufficiently dense. In addition, we provide numerical evidence that our results extend to non-Gaussian kernels relevant to microscopy and telescopy.

中文翻译：

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二维反卷积的一个采样定理

这项工作研究了从它们与高斯核卷积的样本中估计点源或尖峰的二维叠加的问题。我们的结果表明，如果 $\ell_1$ 范数的连续对应物被充分分离并且样本足够密集，那么最小化它们可以准确地恢复真正的峰值。此外，我们提供了数值证据，证明我们的结果扩展到与显微镜和望远镜相关的非高斯内核。